SLH_Hamiltonian.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import qnet.misc.to_sympy_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from two_node_slh import qnet_node_system, setup_qnet_sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_cavity = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SYS, Sym1, Op1, Sym2, Op2 = setup_qnet_sys(n_cavity=n_cavity, stark_shift=True, zero_phi=False, keep_delta=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "${\\rm  \\frac{\\Omega_{{1}}^{2}}{4 \\Delta_{{1}}} {\\Pi_{{\\rm e}}^{{{\\rm atom}}_{{\\rm 1}}}}} +  \\frac{\\Omega_{{2}}^{2}}{4 \\Delta_{{2}}} {\\Pi_{{\\rm e}}^{{{\\rm atom}}_{{\\rm 2}}}} -  \\delta_{{1}}  {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 1}}}} +  i \\kappa  {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}} -  \\delta_{{2}}  {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}} -  i \\kappa  {a_{{{\\rm cav}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} -  \\frac{i \\Omega_{{1}} g_{{1}}}{2 \\Delta_{{1}}} e^{i \\phi_{{1}}}  {\\sigma_{{\\rm e},{\\rm g}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}} +  \\frac{i \\Omega_{{1}} g_{{1}}}{2 \\Delta_{{1}}} e^{- i \\phi_{{1}}}  {\\sigma_{{\\rm g},{\\rm e}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} +  \\frac{g_{{1}}^{2}}{\\Delta_{{1}}}  {\\Pi_{{\\rm g}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 1}}}} -  \\frac{i \\Omega_{{2}} g_{{2}}}{2 \\Delta_{{2}}} e^{i \\phi_{{2}}}  {\\sigma_{{\\rm e},{\\rm g}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}} +  \\frac{i \\Omega_{{2}} g_{{2}}}{2 \\Delta_{{2}}} e^{- i \\phi_{{2}}}  {\\sigma_{{\\rm g},{\\rm e}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} +  \\frac{g_{{2}}^{2}}{\\Delta_{{2}}}  {\\Pi_{{\\rm g}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}}$"
      ],
      "text/plain": [
       "OperatorPlus(ScalarTimesOperator(\\Omega_{1}**2/(4*\\Delta_{1}), LocalSigma(LocalSpace('atom', '1'), 'e', 'e')), ScalarTimesOperator(\\Omega_{2}**2/(4*\\Delta_{2}), LocalSigma(LocalSpace('atom', '2'), 'e', 'e')), ScalarTimesOperator(-\\delta_{1}, OperatorTimes(Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(I*\\kappa, OperatorTimes(Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(-\\delta_{2}, OperatorTimes(Create(LocalSpace('cav', '2')), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(-I*\\kappa, OperatorTimes(Destroy(LocalSpace('cav', '1')), Create(LocalSpace('cav', '2')))), ScalarTimesOperator(-I*\\Omega_{1}*g_{1}*exp(I*\\phi_{1})/(2*\\Delta_{1}), OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'e', 'g'), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(I*\\Omega_{1}*g_{1}*exp(-I*\\phi_{1})/(2*\\Delta_{1}), OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'g', 'e'), Create(LocalSpace('cav', '1')))), ScalarTimesOperator(g_{1}**2/\\Delta_{1}, OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'g', 'g'), Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(-I*\\Omega_{2}*g_{2}*exp(I*\\phi_{2})/(2*\\Delta_{2}), OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'e', 'g'), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(I*\\Omega_{2}*g_{2}*exp(-I*\\phi_{2})/(2*\\Delta_{2}), OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'g', 'e'), Create(LocalSpace('cav', '2')))), ScalarTimesOperator(g_{2}**2/\\Delta_{2}, OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'g', 'g'), Create(LocalSpace('cav', '2')), Destroy(LocalSpace('cav', '2')))))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SYS.H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dw1 = Sym1['Omega']**2 / (4 * Sym1['Delta'])\n",
    "g1t = Sym1['g'] * Sym1['Omega'] / (2 * Sym1['Delta'])\n",
    "dw2 = Sym2['Omega']**2 / (4 * Sym2['Delta'])\n",
    "g2t = Sym2['g'] * Sym2['Omega'] / (2 * Sym2['Delta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = SYS.H.substitute({dw1: sympy.symbols('\\delta\\omega_1', real=True),\n",
    "                  g1t: sympy.symbols('g_{1}^{(t)}', real=True),\n",
    "                  dw2: sympy.symbols('\\delta\\omega_2', real=True),\n",
    "                  g2t: sympy.symbols('g_{2}^{(t)}', real=True),\n",
    "                 })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "${\\rm  \\delta\\omega_{1} {\\Pi_{{\\rm e}}^{{{\\rm atom}}_{{\\rm 1}}}}} +  \\delta\\omega_{2} {\\Pi_{{\\rm e}}^{{{\\rm atom}}_{{\\rm 2}}}} -  \\delta_{{1}}  {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 1}}}} +  i \\kappa  {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}} -  \\delta_{{2}}  {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}} -  i \\kappa  {a_{{{\\rm cav}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} -  i g^{{(t)}}_{{1}} e^{i \\phi_{{1}}}  {\\sigma_{{\\rm e},{\\rm g}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}} +  i g^{{(t)}}_{{1}} e^{- i \\phi_{{1}}}  {\\sigma_{{\\rm g},{\\rm e}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} +  \\frac{g_{{1}}^{2}}{\\Delta_{{1}}}  {\\Pi_{{\\rm g}}^{{{\\rm atom}}_{{\\rm 1}}}} {a_{{{\\rm cav}}_{{\\rm 1}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 1}}}} -  i g^{{(t)}}_{{2}} e^{i \\phi_{{2}}}  {\\sigma_{{\\rm e},{\\rm g}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}} +  i g^{{(t)}}_{{2}} e^{- i \\phi_{{2}}}  {\\sigma_{{\\rm g},{\\rm e}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} +  \\frac{g_{{2}}^{2}}{\\Delta_{{2}}}  {\\Pi_{{\\rm g}}^{{{\\rm atom}}_{{\\rm 2}}}} {a_{{{\\rm cav}}_{{\\rm 2}}}^\\dagger} {a_{{{\\rm cav}}_{{\\rm 2}}}}$"
      ],
      "text/plain": [
       "OperatorPlus(ScalarTimesOperator(\\delta\\omega_1, LocalSigma(LocalSpace('atom', '1'), 'e', 'e')), ScalarTimesOperator(\\delta\\omega_2, LocalSigma(LocalSpace('atom', '2'), 'e', 'e')), ScalarTimesOperator(-\\delta_{1}, OperatorTimes(Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(I*\\kappa, OperatorTimes(Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(-\\delta_{2}, OperatorTimes(Create(LocalSpace('cav', '2')), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(-I*\\kappa, OperatorTimes(Destroy(LocalSpace('cav', '1')), Create(LocalSpace('cav', '2')))), ScalarTimesOperator(-I*g_{1}^{(t)}*exp(I*\\phi_{1}), OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'e', 'g'), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(I*g_{1}^{(t)}*exp(-I*\\phi_{1}), OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'g', 'e'), Create(LocalSpace('cav', '1')))), ScalarTimesOperator(g_{1}**2/\\Delta_{1}, OperatorTimes(LocalSigma(LocalSpace('atom', '1'), 'g', 'g'), Create(LocalSpace('cav', '1')), Destroy(LocalSpace('cav', '1')))), ScalarTimesOperator(-I*g_{2}^{(t)}*exp(I*\\phi_{2}), OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'e', 'g'), Destroy(LocalSpace('cav', '2')))), ScalarTimesOperator(I*g_{2}^{(t)}*exp(-I*\\phi_{2}), OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'g', 'e'), Create(LocalSpace('cav', '2')))), ScalarTimesOperator(g_{2}**2/\\Delta_{2}, OperatorTimes(LocalSigma(LocalSpace('atom', '2'), 'g', 'g'), Create(LocalSpace('cav', '2')), Destroy(LocalSpace('cav', '2')))))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "L = SYS.L[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "${\\rm  \\sqrt{2} \\sqrt{\\kappa} {a_{{{\\rm cav}}_{{\\rm 1}}}}} +  \\sqrt{2} \\sqrt{\\kappa} {a_{{{\\rm cav}}_{{\\rm 2}}}}$"
      ],
      "text/plain": [
       "OperatorPlus(ScalarTimesOperator(sqrt(2)*sqrt(\\kappa), Destroy(LocalSpace('cav', '1'))), ScalarTimesOperator(sqrt(2)*sqrt(\\kappa), Destroy(LocalSpace('cav', '2'))))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "${{\\rm atom}}_{{\\rm 1}} \\otimes {{\\rm atom}}_{{\\rm 2}} \\otimes {{\\rm cav}}_{{\\rm 1}} \\otimes {{\\rm cav}}_{{\\rm 2}}$"
      ],
      "text/plain": [
       "ProductSpace(LocalSpace('atom', '1'), LocalSpace('atom', '2'), LocalSpace('cav', '1'), LocalSpace('cav', '2'))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "M = qnet.misc.to_sympy_matrix.convert_to_sympy_matrix(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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IAqLAfQpwcEHuK906Z1h8rxpnCV2fk2NRQBQQBUQBUUAUIFTgt1wQ+fyX8Kclpr5UgXG1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\n0VrbZ1mfZcwWCK0pqs6sv7s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4eB0hoXzJEFgIouTVLkiJvJbqeSvSU19PzssUJpd5jnv7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\nmAAAAABJRU5ErkJggg==\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_{{2}}} & - i \\kappa & 0 & i g^{{(t)}}_{{2}} e^{- i \\phi_{{2}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & i \\kappa & - \\delta_{{1}} + \\frac{g_{{1}}^{2}}{\\Delta_{{1}}} & 0 & 0 & 0 & 0 & 0 & i g^{{(t)}}_{{1}} e^{- i \\phi_{{1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - \\delta_{{1}} - \\delta_{{2}} + \\frac{g_{{2}}^{2}}{\\Delta_{{2}}} + \\frac{g_{{1}}^{2}}{\\Delta_{{1}}} & 0 & 0 & i g^{{(t)}}_{{2}} e^{- i \\phi_{{2}}} & 0 & 0 & i g^{{(t)}}_{{1}} e^{- i \\phi_{{1}}} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & - i g^{{(t)}}_{{2}} e^{i \\phi_{{2}}} & 0 & 0 & \\delta\\omega_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & \\delta\\omega_{2} - \\delta_{{2}} & - i \\kappa & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - i g^{{(t)}}_{{2}} e^{i \\phi_{{2}}} & 0 & i \\kappa & \\delta\\omega_{2} - \\delta_{{1}} + \\frac{g_{{1}}^{2}}{\\Delta_{{1}}} & 0 & 0 & 0 & 0 & 0 & i g^{{(t)}}_{{1}} e^{- i \\phi_{{1}}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{2} - \\delta_{{1}} - \\delta_{{2}} + \\frac{g_{{1}}^{2}}{\\Delta_{{1}}} & 0 & 0 & 0 & 0 & 0 & i g^{{(t)}}_{{1}} e^{- i \\phi_{{1}}} & 0 & 0\\\\0 & 0 & - i g^{{(t)}}_{{1}} e^{i \\phi_{{1}}} & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - i g^{{(t)}}_{{1}} e^{i \\phi_{{1}}} & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1} - \\delta_{{2}} + \\frac{g_{{2}}^{2}}{\\Delta_{{2}}} & - i \\kappa & 0 & i g^{{(t)}}_{{2}} e^{- i \\phi_{{2}}} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & i \\kappa & \\delta\\omega_{1} - \\delta_{{1}} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1} - \\delta_{{1}} - \\delta_{{2}} + \\frac{g_{{2}}^{2}}{\\Delta_{{2}}} & 0 & 0 & i g^{{(t)}}_{{2}} e^{- i \\phi_{{2}}} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & - i g^{{(t)}}_{{1}} e^{i \\phi_{{1}}} & 0 & 0 & - i g^{{(t)}}_{{2}} e^{i \\phi_{{2}}} & 0 & 0 & \\delta\\omega_{1} + \\delta\\omega_{2} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & - i g^{{(t)}}_{{1}} e^{i \\phi_{{1}}} & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1} + \\delta\\omega_{2} - \\delta_{{2}} & - i \\kappa & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - i g^{{(t)}}_{{2}} e^{i \\phi_{{2}}} & 0 & i \\kappa & \\delta\\omega_{1} + \\delta\\omega_{2} - \\delta_{{1}} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \\delta\\omega_{1} + \\delta\\omega_{2} - \\delta_{{1}} - \\delta_{{2}}\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡0               0                            0                               \n",
       "⎢                                                                             \n",
       "⎢                         2                                                   \n",
       "⎢                    g_{2}                                                    \n",
       "⎢0   -\\delta_{2} + ──────────             -ⅈ⋅\\kappa                           \n",
       "⎢                  \\Delta_{2}                                                 \n",
       "⎢                                                                             \n",
       "⎢                                                      2                      \n",
       "⎢                                                 g_{1}                       \n",
       "⎢0           ⅈ⋅\\kappa             -\\delta_{1} + ──────────                    \n",
       "⎢                                               \\Delta_{1}                    \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0               0                            0               -\\delta_{1} - \\d\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                    ⅈ⋅\\phi_{2}                                               \n",
       "⎢0  -ⅈ⋅g_{2}__{(t)}⋅ℯ                         0                               \n",
       "⎢                                                                             \n",
       "⎢0               0                            0                               \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0               0                            0                          -ⅈ⋅g_\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0               0                            0                               \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                 ⅈ⋅\\phi_{1}                  \n",
       "⎢0               0               -ⅈ⋅g_{1}__{(t)}⋅ℯ                            \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0               0                            0                          -ⅈ⋅g_\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",
       "⎣0               0                            0                               \n",
       "\n",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                    -ⅈ⋅\\phi_{2}               \n",
       "        0                           ⅈ⋅g_{2}__{(t)}⋅ℯ                         0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                  2            2                                              \n",
       "             g_{2}        g_{1}                                               \n",
       "elta_{2} + ────────── + ──────────               0                           0\n",
       "           \\Delta_{2}   \\Delta_{1}                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "        0                                  \\delta\\omega₂                     0\n",
       "                                                                              \n",
       "        0                                        0               \\delta\\omega₂\n",
       "                                                                              \n",
       "                                                                              \n",
       "            ⅈ⋅\\phi_{2}                                                        \n",
       "{2}__{(t)}⋅ℯ                                     0                        ⅈ⋅\\k\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "            ⅈ⋅\\phi_{1}                                                        \n",
       "{1}__{(t)}⋅ℯ                                     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",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "        0                                        0                           0\n",
       "                                                                              \n",
       "        0                                        0                           0\n",
       "\n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                     -ⅈ⋅\\phi_{2}                              \n",
       "                     ⅈ⋅g_{2}__{(t)}⋅ℯ                                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       " - \\delta_{2}                 -ⅈ⋅\\kappa                                       \n",
       "                                                                              \n",
       "                                                   2                          \n",
       "                                              g_{1}                           \n",
       "appa           \\delta\\omega₂ - \\delta_{1} + ──────────                        \n",
       "                                            \\Delta_{1}                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                     \\delta\\omega₂ - \\delta\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                      ⅈ⋅\\phi_{1}                              \n",
       "                     -ⅈ⋅g_{1}__{(t)}⋅ℯ                                        \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                 -ⅈ⋅g_{1}__\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "                                                                              \n",
       "                                  0                                           \n",
       "\n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                -ⅈ⋅\\phi_{1}                   \n",
       "   0                            ⅈ⋅g_{1}__{(t)}⋅ℯ                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                     ⅈ⋅g_{1}__{(\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                           2                                                  \n",
       "                      g_{1}                                                   \n",
       "_{1} - \\delta_{2} + ──────────               0                                \n",
       "                    \\Delta_{1}                                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                   \\delta\\omega₁                          \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0               \\delta\\omega₁ - \\\n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                              ⅈ⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                     -ⅈ⋅g_{2}__{\n",
       "                                                                              \n",
       "       ⅈ⋅\\phi_{1}                                                             \n",
       "{(t)}⋅ℯ                                      0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "                                                                              \n",
       "   0                                         0                                \n",
       "\n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "     -ⅈ⋅\\phi_{1}                                                              \n",
       "t)}⋅ℯ                               0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                   2                                                          \n",
       "              g_{2}                                                           \n",
       "delta_{2} + ──────────          -ⅈ⋅\\kappa                                    0\n",
       "            \\Delta_{2}                                                        \n",
       "                                                                              \n",
       "\\kappa                  \\delta\\omega₁ - \\delta_{1}                           0\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0               \\delta\\omega₁ - \\delta_{1}\n",
       "                                                                              \n",
       "                                                                              \n",
       "      ⅈ⋅\\phi_{2}                                                              \n",
       "(t)}⋅ℯ                              0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                                        0\n",
       "                                                                              \n",
       "                                                                              \n",
       "  0                                 0                           -ⅈ⋅g_{2}__{(t)\n",
       "                                                                              \n",
       "  0                                 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",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                             -ⅈ⋅\\phi_{1}                      \n",
       "                             ⅈ⋅g_{1}__{(t)}⋅ℯ                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                       ⅈ⋅g_{1}__{(t\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                             -ⅈ⋅\\phi_{2}                      \n",
       "                             ⅈ⋅g_{2}__{(t)}⋅ℯ                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                       2                                                      \n",
       "                  g_{2}                                                       \n",
       " - \\delta_{2} + ──────────                0                                   \n",
       "                \\Delta_{2}                                                    \n",
       "                                                                              \n",
       "                                                                              \n",
       "                            \\delta\\omega₁ + \\delta\\omega₂                     \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                \\delta\\omega₁ + \\de\n",
       "                                                                              \n",
       "   ⅈ⋅\\phi_{2}                                                                 \n",
       "}⋅ℯ                                       0                                 ⅈ⋅\n",
       "                                                                              \n",
       "                                          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",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    -ⅈ⋅\\phi_{1}                                                               \n",
       ")}⋅ℯ                                         0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                -ⅈ⋅\\phi_{2}                   \n",
       " 0                              ⅈ⋅g_{2}__{(t)}⋅ℯ                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 0                                           0                                \n",
       "                                                                              \n",
       "                                                                              \n",
       "lta\\omega₂ - \\delta_{2}                  -ⅈ⋅\\kappa                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "\\kappa                   \\delta\\omega₁ + \\delta\\omega₂ - \\delta_{1}           \n",
       "                                                                              \n",
       " 0                                           0                       \\delta\\om\n",
       "\n",
       "                  0                           ⎤\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  0                           ⎥\n",
       "                                              ⎥\n",
       "ega₁ + \\delta\\omega₂ - \\delta_{1} - \\delta_{2}⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
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