AnalyticalEquation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analytical Derivation of the dynamical Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.physics.quantum import TensorProduct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import I, exp, sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def multiply_eq(eq, c, simplify=sympy.expand):\n",
    "    \"\"\"Multiply an equation with a constant\"\"\"\n",
    "    return sympy.Eq(simplify(eq.lhs*c), simplify(eq.rhs*c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def divide_eq(eq, c, simplify=sympy.expand):\n",
    "    \"\"\"Divide an equation by constant\"\"\"\n",
    "    return sympy.Eq(simplify(eq.lhs/c), simplify(eq.rhs/c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def add_eqs(eq1, eq2, fac1=1, fac2=1, simplify=sympy.expand):\n",
    "    \"\"\"Add two equations\"\"\"\n",
    "    return sympy.Eq(\n",
    "        simplify(fac1 * eq1.lhs + fac2 * eq2.lhs),\n",
    "        simplify(fac1 * eq1.rhs + fac2 * eq2.rhs)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def display_eqs(eqs):\n",
    "    for eq in eqs:\n",
    "        display(eq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Hilbert space is the tensor product of qubit 1, qubit 2, cavity 1, cavity 2, all are TLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ketbra(i,j):\n",
    "    level = {'e': 1, 'g': 0, '1':1, '0':0, 1:1, 0:0}\n",
    "    i = level[i]\n",
    "    j = level[j]\n",
    "    result = {\n",
    "        (0,0): sympy.Matrix([(1,0), (0,0)]),\n",
    "        (0,1): sympy.Matrix([(0,1), (0,0)]),\n",
    "        (1,0): sympy.Matrix([(0,0), (1,0)]),\n",
    "        (1,1): sympy.Matrix([(0,0), (0,1)]),\n",
    "    }\n",
    "    return result[(i,j)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dagger(obj):\n",
    "    return obj.conjugate().transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Id = sympy.Matrix([(1,0), (0,1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "δ1, δ2, g1, g2, Δ, κ, t \\\n",
    "= sympy.symbols((r'\\delta_1', r'\\delta_2', 'g_1', 'g_2',\n",
    "                 r'\\Delta', r'\\kappa', 't'), positive=True)\n",
    "ω1, ω2, g1t, g2t, ϕ1, ϕ2 \\\n",
    "= sympy.symbols((r'\\delta\\omega_1', r'\\delta\\omega_2', r'g_1', r'g_2',\n",
    "                 '\\phi_1', '\\phi_2'), cls=sympy.Function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H1 = -δ1 * TensorProduct(Id, Id, ketbra(1,1), Id) \\\n",
    "    + (g1**2/Δ) * TensorProduct(ketbra('g', 'g'), Id, ketbra(1,1), Id) \\\n",
    "    + ω1(t) * TensorProduct(ketbra('e', 'e'), Id, Id, Id) \\\n",
    "    - I * g1t(t) * (\n",
    "        exp(I*ϕ1(t)) * TensorProduct(ketbra('e', 'g'), Id, ketbra(1,1), Id)\n",
    "        - exp(-I*ϕ1(t)) * TensorProduct(ketbra('g', 'e'), Id, ketbra(1,1), Id)\n",
    "      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H2 = -δ2 * TensorProduct(Id, Id, Id, ketbra(1,1)) \\\n",
    "    + (g2**2/Δ) * TensorProduct(Id, ketbra('g', 'g'), Id, ketbra(1,1)) \\\n",
    "    + ω2(t) * TensorProduct(Id, ketbra('e', 'e'), Id, Id) \\\n",
    "    - I * g2t(t) * (\n",
    "        exp(I*ϕ2(t)) * TensorProduct(Id, ketbra('e', 'g'), Id, ketbra(1,1))\n",
    "        - exp(-I*ϕ2(t)) * TensorProduct(Id, ketbra('g', 'e'), Id, ketbra(1,1))\n",
    "      )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "L = sqrt(2*κ) * (  TensorProduct(Id, Id, ketbra(0,1), Id)\n",
    "                 + TensorProduct(Id, Id, Id, ketbra(0,1)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H_int = - I * κ * (\n",
    "            TensorProduct(Id, Id, ketbra(1,1), Id)\n",
    "          + TensorProduct(Id, Id, Id, ketbra(1,1))\n",
    "          + 2 * TensorProduct(Id, Id, ketbra(0,1), ketbra(1,0))\n",
    "        )\n",
    "# The above is the \"effective\" interaction term, including the non-Hermitian MCWF contribution\n",
    "# We want the Hermitian Hamiltonian, not the effective Hamiltonian given in the paper\n",
    "# (or maybe we don't -- this isn't entirely clear)\n",
    "H_int += (I/2) * (dagger(L) * L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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uGMRwD/qajoBc4emU4YEFudkKyMDuerYHVw6yhaIwPr0EH6LBIM5bC/V/sPdx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\nV/zQujkrkgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & - i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & - i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\kappa & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\kappa & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0      -ⅈ⋅\\kappa  0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0  ⅈ⋅\\kappa      0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0      -ⅈ⋅\\kappa  0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0  ⅈ⋅\\kappa      0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0      -ⅈ⋅\\kappa \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0  ⅈ⋅\\kappa      0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎢0     0          0      0  0     0          0      0  0     0          0     \n",
       "⎢                                                                             \n",
       "⎣0     0          0      0  0     0          0      0  0     0          0     \n",
       "\n",
       " 0  0     0          0      0⎤\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0      -ⅈ⋅\\kappa  0⎥\n",
       "                             ⎥\n",
       " 0  0  ⅈ⋅\\kappa      0      0⎥\n",
       "                             ⎥\n",
       " 0  0     0          0      0⎦"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = H1 + H2 + H_int "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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h2MgpYgUtX0ZHvSpYk2fakneFs6ZMGhFHI3/VG0olWkLZeGA65NXkwdtO/avs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GWT5UF5Tm4JyEBlqVncimzXEeEiS8El9UDCXvBLXYClkF5suKbwBaH3SPG3U+GiOsZRSm+RJcQU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\njP1eZnAtAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & - \\delta_{2} + \\frac{g_{2}^{2}}{\\Delta} & - i \\kappa & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & i \\kappa & - \\delta_{1} + \\frac{g_{1}^{2}}{\\Delta} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\delta_{1} - \\delta_{2} + \\frac{g_{1}^{2}}{\\Delta} + \\frac{g_{2}^{2}}{\\Delta} & 0 & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & \\delta\\omega_{2}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & - \\delta_{2} + \\delta\\omega_{2}{\\left (t \\right )} & - i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & i \\kappa & - \\delta_{1} + \\delta\\omega_{2}{\\left (t \\right )} + \\frac{g_{1}^{2}}{\\Delta} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0\\\\0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & - \\delta_{1} - \\delta_{2} + \\delta\\omega_{2}{\\left (t \\right )} + \\frac{g_{1}^{2}}{\\Delta} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \\delta_{2} + \\delta\\omega_{1}{\\left (t \\right )} + \\frac{g_{2}^{2}}{\\Delta} & - i \\kappa & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0\\\\0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & - \\delta_{1} + \\delta\\omega_{1}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \\delta_{1} - \\delta_{2} + \\delta\\omega_{1}{\\left (t \\right )} + \\frac{g_{2}^{2}}{\\Delta} & 0 & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & - \\delta_{2} + \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} & - i \\kappa & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & - \\delta_{1} + \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & - \\delta_{1} - \\delta_{2} + \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )}\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                  2                                                          \n",
       "⎢                g₂                                                           \n",
       "⎢0   -\\delta₂ + ──────         -ⅈ⋅\\kappa                         0            \n",
       "⎢               \\Delta                                                        \n",
       "⎢                                                                             \n",
       "⎢                                        2                                    \n",
       "⎢                                      g₁                                     \n",
       "⎢0        ⅈ⋅\\kappa         -\\delta₁ + ──────                     0            \n",
       "⎢                                     \\Delta                                  \n",
       "⎢                                                                             \n",
       "⎢                                                                       2     \n",
       "⎢                                                                     g₁      \n",
       "⎢0           0                     0            -\\delta₁ - \\delta₂ + ────── + \n",
       "⎢                                                                    \\Delta   \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢             ⅈ⋅\\phi₂(t)                                                      \n",
       "⎢0  -ⅈ⋅g₂(t)⋅ℯ                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                 ⅈ⋅\\phi₂(t)  \n",
       "⎢0           0                     0                    -ⅈ⋅g₂(t)⋅ℯ            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                   ⅈ⋅\\phi₁(t)                                \n",
       "⎢0           0            -ⅈ⋅g₁(t)⋅ℯ                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                 ⅈ⋅\\phi₁(t)  \n",
       "⎢0           0                     0                    -ⅈ⋅g₁(t)⋅ℯ            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                             0            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣0           0                     0                             0            \n",
       "\n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                      -ⅈ⋅\\phi₂(t)                             \n",
       "               0             ⅈ⋅g₂(t)⋅ℯ                                  0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "   2                                                                          \n",
       " g₂                                                                           \n",
       "──────         0                       0                                0     \n",
       "\\Delta                                                                        \n",
       "                                                                              \n",
       "        \\delta\\omega₂(t)               0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0          -\\delta₂ + \\delta\\omega₂(t)               -ⅈ⋅\\kappa \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   ⅈ⋅\\kappa            -\\delta₁ + \\delta\\omega\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "                                                                              \n",
       "                                                                         ⅈ⋅\\ph\n",
       "               0                       0                       -ⅈ⋅g₁(t)⋅ℯ     \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                       0                                0     \n",
       "\n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     -ⅈ⋅\\phi₂(t)                              \n",
       "                            ⅈ⋅g₂(t)⋅ℯ                                 0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "          2                                                                   \n",
       "        g₁                                                                    \n",
       "₂(t) + ──────                        0                                0       \n",
       "       \\Delta                                                                 \n",
       "                                                                              \n",
       "                                                          2                   \n",
       "                                                        g₁                    \n",
       "               -\\delta₁ - \\delta₂ + \\delta\\omega₂(t) + ──────         0       \n",
       "                                                       \\Delta                 \n",
       "                                                                              \n",
       "                                     0                         \\delta\\omega₁(t\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "i₁(t)                                                                         \n",
       "                                     0                                0       \n",
       "                                                                              \n",
       "                                      ⅈ⋅\\phi₁(t)                              \n",
       "                            -ⅈ⋅g₁(t)⋅ℯ                                0       \n",
       "\n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                     -ⅈ⋅\\phi₁(t)              \n",
       "                    0                       ⅈ⋅g₁(t)⋅ℯ                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       ")                   0                                 0                       \n",
       "                                                                              \n",
       "                                    2                                         \n",
       "                                  g₂                                          \n",
       "   -\\delta₂ + \\delta\\omega₁(t) + ──────           -ⅈ⋅\\kappa                   \n",
       "                                 \\Delta                                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                 ⅈ⋅\\kappa                -\\delta₁ + \\delta\\omega₁(t)          \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0               -\\delta₁\n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                     ⅈ⋅\\phi₂(t)                                               \n",
       "           -ⅈ⋅g₂(t)⋅ℯ                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                    0                                 0                       \n",
       "\n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              -ⅈ⋅\\phi₁(t)                                                     \n",
       "     ⅈ⋅g₁(t)⋅ℯ                                           0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "                                   2                                          \n",
       "                                 g₂                                           \n",
       " - \\delta₂ + \\delta\\omega₁(t) + ──────                   0                    \n",
       "                                \\Delta                                        \n",
       "                                                                              \n",
       "              0                         \\delta\\omega₁(t) + \\delta\\omega₂(t)   \n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                   -\n",
       "                                                                              \n",
       "                                                                              \n",
       "              0                                          0                    \n",
       "                                                                              \n",
       "               ⅈ⋅\\phi₂(t)                                                     \n",
       "     -ⅈ⋅g₂(t)⋅ℯ                                          0                    \n",
       "\n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                     -ⅈ⋅\\phi₁(\n",
       "                     0                                      ⅈ⋅g₁(t)⋅ℯ         \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     -ⅈ⋅\\phi₂(t)                                              \n",
       "            ⅈ⋅g₂(t)⋅ℯ                                                0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "                                                                              \n",
       "                                                                              \n",
       "\\delta₂ + \\delta\\omega₁(t) + \\delta\\omega₂(t)                    -ⅈ⋅\\kappa    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                  ⅈ⋅\\kappa                     -\\delta₁ + \\delta\\omega₁(t) + \\\n",
       "                                                                              \n",
       "                                                                              \n",
       "                     0                                               0        \n",
       "\n",
       "                                            0                            ⎤\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "t)                                                                       ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            -ⅈ⋅\\phi₁(t)                  ⎥\n",
       "                                   ⅈ⋅g₁(t)⋅ℯ                             ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            -ⅈ⋅\\phi₂(t)                  ⎥\n",
       "                                   ⅈ⋅g₂(t)⋅ℯ                             ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                                            0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "delta\\omega₂(t)                             0                            ⎥\n",
       "                                                                         ⎥\n",
       "                                                                         ⎥\n",
       "                 -\\delta₁ - \\delta₂ + \\delta\\omega₁(t) + \\delta\\omega₂(t)⎦"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Some of the constants are the same for both systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "δ, g = sympy.symbols((r'\\delta', 'g'), positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = H.subs({δ1:δ, δ2:δ, g1:g, g2:g})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above Hamiltonian has been cross-checked with the output from QNET (application of SLH)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*  Choose the detuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = H.subs({δ: g**2/Δ})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* we may or may not claim a-priori that we can choose the the pulse phases such that they cancel the stark shifts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "drop_phase_and_stark_shift = False # set to false to leave this for later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if drop_phase_and_stark_shift:\n",
    "    zero_phase_zero_stark = {\n",
    "            ϕ1(t): 0, ϕ2(t): 0,\n",
    "            ω1(t): 0, ω2(t): 0}\n",
    "    H = H.subs(zero_phase_zero_stark)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This yields the following Hamitonian:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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oOPDAZxfowdEnkyHylIKhExRIKejJWNkj42pF7k+nbwnap/GjlEElL1DI5wTh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\negiorCKKdOwipBMtYC9GPLL/ADClMPm7XqoNAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & - i \\kappa & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & \\delta\\omega_{2}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & \\delta\\omega_{2}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & - i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & i \\kappa & \\delta\\omega_{2}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} & 0\\\\0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & \\delta\\omega_{2}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\operatorname{g_{1}}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} & - i \\kappa & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} & 0 & 0\\\\0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & \\delta\\omega_{1}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & 0 & 0 & 0 & i \\operatorname{g_{2}}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & - i \\kappa & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} - \\frac{g^{2}}{\\Delta} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & - i \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}} & 0 & 0 & 0 & - i \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}} & 0 & 0 & 0 & \\delta\\omega_{1}{\\left (t \\right )} + \\delta\\omega_{2}{\\left (t \\right )} - \\frac{2 g^{2}}{\\Delta}\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                 -ⅈ⋅\\kappa                 0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0        ⅈ⋅\\kappa                 0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0            \\delta\\o\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢             ⅈ⋅\\phi₂(t)                                                      \n",
       "⎢0  -ⅈ⋅g₂(t)⋅ℯ                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                         ⅈ⋅\\phi₂(t)          \n",
       "⎢0           0                     0            -ⅈ⋅g₂(t)⋅ℯ                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                   ⅈ⋅\\phi₁(t)                                \n",
       "⎢0           0            -ⅈ⋅g₁(t)⋅ℯ                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                         ⅈ⋅\\phi₁(t)          \n",
       "⎢0           0                     0            -ⅈ⋅g₁(t)⋅ℯ                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0           0                     0                     0                   0\n",
       "⎣                                                                             \n",
       "\n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                     -ⅈ⋅\\phi₂(t)                                              \n",
       "            ⅈ⋅g₂(t)⋅ℯ                         0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                      -ⅈ⋅\\phi₂\n",
       "                      0                       0              ⅈ⋅g₂(t)⋅ℯ        \n",
       "                                                                              \n",
       "mega₂(t)              0                       0                        0      \n",
       "                                                                              \n",
       "                                2                                             \n",
       "                               g                                              \n",
       "          \\delta\\omega₂(t) - ──────       -ⅈ⋅\\kappa                    0      \n",
       "                             \\Delta                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                  ⅈ⋅\\kappa             \\delta\\omega₂(t)                0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0            \\delta\\omega₂(t) - \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                      0                       0                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                               ⅈ⋅\\phi₁(t)                     \n",
       "                      0              -ⅈ⋅g₁(t)⋅ℯ                        0      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                       ⅈ⋅\\phi₁\n",
       "                      0                       0              -ⅈ⋅g₁(t)⋅ℯ       \n",
       "                                                                              \n",
       "\n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                           -ⅈ⋅\\phi₁(t)        \n",
       "               0                   0              ⅈ⋅g₁(t)⋅ℯ                   \n",
       "                                                                              \n",
       "(t)                                                                           \n",
       "               0                   0                        0                ⅈ\n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "   2                                                                          \n",
       "  g                                                                           \n",
       "──────         0                   0                        0                 \n",
       "\\Delta                                                                        \n",
       "                                                                              \n",
       "        \\delta\\omega₁(t)           0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0            \\delta\\omega₁(t)            -ⅈ⋅\\kappa             \n",
       "                                                                              \n",
       "                                                                      2       \n",
       "                                                                     g        \n",
       "               0                ⅈ⋅\\kappa        \\delta\\omega₁(t) - ──────     \n",
       "                                                                   \\Delta     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0              \\de\n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                    ⅈ⋅\\phi₂(t)                                \n",
       "               0          -ⅈ⋅g₂(t)⋅ℯ                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "               0                   0                        0                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(t)                                                                           \n",
       "               0                   0                        0                -\n",
       "                                                                              \n",
       "\n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "        -ⅈ⋅\\phi₁(t)                                                           \n",
       "⋅g₁(t)⋅ℯ                                 0                                    \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                               ⅈ⋅g₂(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                   2                                                          \n",
       "                  g                                                           \n",
       "lta\\omega₁(t) - ──────                   0                                    \n",
       "                \\Delta                                                        \n",
       "                                                                              \n",
       "         0              \\delta\\omega₁(t) + \\delta\\omega₂(t)                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                   \\delta\\omega₁(t) \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                               0                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         ⅈ⋅\\phi₂(t)                                                           \n",
       "ⅈ⋅g₂(t)⋅ℯ                                0                                    \n",
       "                                                                              \n",
       "\n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                  -ⅈ⋅\\phi₁(t)                 \n",
       "    0                                    ⅈ⋅g₁(t)⋅ℯ                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "    -ⅈ⋅\\phi₂(t)                                                               \n",
       "t)⋅ℯ                                              0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                           \n",
       "                                                                              \n",
       "                        2                                                     \n",
       "                       g                                                      \n",
       "+ \\delta\\omega₂(t) - ──────                   -ⅈ⋅\\kappa                       \n",
       "                     \\Delta                                                   \n",
       "                                                                              \n",
       "                                                                      2       \n",
       "                                                                     g        \n",
       " ⅈ⋅\\kappa                    \\delta\\omega₁(t) + \\delta\\omega₂(t) - ──────     \n",
       "                                                                   \\Delta     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    0                                             0                        \\de\n",
       "                                                                              \n",
       "\n",
       "                  0                      ⎤\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  -ⅈ⋅\\phi₁(t)            ⎥\n",
       "         ⅈ⋅g₁(t)⋅ℯ                       ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  -ⅈ⋅\\phi₂(t)            ⎥\n",
       "         ⅈ⋅g₂(t)⋅ℯ                       ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                  0                      ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                       2 ⎥\n",
       "                                    2⋅g  ⎥\n",
       "lta\\omega₁(t) + \\delta\\omega₂(t) - ──────⎥\n",
       "                                   \\Delta⎦"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Parametrization (Ansatz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ket0 = sympy.Matrix([1,0])\n",
    "ket1 = sympy.Matrix([0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ket(*i_tupel):\n",
    "    basis = {'e': ket1, 'g': ket0, '1':ket1, '0':ket0, 1:ket1, 0:ket0}\n",
    "    result = basis[i_tupel[0]]\n",
    "    for i in i_tupel[1:]:\n",
    "        result = TensorProduct(result, basis[i])\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bra(*i_tupel):\n",
    "    return dagger(ket(*i_tupel))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cg, ce = sympy.symbols(\n",
    "(r'c_g', r'c_e'), positive=True)\n",
    "α1, α2, β1, β2, βa, βs = sympy.symbols(\n",
    "(r'\\alpha_1', r'\\alpha_2', r'\\beta_1',\n",
    "r'\\beta_2', r'\\beta_a', r'\\beta_s'), cls=sympy.Function, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Psi \\\n",
    "=   cg * ket('g', 'g', 0, 0) \\\n",
    "  + ce * (\n",
    "          α1(t) * exp(-I*ϕ1(t)) * ket('e', 'g', 0, 0)\n",
    "        + α2(t) * exp(-I*ϕ2(t)) * ket('g', 'e', 0, 0)\n",
    "        + β1(t) * ket('g', 'g', 1, 0)\n",
    "        + β2(t) * ket('g', 'g', 0, 1)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "if drop_phase_and_stark_shift:\n",
    "    Psi = Psi.subs(zero_phase_zero_stark)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def print_psi(psi, skip_zero=True):\n",
    "    from IPython.display import display, Math\n",
    "    qubit = {'0': 'g', '1': 'e'}\n",
    "    cav = {'0': '0', '1': '1'}\n",
    "    for i, a in enumerate(psi):\n",
    "        if a == 0:\n",
    "            if skip_zero:\n",
    "                continue\n",
    "        i, j, k, l = \"{0:04b}\".format(i)\n",
    "        label = qubit[i] + qubit[j] + cav[k] + cav[l]\n",
    "        line = r'\\langle %s \\vert \\Psi \\rangle = %s ' \\\n",
    "               % (label, sympy.latex(a))\n",
    "        display(Math(line))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's assume the initial state is the fully excited state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Psi = Psi.subs({cg: 0, ce: 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Boundary conditions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "boundary_start = {  # -infty\n",
    "    cg: 0, ce: 1, α2(t): 1, ϕ2(t): 0, α1(t): 0, ϕ1(t) :0,\n",
    "    β1(t): 0, β2(t): 0\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "boundary_end = {  # -infty\n",
    "    cg: 0, ce: 1, α2(t): 0, ϕ2(t): 0, α1(t): 1, ϕ1(t) :0,\n",
    "    β1(t): 0, β2(t): 0\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\langle ge00 \\vert \\Psi \\rangle = 1 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_psi(Psi.subs(boundary_start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\langle eg00 \\vert \\Psi \\rangle = 1 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_psi(Psi.subs(boundary_end))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We rewrite the $\\beta$ into a symmetric and anti-symmetric term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta_symmetry = {\n",
    "    β1(t): ((βs(t) - βa(t)) / sqrt(2)),\n",
    "    β2(t): ((βs(t) + βa(t)) / sqrt(2))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Psi = Psi.subs(beta_symmetry)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The dark state condition is that probability of a quantum jump is zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eq_dark = sympy.Eq(((L * Psi)[0]).expand(), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIoAAAAWBAMAAADtDRlvAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$2 \\sqrt{\\kappa} c_{e} \\beta_{s}{\\left (t \\right )} = 0$$"
      ],
      "text/plain": [
       "    ________                  \n",
       "2⋅╲╱ \\kappa ⋅cₑ⋅\\beta_s(t) = 0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_dark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dark_state_cond = {βs(t): sympy.solve(eq_dark, βs(t))[0]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Psi = Psi.subs(dark_state_cond)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\langle gg00 \\vert \\Psi \\rangle = c_{g} $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle gg01 \\vert \\Psi \\rangle = \\frac{\\sqrt{2} c_{e}}{2} \\beta_{a}{\\left (t \\right )} $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle gg10 \\vert \\Psi \\rangle = - \\frac{\\sqrt{2} c_{e}}{2} \\beta_{a}{\\left (t \\right )} $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle gg11 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ge00 \\vert \\Psi \\rangle = c_{e} \\alpha_{2}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ge01 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ge10 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ge11 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle eg00 \\vert \\Psi \\rangle = c_{e} \\alpha_{1}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle eg01 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle eg10 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle eg11 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ee00 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ee01 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ee10 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\langle ee11 \\vert \\Psi \\rangle = 0 $$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_psi(Psi, skip_zero=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Normalization condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAApoAAAAfBAMAAAC1wHCOAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nr86o4+HVmddWZPVxPLAVYa/SmHuaz+C/7wYv/KqshpUAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$c_{e}^{2} \\alpha_{1}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} e^{i \\overline{\\phi_{1}{\\left (t \\right )}}} \\overline{\\alpha_{1}{\\left (t \\right )}} + c_{e}^{2} \\alpha_{2}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} e^{i \\overline{\\phi_{2}{\\left (t \\right )}}} \\overline{\\alpha_{2}{\\left (t \\right )}} + c_{e}^{2} \\beta_{a}{\\left (t \\right )} \\overline{\\beta_{a}{\\left (t \\right )}} + c_{g}^{2}$$"
      ],
      "text/plain": [
       "                               ________                                       \n",
       "  2             -ⅈ⋅\\phi₁(t)  ⅈ⋅\\phi₁(t) __________     2             -ⅈ⋅\\phi₂(\n",
       "cₑ ⋅\\alpha₁(t)⋅ℯ           ⋅ℯ          ⋅\\alpha₁(t) + cₑ ⋅\\alpha₂(t)⋅ℯ         \n",
       "\n",
       "      ________                                            \n",
       "t)  ⅈ⋅\\phi₂(t) __________     2           _________      2\n",
       "  ⋅ℯ          ⋅\\alpha₂(t) + cₑ ⋅\\betaₐ(t)⋅\\betaₐ(t) + c_g "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(dagger(Psi) * Psi)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dynamic_equations(H, psi, t):\n",
    "    lhs = I*psi.diff(t)\n",
    "    rhs = H * psi\n",
    "    eqs = []\n",
    "    for i in range(len(lhs)):\n",
    "        if lhs[i] == rhs[i] == 0:\n",
    "            continue\n",
    "        else:\n",
    "            eqs.append(sympy.Eq(lhs[i], rhs[i]))\n",
    "    return eqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eqs = dynamic_equations(H, Psi, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQgAAAArBAMAAAB2lwvgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{i c_{e}}{2} \\sqrt{2} \\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\frac{i \\kappa}{2} \\sqrt{2} c_{e} \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "  ___      d                                          \n",
       "╲╱ 2 ⋅ⅈ⋅cₑ⋅──(\\betaₐ(t))     ___                      \n",
       "           dt              ╲╱ 2 ⋅ⅈ⋅\\kappa⋅cₑ⋅\\betaₐ(t)\n",
       "──────────────────────── = ───────────────────────────\n",
       "           2                            2             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARoAAAArBAMAAABVzFo1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nxH7FfwbxrwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\frac{i c_{e}}{2} \\sqrt{2} \\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\frac{i \\kappa}{2} \\sqrt{2} c_{e} \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "   ___      d                                           \n",
       "-╲╱ 2 ⋅ⅈ⋅cₑ⋅──(\\betaₐ(t))      ___                      \n",
       "            dt               ╲╱ 2 ⋅ⅈ⋅\\kappa⋅cₑ⋅\\betaₐ(t)\n",
       "────────────────────────── = ───────────────────────────\n",
       "            2                             2             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/latex": [
       "$$i \\left(- i c_{e} \\alpha_{2}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}} \\frac{d}{d t} \\phi_{2}{\\left (t \\right )} + c_{e} e^{- i \\phi_{2}{\\left (t \\right )}} \\frac{d}{d t} \\alpha_{2}{\\left (t \\right )}\\right) = c_{e} \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )} e^{- i \\phi_{2}{\\left (t \\right )}}$$"
      ],
      "text/plain": [
       "  ⎛                   -ⅈ⋅\\phi₂(t) d                  -ⅈ⋅\\phi₂(t) d            \n",
       "ⅈ⋅⎜- ⅈ⋅cₑ⋅\\alpha₂(t)⋅ℯ           ⋅──(\\phi₂(t)) + cₑ⋅ℯ           ⋅──(\\alpha₂(t)\n",
       "  ⎝                               dt                             dt           \n",
       "\n",
       " ⎞                                   -ⅈ⋅\\phi₂(t)\n",
       ")⎟ = cₑ⋅\\alpha₂(t)⋅\\delta\\omega₂(t)⋅ℯ           \n",
       " ⎠                                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQMAAAAqBAMAAABFKyOyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+K23GYNmUw9n7ioEDeotnxdf7caW8C/1rSyp9iBQCgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = - \\frac{i c_{e}}{2} \\sqrt{2} \\beta_{a}{\\left (t \\right )} \\operatorname{g_{2}}{\\left (t \\right )} e^{i \\phi_{2}{\\left (t \\right )}}$$"
      ],
      "text/plain": [
       "       ___                       ⅈ⋅\\phi₂(t) \n",
       "    -╲╱ 2 ⋅ⅈ⋅cₑ⋅\\betaₐ(t)⋅g₂(t)⋅ℯ           \n",
       "0 = ────────────────────────────────────────\n",
       "                       2                    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAo8AAAAyBAMAAADPdSzKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfwEt7uxIPe6XbAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$i \\left(- i c_{e} \\alpha_{1}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}} \\frac{d}{d t} \\phi_{1}{\\left (t \\right )} + c_{e} e^{- i \\phi_{1}{\\left (t \\right )}} \\frac{d}{d t} \\alpha_{1}{\\left (t \\right )}\\right) = c_{e} \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )} e^{- i \\phi_{1}{\\left (t \\right )}}$$"
      ],
      "text/plain": [
       "  ⎛                   -ⅈ⋅\\phi₁(t) d                  -ⅈ⋅\\phi₁(t) d            \n",
       "ⅈ⋅⎜- ⅈ⋅cₑ⋅\\alpha₁(t)⋅ℯ           ⋅──(\\phi₁(t)) + cₑ⋅ℯ           ⋅──(\\alpha₁(t)\n",
       "  ⎝                               dt                             dt           \n",
       "\n",
       " ⎞                                   -ⅈ⋅\\phi₁(t)\n",
       ")⎟ = cₑ⋅\\alpha₁(t)⋅\\delta\\omega₁(t)⋅ℯ           \n",
       " ⎠                                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPMAAAAqBAMAAACU6XDrAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = \\frac{i c_{e}}{2} \\sqrt{2} \\beta_{a}{\\left (t \\right )} \\operatorname{g_{1}}{\\left (t \\right )} e^{i \\phi_{1}{\\left (t \\right )}}$$"
      ],
      "text/plain": [
       "      ___                       ⅈ⋅\\phi₁(t)\n",
       "    ╲╱ 2 ⋅ⅈ⋅cₑ⋅\\betaₐ(t)⋅g₁(t)⋅ℯ          \n",
       "0 = ──────────────────────────────────────\n",
       "                      2                   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_eqs(eqs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* we assume that $c_e > 0$, and cancel constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c1 = I*sqrt(2)*ce / 2\n",
    "c2 = -I*ce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "if drop_phase_and_stark_shift:\n",
    "    eqs[0] = divide_eq(eqs[0], c1, simplify=sympy.simplify)\n",
    "    eqs[1] = divide_eq(eqs[1], c1, simplify=sympy.simplify)\n",
    "    eqs[2] = divide_eq(eqs[2], c2, simplify=sympy.simplify)\n",
    "    eqs[3] = divide_eq(eqs[3], c1, simplify=sympy.simplify)\n",
    "    eqs[4] = divide_eq(eqs[4], c2, simplify=sympy.simplify)\n",
    "    eqs[5] = divide_eq(eqs[5], c1, simplify=sympy.simplify)\n",
    "else:\n",
    "    eqs[0] = divide_eq(eqs[0], c1, simplify=sympy.simplify)\n",
    "    eqs[1] = divide_eq(eqs[1], c1, simplify=sympy.simplify)\n",
    "    eqs[2] = divide_eq(eqs[2], (c2*exp(-I*ϕ2(t))), simplify=sympy.simplify)\n",
    "    eqs[3] = divide_eq(eqs[3], (c1*exp(+I*ϕ2(t))), simplify=sympy.simplify)\n",
    "    eqs[4] = divide_eq(eqs[4], (c2*exp(-I*ϕ1(t))), simplify=sympy.simplify)\n",
    "    eqs[5] = divide_eq(eqs[5], (c1*exp(+I*ϕ1(t))), simplify=sympy.simplify)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAArBAMAAACDTNd5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\kappa \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "d                               \n",
       "──(\\betaₐ(t)) = \\kappa⋅\\betaₐ(t)\n",
       "dt                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAAArBAMAAAAAiO5CAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nF/MvW9vKtllOy+YAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- \\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\kappa \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       " d                               \n",
       "-──(\\betaₐ(t)) = \\kappa⋅\\betaₐ(t)\n",
       " dt                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAArBAMAAAAtX5bRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nqDJTE1eRHGb+Bb9Y4Gzb3cLhAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$i \\alpha_{2}{\\left (t \\right )} \\frac{d}{d t} \\phi_{2}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{2}{\\left (t \\right )} = i \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "             d              d                                             \n",
       "ⅈ⋅\\alpha₂(t)⋅──(\\phi₂(t)) - ──(\\alpha₂(t)) = ⅈ⋅\\alpha₂(t)⋅\\delta\\omega₂(t)\n",
       "             dt             dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAUBAMAAAB7fhJGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wANeZVjUqtQAwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = - \\beta_{a}{\\left (t \\right )} \\operatorname{g_{2}}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = -\\betaₐ(t)⋅g₂(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAArBAMAAAAtX5bRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$i \\alpha_{1}{\\left (t \\right )} \\frac{d}{d t} \\phi_{1}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{1}{\\left (t \\right )} = i \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "             d              d                                             \n",
       "ⅈ⋅\\alpha₁(t)⋅──(\\phi₁(t)) - ──(\\alpha₁(t)) = ⅈ⋅\\alpha₁(t)⋅\\delta\\omega₁(t)\n",
       "             dt             dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAAUBAMAAABc0JOuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAACL0lEQVQ4EW2UPWjUYBjH/2kuzV1zOUO76A02\nQ3XoIIetazjBxS2ICJ3M4td2YxHUAynVQTykQ1HwipuDcENFBMGACB2kOFgRFAw6uEipODhp/b8f\nl3uT3gPv8/V78uR5874EGCu1Mz2dr7WFc1ZHhjHA9OIpA2j3h/Vce4+krQ87jkoNcAWHD/BKjM+6\n+Bpg3YWVjJ49ACobsBOdzc0asKyCSgi4e0CUM+0YwEvh/irzDHinclVOOJEAzXKJAQ6l8P+UeQb/\nqcqt01RbwOT7Uo0BZkP4/0rYXzpxNVC5b8CX168y2CFj/83c7kDXGqDfgvObafuyFFGJhrUwHwsH\n2OS6xVVJqL4G1XaGC/QKoB+qFjKvlc0uifJXaY5zuV2qLdS7OLdFDzDAuI00OPOeLMQzmttcjojn\nRQt9Vgbg53TLn3OHg2/wEQorrb+0skU/bnaMFkPgDVARh2rfkZLSRQuop5j+eUnOy4EC+F3mH0fi\nIqsbw40MAV8nzr0gjB/2rBWHrfk57cSN1ee8IatUCxOsohkXGojnnHuYCJ0ucJI3Kz1KxcnwcWeJ\nWrUwwczu21IH/3y0EGCq00iBT0Bts82rJV4zub//ZNiiAEoNOLnMzPa80wHEPRayLtQLHFnO9BQF\nIGBBVIup+OIHnkyoUETjDhgPcF1mTKBKTM2tU/ztm3M0L2VgJTTWCuB1HtzflikDyLigeC1Gov4s\nntzPTPT9WE5MkCfHOsb/rchz8B9TWY5Cc9jengAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = \\beta_{a}{\\left (t \\right )} \\operatorname{g_{1}}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = \\betaₐ(t)⋅g₁(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_eqs(eqs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We choose a chirp to compensate for the Stark shift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if not drop_phase_and_stark_shift:\n",
    "    chirp = {ϕ1(t).diff(t): ω1(t), ϕ2(t).diff(t): ω2(t)}\n",
    "    for i, eq in enumerate(eqs):\n",
    "        eqs[i] = eq.subs(chirp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAArBAMAAACDTNd5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\kappa \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "d                               \n",
       "──(\\betaₐ(t)) = \\kappa⋅\\betaₐ(t)\n",
       "dt                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAAArBAMAAAAAiO5CAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nF/MvW9vKtllOy+YAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- \\frac{d}{d t} \\beta_{a}{\\left (t \\right )} = \\kappa \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       " d                               \n",
       "-──(\\betaₐ(t)) = \\kappa⋅\\betaₐ(t)\n",
       " dt                              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVMAAAArBAMAAAA3Y3ZfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAq7tmEHaZiUTvIlTN\n3TIT0Hn9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAE/0lEQVRYCdVYXWgcVRT+sjPZmZ3sbkJLEcSH\nlUoffDALgSBqdRR8CFSyoImID06LUIVAFupGooJrQfRFW1q0WkGHFBUpweCTWDQrKIjakpdiiQYG\nKX2Qwq5arRjJes692ey9sztDkRlYD+z9Od93v3Nm5s6duxdIzH5+MzGp1IU2U4+QVAD7WlJKqetY\na6mHSCpA3ktKKWWdD2rNlZRDJCRvn8a4m5BWyjJTZcylHCIp+XkXPySllbLOCZh/pRwiIXnzOkZa\nCWmlLGNuItP4LOUgCcl/jf1j1YS0bljGKTP1LsG3Hw5E3SlUrOOT9f2P/rKnrruod4Y9hs9lrKm6\nL9+rU1Vslw4tie6Qz9XdR7dEr1OoWMcXUzslAd7cS4mOaXw6Hmh8NeZuDcG3gLkOs8HeMbhc7ZiK\n7TijG3kfeMjHgV5GdMwhmDo9OqbhQbzMNR5whIuuGZ6Cdd2RrUlCVgGrEsmQgOF1dS0x/7oDVKzr\nFa2CD2QbwBTIjvlc7piG7XijG+sE0TfMPB5NEYiqa/+tk1VMR7BM/UIVyNepkV/TUA3TkL4dh0fz\nN+ybvnDXqeme7/q5pWDmbIUe0cxTHcIs8NL4rRVYHuDMXAdKhHxUpwJQMeHoV9Rm69vuYQ/2rt/2\nAAshXlzM95+oIkN85y05SIlp2cfhXMKUfxYL+1xgLzFofsFoAFfdcRh16kxXrENP6hh5+9py3Tzt\nrAh6piynIO5hpvW9MI+b0TGLX2VauJM45h89+ZzNNpCjC/EesfyhBvAj0XiPNLIG813cF2SpDWvl\nOdyiYezta6eAfcOuoBdW5LTH5yFmTMypwNiCx/zne/JxRyuYd5FtVAt+kaY033eeX8UWsiU0g1eB\nBq3i62j6KkaXfX6D7KeAuIpl6Q/WnAVBz9XltEdTIXAzJuYhFLfsOvL0EerJB6suTtB9O+UW6g5t\njihVsUeiVHNlNN0Kih4sXMLHdRXTgo+2O4ZcCVh8RtI51Wn69aQaE/MkiteGgStAtScffGnStggW\n/zMeoVtCE8Bu0cpvr2E6wH56GMMr+JBAuiQFI0dfm64CL9KDZzpPgGO8or/GVIsfwsbGGLcjY5pb\nMNZozj0Oh4RC+ZibFn4noRYpFCri1bEaIwG/VqMBvWR3oOnxFwwXNYwD9rPRMqXKANH5tXoBX0C+\nVgo7JuYWjcoExT/BX7pQPnbrDA4Ck63LclGhhSU79iAVVfrK2CUsLrzz6yLFtDyBdzAlsNbMjsGY\nL7qCzkMOmnT5hzUKP7bImDUcpcn49OpNJ2kML3JKPthdhnVkAocrMDyC6GE5eym1fADUaFF74J/g\nsTfIPxnCqNvXnp0oZ2uSTnMISxPEuhBmRse0ZjyY4xeG36YrNDwap+ZD3W17Ba/TTfdlb7njlbVd\ntYMoTGeKnqDTOiBMfLX6kNgVFzMaK3537rbtSyENujOqXT33iQvDk64QJpz64ZqgiydBYMx2JS5m\nDJZrt1skfLuILDeBoimK99rtSEyyNnnv2DFJz/iif6Dj7a3jYsZhUmlJVNtRQuIxGB2ujfCVquaU\nRE9evAqE2zG6iMHUPwhhyRiMDteyjTD/v/xhCWvExAxTb7BPh2u8dxx848M1sXcc+FTl4RrvHQfe\n5OHa3MDnSQnOi8M13jsOvInDtf/F+Zo8XBN7x0G/q/JwTewdBz1ViMM1sT8c+FTF4ZrYO6aY6r8D\nPrQKQ0MjewAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$i \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{2}{\\left (t \\right )} = i \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "                                d                                             \n",
       "ⅈ⋅\\alpha₂(t)⋅\\delta\\omega₂(t) - ──(\\alpha₂(t)) = ⅈ⋅\\alpha₂(t)⋅\\delta\\omega₂(t)\n",
       "                                dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAUBAMAAAB7fhJGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wANeZVjUqtQAwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = - \\beta_{a}{\\left (t \\right )} \\operatorname{g_{2}}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = -\\betaₐ(t)⋅g₂(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVMAAAArBAMAAAA3Y3ZfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$i \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{1}{\\left (t \\right )} = i \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "                                d                                             \n",
       "ⅈ⋅\\alpha₁(t)⋅\\delta\\omega₁(t) - ──(\\alpha₁(t)) = ⅈ⋅\\alpha₁(t)⋅\\delta\\omega₁(t)\n",
       "                                dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAAUBAMAAABc0JOuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nntzPTPT9WE5MkCfHOsb/rchz8B9TWY5Cc9jengAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0 = \\beta_{a}{\\left (t \\right )} \\operatorname{g_{1}}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = \\betaₐ(t)⋅g₁(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_eqs(eqs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eqs2 = []\n",
    "eqs2.append(divide_eq(add_eqs(eqs[0], eqs[1]), 2))\n",
    "eqs2.append(add_eqs(eqs[3], eqs[5]))\n",
    "eqs2.append(eqs[2])\n",
    "eqs2.append(eqs[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF0AAAAUBAMAAAAdCCxUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$0 = \\kappa \\beta_{a}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = \\kappa⋅\\betaₐ(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP0AAAAUBAMAAAC0UCaFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEEUlEQVRIDYVWX2hbZRT/3SZpcpveGFcYtYIN\nOn0YMmKqPoY4p6CCXERle+p90enDsC/iUNSIjq0PahgFhwVbhDH2IESpiCAYEKWijIJ2iBZ2WWF7\ncJQOEZky4++cc+/NTdrggZx/v/Od833nO18SYFdyD7Uiv9sQ5bHISomhABaS6AWJz8apUosVsKx7\n7n8gBUTqVefzSFtUOb4zx1CgNHe7b4vdtsrvo1Q9EQGa9SgmdyTP+vgtin4RcObhBL3F/wc8As/q\nYpSJmXzvjrUCRFmzy8gEgwFsz3HzZStAfhuoD4YMBXgv+aZFH6R4E8iEZva4AFHWYgf56z3EtBD4\n0bQCdzoSAFNm9vhQoASMdyxunuIennTZzB4XIMp6SwfeXz3EtBDeedPOUBSqwOjaQMxQgPV/5aZJ\nbpPsbX6O8ZMmBaKs0xV4/6ZB6t6RAy+UzXcZ2Pj6qxCZivi/2bfVNj/6gMinYv30lbfMLjH1D/9c\nAGpib9Se/N38IJBkXaoi9wf9meeViAAlZ2a/Lwqwwg+vENmA7FK50AjxLLUBQD0RCydqZ00tNuyW\n8Sht7zreKaH2mZxLgDjrUsXq05NQhlsIzDpJwSu0kVrFeBNPrSrSB1is8SpwxbTCnN2yzjJXriLT\nGg+ICRBn3a3/vEJv23J8QiFXmBN7v9SPXkYfgL2nhJ5jDEL2SSQwtmazg1kaI8usX2jlbkRAnJXz\nlx+cv3X2e5lxJJZxblJq/SV/iju3l9kHaKgxzwceN1XqT/Oj9d0/nXMorLmSTIA4a7GNrLy/jJ7g\nVIcqqvqE9lzjedhmtqIMr0n/R3X5qrT6fQC9MfHu+HadA9/52uZLcIBf6HM3N30KfevS/zgrDzoS\nEEhTAHzYck7kuC/OXybI+zZ/r2uQ1e8DUotHWeo8Jv3Zso7Zg3gZOn95nplUCMlk/pKsJzElG0vT\nCnLvYqSSa+rTGencweurMuDi+hFyq8831QNSi5n78BruxGGWqAD3OiFwF3Hv2DMtCn2KAiSLJ7a+\npT9N3tP1mTLG5kodbZ270uD3j+xxtNv9OK7PnvaA1Or1hzfvA87hGks2gcVDxHQuX+r+XUG2IqEC\n7LpYQO5b+XSr+FCZE6sGzoj4ArcdD6Pz9wEWo1z6BOcGVm4F5s3vNimLc84H7+EncLYTwLKKo4+s\n/pg/+zPfQcWgOkW+TbuNV9WTBizEuNbH2dzNBnDQXPr78xr1J3JHX/lUfBGw81dNF/C6Sd6FN/ZR\nfKmGE1A4J+QYp9/nNyopBahtTK6btHH1coPB1jz9/Z302b+xbnebaAxoVrH7SVsUuxZVsUwT9c27\nYz/SQOKEPP+E3LaqulNnZquWYBEQ7S+J300Z+jdrKJDKsiB6tpXyRKoC8v/rP5kZDwxSKfSqAAAA\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$0 = \\beta_{a}{\\left (t \\right )} \\operatorname{g_{1}}{\\left (t \\right )} - \\beta_{a}{\\left (t \\right )} \\operatorname{g_{2}}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "0 = \\betaₐ(t)⋅g₁(t) - \\betaₐ(t)⋅g₂(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/latex": [
       "$$i \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{2}{\\left (t \\right )} = i \\alpha_{2}{\\left (t \\right )} \\delta\\omega_{2}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "                                d                                             \n",
       "ⅈ⋅\\alpha₂(t)⋅\\delta\\omega₂(t) - ──(\\alpha₂(t)) = ⅈ⋅\\alpha₂(t)⋅\\delta\\omega₂(t)\n",
       "                                dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVMAAAArBAMAAAA3Y3ZfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$i \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )} - \\frac{d}{d t} \\alpha_{1}{\\left (t \\right )} = i \\alpha_{1}{\\left (t \\right )} \\delta\\omega_{1}{\\left (t \\right )}$$"
      ],
      "text/plain": [
       "                                d                                             \n",
       "ⅈ⋅\\alpha₁(t)⋅\\delta\\omega₁(t) - ──(\\alpha₁(t)) = ⅈ⋅\\alpha₁(t)⋅\\delta\\omega₁(t)\n",
       "                                dt                                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_eqs(eqs2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "goerz-QNET",
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   "name": "goerz_qnet"
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.5"
  },
  "toc": {
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  }
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}