{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimization of a dissipative state-to-state transfer in a Lambda system" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "attributes": { "classes": [], "id": "", "n": "1" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "matplotlib 3.0.2\n", "matplotlib.pylab 1.15.4\n", "krotov 0.1.0.post1+dev\n", "qutip 4.3.1\n", "scipy 1.2.0\n", "numpy 1.15.4\n", "CPython 3.6.8\n", "IPython 7.2.0\n" ] } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "%load_ext watermark\n", "import qutip\n", "import numpy as np\n", "import scipy\n", "import matplotlib\n", "import matplotlib.pylab as plt\n", "import krotov\n", "import qutip\n", "from qutip import Qobj\n", "import pickle\n", "%watermark -v --iversions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\newcommand{tr}[0]{\\operatorname{tr}}\n", "\\newcommand{diag}[0]{\\operatorname{diag}}\n", "\\newcommand{abs}[0]{\\operatorname{abs}}\n", "\\newcommand{pop}[0]{\\operatorname{pop}}\n", "\\newcommand{aux}[0]{\\text{aux}}\n", "\\newcommand{opt}[0]{\\text{opt}}\n", "\\newcommand{tgt}[0]{\\text{tgt}}\n", "\\newcommand{init}[0]{\\text{init}}\n", "\\newcommand{lab}[0]{\\text{lab}}\n", "\\newcommand{rwa}[0]{\\text{rwa}}\n", "\\newcommand{bra}[1]{\\langle#1\\vert}\n", "\\newcommand{ket}[1]{\\vert#1\\rangle}\n", "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n", "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n", "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2} \\mid\n", "#2\\vphantom{#1}\\right\\rangle}\n", "\\newcommand{Ketbra}[2]{\\left\\vert#1\\vphantom{#2}\n", "\\right\\rangle \\hspace{-0.2em} \\left\\langle #2\\vphantom{#1} \\right\\vert}\n", "\\newcommand{op}[1]{\\hat{#1}}\n", "\\newcommand{Op}[1]{\\hat{#1}}\n", "\\newcommand{dd}[0]{\\,\\text{d}}\n", "\\newcommand{Liouville}[0]{\\mathcal{L}}\n", "\\newcommand{DynMap}[0]{\\mathcal{E}}\n", "\\newcommand{identity}[0]{\\mathbf{1}}\n", "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n", "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n", "\\newcommand{avg}[1]{\\langle#1\\rangle}\n", "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n", "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n", "\\newcommand{Re}[0]{\\operatorname{Re}}\n", "\\newcommand{Im}[0]{\\operatorname{Im}}\n", "\\newcommand{toP}[0]{\\omega_{12}}\n", "\\newcommand{toS}[0]{\\omega_{23}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The aim of this example is to test the\n", "behaviour of Krotov's algorithm when\n", "dealing with non-Hermitian Hamiltonians.\n", "This notebook is heavily based on the\n", "example \"Optimization of a state-to-state\n", "transfer in a lambda system with RWA\",\n", "and therefore it is recommended that the\n", "reader become familiar with the system\n", "before hand. The main change in the\n", "results will be represented by the loss of\n", "norm during the propagation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start with the usual 3-level lambda system such that\n", "$E_1 < E_2$ and $E_3 <\n", "E_2$. The states $\\Ket{1}$ and $\\Ket{2}$ are coupled\n", "coupled through a pump\n", "laser with frequency $\\omega_{P}=\\omega_{P}(t)$ and\n", "similarly for the states\n", "$\\Ket{2}$ and $\\Ket{3}$ through a Stokes laser with\n", "frequency\n", "$\\omega_{S}=\\omega_{S}(t)$.\n", "\n", "The level $\\Ket{2}$ is assumed to\n", "experience a\n", "spontaneous decay into a reservoir that is out of the Hilbert\n", "space. This can be\n", "reproduced with a simple model that adds a dissipative\n", "coefficient $\\gamma > 0$,\n", "such that the original eigenvalue for the second level\n", "is modified into $E_2\n", "\\rightarrow E_2 - i \\gamma$.\n", "\n", "We perform the same\n", "rotating wave approximation as\n", "described in the aforementioned example and\n", "obtain the time independent\n", "Hamiltonian\n", "\n", "\\begin{equation}\n", " \\op{H}_{0} =\n", " \\Delta_{P}\\Ketbra{1}{1} -i\n", "\\gamma \\Ketbra{2}{2} +\\Delta_{S} \\Ketbra{3}{3}\n", "\\end{equation}\n", "\n", "with the\n", "detunings $\\Delta_{P}=E_{1} + \\omega_{P} - E_{2}$ and\n", "$\\Delta_{S} = E_{3} +\n", "\\omega_{S} -E_{2}$.\n", "\n", "The control Hamiltonian is again given by\n", "\n", "\\begin{equation}\n", "\\op{H}_{1}(t)\n", " = \\op{H}_{1,P}(t) + \\op{H}_{1,S}(t)\n", " = \\Omega_{P}(t)\n", "\\Ketbra{1}{2} +\n", " \\Omega_{S}(t)\\Ketbra{2}{3} + \\text{H.c.}\\,,\n", "\\end{equation}\n", "where $\\Omega_{P} = \\Omega_{P}(t) = \\frac{\\mu_{21} \\varepsilon_{P}(t)}{2}\n", "e^{-i\\Phi_{S}(t) t}$\n", "and $\\Omega_{S} = \\Omega_{S}(t) = \\frac{\\mu_{23}\n", "\\varepsilon_{S}(t)}{2} e^{-i\\Phi_{P}(t) t}$\n", "with the phases $\\Phi_{P}(t) = \\toP\n", "- \\omega_{P}(t)$ and\n", "$\\Phi_{S}(t) = \\toS - \\omega_{S}(t)$ and $\\mu_{ij}$ the\n", "$ij^{\\text{th}}$ dipole-transition moment.\n", "\n", "For optimizing the complex pulses we\n", "once again\n", "separate them into their real and imaginary parts, i.e.,\n", "$\\Omega_{P}(t) = \\Omega_{P}^\\text{Re}(t) + i\\Omega_{P}^\\text{Im}(t)$\n", "and\n", "$\\Omega_{S}(t) = \\Omega_{S}^\\text{Re}(t) + i\\Omega_{S}^\\text{Im}(t)$,\n", "so we can\n", "optimize four real pulses." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "attributes": { "classes": [], "id": "", "n": "2" } }, "outputs": [], "source": [ "def ham_and_states():\n", " \"\"\"Lambda-system Hamiltonian\"\"\"\n", " E1 = 0.0\n", " E2 = 10.0\n", " E3 = 5.0\n", " ω_P = 9.5\n", " ω_S = 4.5\n", " gamma = 0.5\n", " Ω_init = 5.0\n", " H0 = Qobj(\n", " [\n", " [E1 + ω_P - E2, 0.0, 0.0],\n", " [0.0, -gamma * 1.0j, 0.0],\n", " [0.0, 0.0, E3 + ω_S - E2],\n", " ]\n", " )\n", "\n", " H1P_re = Qobj([[0.0, -1.0, 0.0], [-1.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n", " H1P_im = Qobj([[0.0, -1.0j, 0.0], [1.0j, 0.0, 0.0], [0.0, 0.0, 0.0]])\n", " ΩP_re = lambda t, args: Ω_init\n", " ΩP_im = lambda t, args: Ω_init\n", "\n", " H1S_re = Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]])\n", " H1S_im = Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0j], [0.0, -1.0j, 0.0]])\n", " ΩS_re = lambda t, args: Ω_init\n", " ΩS_im = lambda t, args: Ω_init\n", "\n", " \"\"\"Initial and target states\"\"\"\n", " psi0 = qutip.Qobj(np.array([1.0, 0.0, 0.0]))\n", " psi1 = qutip.Qobj(np.array([0.0, 0.0, 1.0]))\n", "\n", " return (\n", " [\n", " H0,\n", " [H1P_re, ΩP_re],\n", " [H1P_im, ΩP_im],\n", " [H1S_re, ΩS_re],\n", " [H1S_im, ΩS_im],\n", " ],\n", " psi0,\n", " psi1,\n", " )\n", "\n", "\n", "H, psi0, psi1 = ham_and_states()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check whether our Hamiltonians are Hermitian:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "attributes": { "classes": [], "id": "", "n": "3" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "H0 is Hermitian: False\n", "H1 is Hermitian: True\n" ] } ], "source": [ "print(\"H0 is Hermitian: \" + str(H[0].isherm))\n", "print(\"H1 is Hermitian: \"+ str(\n", " H[1][0].isherm\n", " and H[2][0].isherm\n", " and H[3][0].isherm\n", " and H[4][0].isherm))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduce projectors for each of the three energy levels\n", "$\\op{P}_{i} =\n", "\\Ketbra{i}{i}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "attributes": { "classes": [], "id": "", "n": "4" } }, "outputs": [], "source": [ "proj1 = Qobj([[1.,0.,0.],[0.,0.,0.],[0.,0.,0.]])\n", "proj2 = Qobj([[0.,0.,0.],[0.,1.,0.],[0.,0.,0.]])\n", "proj3 = Qobj([[0.,0.,0.],[0.,0.,0.],[0.,0.,1.]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the optimization target\n", "\n", "It is necessary to create a time grid to work\n", "with. In this example we choose a time interval starting at $t_0 = 0$ and ending\n", "at $t_f = 5$ with $n_t = 500$ equidistant time steps." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "attributes": { "classes": [], "id": "", "n": "5" } }, "outputs": [], "source": [ "t0 = 0.\n", "tf = 5.\n", "nt = 500\n", "tlist = np.linspace(t0, tf, nt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the objective to be a state to state transfer from the initial state\n", "$\\Ket{\\Psi_{\\init}} = \\Ket{1}$ into the final state $\\Ket{\\Psi_{\\tgt}} =\n", "\\Ket{3}$ at the\n", "final time $t_{f}$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "attributes": { "classes": [], "id": "", "n": "6" } }, "outputs": [], "source": [ "objectives = [ krotov.Objective(initial_state=psi0, target=psi1, H=H) ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial guess shapes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"stimulated Raman adiabatic passage\" (STIRAP) is a\n", "process in which population in $\\Ket{1}$ is transferred into\n", "$\\Ket{3}$ without\n", "having to pass through $\\Ket{2}$ (which could for instance be a rapidly decaying\n", "level).\n", "In order for this process to occur, a temporally finite Stokes pulse of\n", "sufficient amplitude driving the $\\Ket{2} \\leftrightarrow \\Ket{3}$ transition is\n", "applied first, whilst second pump pulse of similar intensity follows some time\n", "later such that the pulses still have a partial temporal overlap.\n", "\n", "In order to\n", "demonstrate the Krotov's optimization method however, we choose an initial guess\n", "consisting of two low intensity and real Blackman pulses which are temporally\n", "disjoint.\n", "\n", "For the real components of the matrix elements, we supply our guess\n", "pulses shaped as Blackman window functions `S(t,offset)`, with an offset\n", "ensuring that the two pulses don't overlap.\n", "The imaginary components are coupled\n", "to pulses that are zero at all times." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "attributes": { "classes": [], "id": "", "n": "7" } }, "outputs": [], "source": [ "def S(t,offset):\n", " \"\"\"Shape envelope function for the field update\"\"\"\n", " return krotov.shapes.blackman(t,1.+offset,4.+offset)\n", "\n", "def shape_field_real(eps,offset):\n", " \"\"\"Applies the total pulse shape to the real part of a guess pulse\"\"\"\n", " field_shaped = lambda t, args: eps(t, args)*S(t,offset)\n", " return field_shaped\n", "\n", "def shape_field_imag(eps,offset):\n", " \"\"\"Initializes the imaginary parts of the guess pulses to zero\"\"\"\n", " field_shaped = lambda t, args: eps(t, args)*0.\n", " return field_shaped\n", "\n", "H[1][1] = shape_field_real(H[1][1],1.)\n", "H[2][1] = shape_field_imag(H[2][1],1.)\n", "H[3][1] = shape_field_real(H[3][1],-1.)\n", "H[4][1] = shape_field_imag(H[4][1],-1.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose an appropriate update factor $\\lambda_{a}$ for the problem at hand and\n", "make sure Krotov considers pulses which start and end with zero amplitude." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "attributes": { "classes": [], "id": "", "n": "8" } }, "outputs": [], "source": [ "def update_shape(t):\n", " \"\"\"Scales the Krotov methods update of the pulse value at the time t\"\"\"\n", " return krotov.shapes.flattop(t,0.,5.,0.3,func='sinsq')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "opt_lambda = 2.0\n", "pulse_options = {\n", " H[1][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n", " H[2][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n", " H[3][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n", " H[4][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible to keep track of the fidelity during optimization by printing it\n", "after every iteration:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "attributes": { "classes": [], "id": "", "n": "10" } }, "outputs": [], "source": [ "def print_fidelity(**args):\n", " F_re = np.average(np.array(args['tau_vals']).real)\n", " print(\" F = %f\" % F_re)\n", " return F_re" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate dynamics of the guess field" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "attributes": { "classes": [], "id": "", "n": "11" } }, "outputs": [], "source": [ "def plot_pulse(pulse, tlist, plottitle=None):\n", " fig, ax = plt.subplots()\n", " if callable(pulse):\n", " pulse = np.array([pulse(t, args=None) for t in tlist])\n", " ax.plot(tlist, pulse)\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('pulse amplitude')\n", " if(isinstance(plottitle, str)):\n", " ax.set_title(plottitle, fontsize = 15)\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "attributes": { "classes": [], "id": "", "n": "12" } }, "outputs": [ { "data": { "image/png": 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\n", 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4ZjbJzF4xs23x+zPM7OvBR5NEuDsrS6uYNz6v1y2H3J75xfmcPd/EtqPVYUcRSQmJjPB/BHwNaARw9y3E9qiVHuBgVS1lp+tYMKH3z7+/0Lz4NQWtK4CKSNckUvD7ufuaCx5rCiKMdFxr/35eCvXvW+X3z2bK0FxWxT+jiHRNIgW/0syKAQcwsz8HjgWaShK2orSSogHZFBfkhB0lEPOK81h74CTnm5rDjiLS6yVS8D8P/BCYYmZlwIPAXweaShLS0uKsKq1iQXE+ZqnVv2+1oDif800tbDio5ZJFuqrdVbbcfR9wo5nlAGnufjb4WJKIXcfPcrKmISWWU7iUueOHkGaxdXXmpcA6QSJhumTBN7MvXuJxANz9uwFlkgStjC8uloonbFsN6JPJlSMHsbK0iov+gRSRhF2upZMbv80m1sIZEb99Frg6+GjSnhUllYzPz2HYwL5hRwnUguI8Nh0+Tc15zRUQ6YpLFnx3/6a7fxMYCVzt7l9y9y8B1wCjkxVQLq6xuYU1+08yP4VH963mF+fT1OKsOXAy7CgivVoiJ22LgIY29xvij0mINh8+TU1Dc0otp3Ap14wZTFZ6mqZninRRIlsj/QJYY2ZPxe/fBfw8uEiSiBUlVZjBdeNTf4TfNyudWaMH6QIskS5qd4Tv7t8C7gVOxW/3uvu3gw4ml7eitJKpwwYwOCcr7ChJsWBCPjuOVXOqpqH9J4vIRSWyls5ooBJ4Kn6rij8mIalraGbjoVMptRxye+YX5+EOb+xXW0eksxJp6TxP/CpboC8wDtgNTAsqlFze2gMnaWz2lNi/NlEzRg6iX1Y6K0uruHX6sLDjiPRKiVx4dWXb+2Z2NfC5wBJJu1aUVpKZbswdNyTsKEmTlZHG3HFD1McX6YIOr4fv7huAa9t7npn1MbM1ZrbZzLab2Tc7lVDeYWVJFbNGDaZfViK/oKWO+cV5lFbUcKK6PuwoIr1SuxXjgitu04hddHU0gfc+Dyx293NmlgksN7M/uPvqzkUVgNO1DWw7eoYH3jMx7ChJNz8+BXVVaRV3zRoRchqR3ieREX5um1s2sZ7+ne29yGPOxe9mxm9+mZdIAlbvq8KdSJ2wbTV12AAG9s1UW0ekkxLpCexw9yfaPmBmdwNPXOL5bZ+XDqwHJgD/4e5vXOQ59wP3A4werck/7VlRUkW/rHRmjhwUdpSkS0sz5o3PY2VpFe6esiuEigQlkRH+1xJ87B3cvdndryK2PMNcM5t+kec87O6z3X12QUFBIm8baStKK5k7bghZGdHcjnj+hDzKTtdx+GRd2FFEep3LrZZ5G3A7MMLMvt/mRwPo4I5X7n7azJYAtwLbOhNU4PiZevZV1HDPnFFhRwlN61TUFaWVjM7Tb4QiHXG5YeJRYB1QT6wt03p7BrilvTc2swIzGxT/vi9wE7Crq4GjrLV3PT8C6+dcSnFBfwpzs9/c2lFEEnfJEb67bwY2m9l/u3tn1qUdBvw83sdPAx539+c6mVOIjWoH98tk6rABYUcJjZkxvziP5SWV6uOLdNDlWjqPu/uHgI1m9o7ZNe4+43Jv7O5bgFldjygA7rHtDOcV55GWFu0iN784n99vOsre8nNMKsoNO45Ir3G5WToPxL/ekYwgcnn7K2s4dqaez0e4ndOqdavDlSWVKvgiHXC5DVCOxb8evNgteREFYEW8Zx3F+fcXGjWkH6OH9Hvzv4mIJOZyLZ2zvP1CKYvfN2LXVUW3kRyClSWVDB/Yh7F5/cKO0iPML87j+a3HaG5x0iPe4hJJ1OVG+LnuPqDNLbft12SGjLqWFmfVvirmT8jXScq4ecV5nK1vYvvRM2FHEek1Elp9K75C5kJiI/zl7r4x0FTyNjuOVXO6tpEFEdi/NlFv9vFLq5gRwauORTojkQ1Q/p7YloZ5QD7wMzP7etDB5C2af/9Ohbl9mFjYX/PxRTogkRH+x4CZ7l4PYGbfATYB/xhkMHnLitIqigtyKBrQJ+woPcqCCfn8Zu1hGppaIrvUhEhHJPK35CjQttJkA2XBxJELNTS1sHb/Sc3OuYh5xXnUNTaz6fDpsKOI9AqJFPwzwHYz+5mZ/ZTYWjinzez7F6yxIwHYeOgUdY3NaudcxHXj8jCDlaVaLlkkEYm0dFo3L2/1WjBR5GJWllaRZjBvvE7YXmhgv0ymDx/IytIqHrwx7DQiPV8ie9r+PBlB5OJWllYyfcRABvbLDDtKjzS/OI+frNhPXUMzfbPSw44j0qMlMkvnDjPbaGYnzazazM6aWXUywkVdzfkmNh46rXbOZcyfkE9js7P2wMmwo4j0eIn08P8N+CSQpwuvkmvNgZM0tbjm31/GnLGDyUgzTc8USUAiBf8wsM3dtR9tkq0sqSQrPY3ZY4aEHaXH6peVwazRg1ilE7ci7UrkpO1XgBfMbClwvvVBd/9uYKkEiO1fO2v0IPWm2zGvOJ+HXt3LmbpGBvbVuQ6RS0lkhP8toJbYXPzcNjcJ0MmaBnYcq9b8+wTML86jxWHNfvXxRS4nkRH+cHd/x+bjEqxVby6HrP59e2aNHkSfzDRWlFRy09SisOOI9FiJjPBfMLObA08ib7O8pJL+2RnM1MJg7crOSGfO2CFv/iMpIheXSMH/a+CPZlanaZnJs6KkkuvG55GRrjViEjGvOI/dJ85ScfZ8+08Wiah2q0l8Gmaau/fVtMzkOFRVy6GTtSxUOydhrdcqrN6nUb7IpSQ0fDSzwWY218xuaL0FHSzKVsSnGC6cqBO2iZo+fAC5fTI0H1/kMto9aWtmnya2oflIYssiXwesAhYHGy26lpdUUjQgm+KC/mFH6TUy0tO4dlyeFlITuYxERvgPAHOAg+6+CJgFaD3agLS0OCtLKlk4oUDbGXbQ/OI8DlbVcuRUbdhRRHqkRAp+fZvNT7LdfRcwOdhY0bXjWDWnahtZOFH9+46aHz/nodk6IheXSME/YmaDgN8DL5nZ08DBYGNF1/L4doYLtGBah00qzCUvJ0t9fJFLSGR55A/Ev/2GmS0BBgJ/DDRVhK0oqWRSUX8KtZ1hh6WlGQsm5PP63krcXS0xkQt0aJK3uy9192fcvSGoQFFW39jMGm1n2CXXT8yn8tx5dh0/G3YUkR5HV/X0IBsOnuJ8UwvXazpmp10/sQCAZXsqQk4i0vOo4Pcgy0sqyUgz5o7TCdvOGjqwD5OLcnl9r6Znilwo0QuvxpjZjfHv+5qZVssMwIqSSmaNHkT/7ETWtJNLuX5iPmsOnKSuoTnsKCI9SiJbHP4V8Fvgh/GHRhKbsdPe60aZ2RIz22Fm283sga5FTW2naxvYUnZG/ftucP2kAhqaWlijbQ9F3iaREf7ngQVANYC77wUKE3hdE/Ald59K7Orcz5vZ1M4GTXWrSqtwh4Uq+F02d+wQsjLS1McXuUAiBf9821k5ZpYBtLvdobsfc/cN8e/PAjuBEZ0Nmupeb10OeZSWQ+6qvlnpXDtuCK/vVcEXaSuRgr/UzP430NfMbgKeAJ7tyEHMbCyxJRne6GjAKHB3lu6uYH5xHplaDrlbXD8xnz0nznH8TH3YUUR6jESqy1eBCmAr8BngBeDriR7AzPoDvwMedPd3rKNvZveb2TozW1dREc0RWWnFOcpO1/HuyYl0yiQRrdMzNcoXeUsi6+G3uPuP3P1u4H7gDXdvt6UDYGaZxIr9f7v7k5d4/4fdfba7zy4oKOhI9pTx2u5YUXrX5Gh+/iBMGZpLQW42yzQ9U+RNiczSec3MBpjZEGA98CMz+9cEXmfAI8BOd/9u16OmrqV7KphY2J8Rg/qGHSVlmBnXT8xn+d4KWloSGp+IpLxEWjoD462YDwK/cPdrgfck8LoFwF8Ai81sU/x2exeypqTahibe2HeSd03S6L673TCxgFO1jWw/qh05RSCBxdOADDMbBnwI+LtE39jdlwNavaodq/dV0dDconZOAFp3DFu2t4IrRw4MOY1I+BIZ4f8D8CJQ4u5rzWw8sDfYWNGxdHcFfTPTmTN2SNhRUk5+/2ymDR+g+fgicYmctH3C3We4++fi9/e5+58FHy0alu6pYF5xHn0y08OOkpKun1jA+oOnOFvfGHYUkdBdsqVjZv/OZS6wcve/DSRRhByorOFAVS1/uXBc2FFS1uIphfzX0lKW763ktiuHhR1HJFSX6+GvS1qKiFoabzXohG1wrh49iIF9M3llV7kKvkTeJQu+u/88mUGi6LXd5YzLz2FMXk7YUVJWRnoaN0wq4LXd5bS0OGlpmkcg0dXuLJ34tobvaO24++JAEkVEfWMzq/ZVcc+c0WFHSXnvmVLIs5uPsrXsjNYqkkhLZFrml9t83wf4M2IrYUoXvLH/JPWNmo6ZDO+aVECawSu7ylXwJdIS2cR8/QUPrTCzNQHliYyXd5ygb2Y688Zrd6ugDc7JYtbowSzZVc4Xb5oUdhyR0CSytMKQNrd8M7sF0FUsXeDuvLzzBDdMytd0zCRZPKWQrWVnKK/W6pkSXYlceLWe2Iyd9cAq4EvAfUGGSnXbj1Zz7Ew9N15RFHaUyFg8JbYSaetCdSJRlEhLR5PEu9nLO09g9lYRkuBNGZrLsIF9eGXXCT40Z1TYcURCkcgsnT7A54CFxGbrvA78l7vrd+NOennnCa4ZPZi8/tlhR4kMM2PRlEKe3ljG+aZmsjPUSpPoSaSl8wtgGvDvwEPx7x8NMlQqO3amjm1l1bxH7Zyku2lqETUNzawsqQo7ikgoEpmWOT2+EXmrJWa2I6hAqe7lneUA3DRV7Zxkm1+cR//sDF7cfpxFaqdJBCUywt9gZte13jGza9GyC532ys4TjM3rR3FB/7CjRE52RjqLphTy0o4TNGtTFImgRAr+NcBKMztgZgeIzdSZY2ZbzWxLoOlSTM35JlaWVHHjFUXENgSTZLtlWhFVNQ2sO3Ay7CgiSZdIS+fWwFNExNI9FTQ0t3DjVPXvw/LuyYVkZaTx4vYTXKuL3iRiElkP/+DlbskImSqe33qM/P5Z2uwkRP2zM1g4IZ8Xtx/HXW0diZZEWjrSDeoamnl1Zzm3TBtKulZsDNUt04ooO12nvW4lclTwk2TpnnLqGpu5XWuyh+7GK4pIM/jT9uNhRxFJKhX8JHl+63GG5GRx7Ti1c8KW1z+bOWOH8OL2E2FHEUkqFfwkqG9s5tWdJ7hlWhEZ6fpP3hPcOn0ou0+cpaT8XNhRRJJG1ScJlu6poKZB7Zye5PYrh2EGz24+GnYUkaRRwU+CP2w9xqB+mVynaYA9RtGAPlw3Lo9ntxzVbB2JDBX8gNU3NvPyznJunlpEpto5Pcr7Zg5nX0WNZutIZKgCBWzZngrOnW/iNrVzepzbpg8lI83U1pHIUMEP2NObjjIkJ4uFE/LDjiIXGJyTxQ2TCnh281FatLaORIAKfoCq6xt5aecJ3jdjmNo5PdT7Zg7j6Jl6Nhw6FXYUkcCpCgXoj1uP09DUwl2zRoQdRS7hpqlDyc5I4xm1dSQCVPAD9OTGI4zLz+GqUYPCjiKX0D87gxuvKOL5Lcdoam4JO45IoFTwA1J2uo7V+05y11UjtBRyD3fnVcOpqmlg2V5tcC6pLbCCb2Y/MbNyM9sW1DF6smc2xVoEd80aHnISac+iKYXk5WTx+NojYUcRCVSQI/yfEdG19N2d3204wtWjBzEmLyfsONKOzPQ0PjBrBK/sOkHVufNhxxEJTGAF392XAZHcVmj9wVOUlJ/jw3NGhR1FEnT37FE0Nju/36STt5K6Qu/hm9n9ZrbOzNZVVKRGD/WxtYfJyUrnjhlq5/QWk4fmMnPkQJ5Yd1hLLUjKCr3gu/vD7j7b3WcXFBSEHafLqusbeW7LUd5/1XByshPZQVJ6irtnj2LX8bNsK9NSC5KaQi/4qebpTUepb2zhnjmjw44iHfS+mcPJzkjj12sPhR1FJBAq+N3sN2sPccWwAcwYOTDsKNJBA/tm8r6Zw/n9xjKq6xvDjiPS7YKclvlrYBUw2cyOmNl9QR2rp9hy5DTbyqq5Z84ozb3vpT4xbwy1Dc38br2maErqCXKWzkfcfZi7Z7r7SHd/JKhj9RQ/XXGAnKx0PnC1llLorWaMHMTMUYN4dPVBnbyVlKOWTjcpr67nuS1HuXv2KAb0yQyPEm+JAAALCklEQVQ7jnTBJ+eNYV9FDStKqsKOItKtVPC7yS/fOERTi/Op+WPDjiJddPuVwxiSk8UvVh0IO4pIt1LB7wbnm5r51RsHWTy5kLH5urK2t+uTmc49c0bx8s4THKisCTuOSLdRwe8Gz24+RuW5Bu5dMC7sKNJNPjV/LBlpafzo9X1hRxHpNir4XdTS4jy8rJTJRbksmKBNylNF4YA+fPDqETyx/ggVZ7W+jqQGFfwu+tOOE+w5cY7PLSrWVMwUc/8N42lsbuFnK/eHHUWkW6jgd4G789CSvYzN68d7tUl5yhlf0J9bpg7l0VUHOXe+Kew4Il2mgt8Fr+2pYFtZNZ979wQytGdtSvrsu4uprm/i0VUHw44i0mWqUp3k7jz0agkjBvXVnrUp7KpRg3j35AL+a2mplluQXk8Fv5Ne21PB+oOn+Oy7xpOVof+MqezLN0/mTF0jP16mGTvSu6lSdUJzi/NPf9jFmLx+fFirYqa86SMGcvuVQ3lk+X7tiCW9mgp+Jzy54Qi7jp/lf94yWaP7iPjiTZOoa2zmB6+Vhh1FpNNUrTqovrGZ7760h5kjB2pmToRMKMzlz64eyaOrDrJfV99KL6WC30GPLN/PsTP1fPW2KzTvPmJaf6P7h2e3hx1FpFNU8Dvg8Mla/v3Vvdw6bSjzinVVbdQUDujDgzdOZMnuCl7ZeSLsOCIdpoKfIHfn/3l6G+lm/J/3Tw07joTkk/PHMqGwP998dgf1jc1hxxHpEBX8BL2w9Tiv7a7gSzdPZtjAvmHHkZBkpqfxzfdP49DJWr73yt6w44h0iAp+Ak7VNPCNZ7czfcQAPqn17iNvwYR8Pjx7FD9cWsr6g6fCjiOSMBX8drg7X3tyK6drG/inP5tBeppO1Ap8/Y4rGDawL19+YjN1DWrtSO+ggt+O364/wh+3H+fLN09m2vCBYceRHiK3Tyb//Ocz2F9Zw7df2Bl2HJGEqOBfxq7j1fz909u5bvwQPn39+LDjSA8zf0I+9y0cx6OrD/L7jWVhxxFplwr+JZypa+Qzj64nt08G379nllo5clFfvW0Kc8cO4atPbmHH0eqw44hclgr+RTQ2t/A3v9pA2ak6/vPjV1M4oE/YkaSHykxP46GPzWJg30w+88t1nKxpCDuSyCWp4F/A3flfv9vC63sr+fYHruSaMUPCjiQ9XGFuH/7z49dQXn2ee3+6hhptliI9lAp+G+7O/31uJ09uKOOLN03iQ3NGhR1JeomrRw/moY9ezbaj1Xz2l+t1UZb0SCr4ce7ON5/dwU9W7OfeBWP5wuIJYUeSXuamqUV854NXsrykkvt+vpbaBo30pWdRwQfONzXzxcc387OVB7hv4Tj+/o6pWhhNOuXu2aP4/+6eyarSKj724zeo1Pr50oNEvuCXn63nL368hqc2lvHlmyfx9fdqFUzpmg9ePZIffOxqdhyt5s6HVmj2jvQYkS74r++t4Pbvvc6WstN8756r+JvFE1XspVvcOn0Yj39mHo3NLdz1gxX8+PV9tLR42LEk4iJZ8E/VNPDlJzbzF4+sYXC/LJ75m4XceZU2IpfuNXPUIF544HpumJjPPz6/k48/8gZ7T5wNO5ZEmLkHN+ows1uB7wHpwI/d/TuXe/7s2bN93bp1geWprm/kJ8v388jr+6lrbOb+G8bzhcUT6ZuVHtgxRdydx9Ye5tsv7KTmfBP3zB3N3y6eyNCBur5Dus7M1rv77ISeG1TBN7N0YA9wE3AEWAt8xN13XOo1QRX8bWVneGLdYZ7aWEZ1fRO3TCviSzdPZlJRbrcfS+RSTtY08P1X9vLL1QcBuGX6UD5+7RjmjhuiK7ml0zpS8DMCzDEXKHH3ffFQjwF3Apcs+N3hfFMzB6tq2XPiLKv3VbF8byUHqmrJykjjlmlD+cwN45k+QougSfINycniG++fxn0Lx/GLVQf4zdrDPL/lGIP7ZbJoSiFzxg5h2vABTCzM1W+dEoggC/4I4HCb+0eAa4M40Hu//zqnaxupaWiiuq6R1nNjOVnpXDc+j/sWjuN9M4czqF9WEIcX6ZBRQ/rxd++dyv+4aRKv7irn5R0neGVnOU9ueGsBtpysdIb0zyIzLQ3ig38DzAz9LpB6BvfL4vHPzgv8OEEW/ISY2f3A/QCjR4/u1HtMKsrFDPpnZzCoXxbFBTkUF/Rn8tBcMtMjeV5aeoF+WRncMWM4d8wYTkuLc/hULdvKqjlQVUPlufOcqmmgqcV5s+nq0OaepJABfTKTcpwgC34Z0HZtgpHxx97G3R8GHoZYD78zB/rXD1/VmZeJ9BhpacaYvBzG5OWEHUVSWJDD37XARDMbZ2ZZwD3AMwEeT0RELiOwEb67N5nZ3wAvEpuW+RN33x7U8URE5PIC7eG7+wvAC0EeQ0REEqMzmiIiEaGCLyISESr4IiIRoYIvIhIRKvgiIhER6GqZHWVmFcDBTr48H6jsxji9gT5z6ova5wV95o4a4+4FiTyxRxX8rjCzdYmuGJcq9JlTX9Q+L+gzB0ktHRGRiFDBFxGJiFQq+A+HHSAE+sypL2qfF/SZA5MyPXwREbm8VBrhi4jIZfT6gm9mt5rZbjMrMbOvhp0nGczsJ2ZWbmbbws6SDGY2ysyWmNkOM9tuZg+EnSloZtbHzNaY2eb4Z/5m2JmSxczSzWyjmT0XdpZkMLMDZrbVzDaZWfdv6t32WL25pdOZjdJTgZndAJwDfuHu08POEzQzGwYMc/cNZpYLrAfuSuX/z2ZmQI67nzOzTGA58IC7rw45WuDM7IvAbGCAu98Rdp6gmdkBYLa7B37tQW8f4b+5Ubq7NwCtG6WnNHdfBpwMO0eyuPsxd98Q//4ssJPYnskpy2POxe9mxm+9d3SWIDMbCbwX+HHYWVJRby/4F9soPaULQdSZ2VhgFvBGuEmCF29tbALKgZfcPeU/M/BvwFeAlrCDJJEDfzKz9fE9vgPT2wu+RIiZ9Qd+Bzzo7tVh5wmauze7+1XE9oOea2Yp3b4zszuAcndfH3aWJFvo7lcDtwGfj7dsA9HbC35CG6VL7xfvY/8O+G93fzLsPMnk7qeBJcCtYWcJ2ALg/fGe9mPAYjP7ZbiRgufuZfGv5cBTxFrVgejtBV8bpUdA/ATmI8BOd/9u2HmSwcwKzGxQ/Pu+xCYm7Ao3VbDc/WvuPtLdxxL7u/yqu3885FiBMrOc+EQEzCwHuBkIbPZdry747t4EtG6UvhN4PAobpZvZr4FVwGQzO2Jm94WdKWALgL8gNuLbFL/dHnaogA0DlpjZFmIDm5fcPRLTFCOmCFhuZpuBNcDz7v7HoA7Wq6dliohI4nr1CF9ERBKngi8iEhEq+CIiEaGCLyISESr4IiIRoYIvkWVmg8zsc/Hvh5vZb8POJBIkTcuUyIqvy/NcFFYcFQHICDuASIi+AxTHFyjbC1zh7tPN7FPAXUAOMBH4FyCL2MVf54Hb3f2kmRUD/wEUALXAX7l7Sl8NK72bWjoSZV8FSuMLlP3PC342HfggMAf4FlDr7rOIXeH8ifhzHga+4O7XAF8GfpCU1CKdpBG+yMUtia+9f9bMzgDPxh/fCsyIr9w5H3gittQPANnJjymSOBV8kYs73+b7ljb3W4j9vUkDTsd/OxDpFdTSkSg7C+R25oXx9fj3m9ndEFvR08xmdmc4ke6mgi+R5e5VwIr4ZvD/3Im3+BhwX3ylw+1EYHtN6d00LVNEJCI0whcRiQgVfBGRiFDBFxGJCBV8EZGIUMEXEYkIFXwRkYhQwRcRiQgVfBGRiPj/ARAgAFNnwfXDAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_pulse(H[1][1], tlist, plottitle='Re($\\Omega_P$)')\n", "plot_pulse(H[2][1], tlist, plottitle='Im($\\Omega_P$)')\n", "plot_pulse(H[3][1], tlist, plottitle='Re($\\Omega_S$)')\n", "plot_pulse(H[4][1], tlist, plottitle='Im($\\Omega_S$)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After assuring ourselves that our guess pulses appear as expected, we propagate\n", "the system using our guess. Since the pulses are temporally disjoint, we expect\n", "the first pulse to have no effect, whilst the second merely transfers population\n", "out of $\\Ket{1}$ into $\\Ket{2}$ and back again." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "attributes": { "classes": [], "id": "", "n": "13" } }, "outputs": [], "source": [ "guess_dynamics = objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, e_ops=[proj1, proj2, proj3]\n", ")\n", "guess_states = objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm\n", ")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "attributes": { "classes": [], "id": "", "n": "14" } }, "outputs": [], "source": [ "def plot_population(result):\n", " fig, ax = plt.subplots()\n", " ax.axhline(y=1.0, color='black', lw=0.5, ls='dashed')\n", " ax.axhline(y=0.0, color='black', lw=0.5, ls='dashed')\n", " ax.plot(result.times, result.expect[0], label='1')\n", " ax.plot(result.times, result.expect[1], label='2')\n", " ax.plot(result.times, result.expect[2], label='3')\n", " ax.legend()\n", " ax.set_title('Expected values', fontsize = 15)\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('population')\n", " plt.show(fig)\n", " \n", "def plot_norm(result):\n", " \n", " state_norm = lambda i: result.states[i].norm()\n", " states_norm=np.vectorize(state_norm)\n", " \n", " fig, ax = plt.subplots()\n", " ax.plot(result.times, states_norm(np.arange(len(result.states))))\n", " ax.set_title('Norm loss', fontsize = 15)\n", " ax.set_xlabel('time')\n", " ax.set_ylabel('state norm')\n", " plt.show(fig) " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "attributes": { "classes": [], "id": "", "n": "15" } }, "outputs": [ { "data": { "image/png": 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\n", 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+Ku0JbjNL2ZCaSo4+fBgLPG9hB+CwMDPmTBnJ06v9nCjrnsPCzDh5cmZ9i8Wrfb+Fdc1hYWbMmpxZl3tBs68jsa45LMyMYQMqmTl2qG/Os245LMwMyAxFLXplM3vbPG9hb+awMDMATp4ykr1tHSxdszXtUqwfcliYGQCzJ40E8CW01iWHhZkBMGJQFdMPG8ITnuS2LjgszOwNc6Zk5i1a2zvSLsX6mR7DInkQ4Nck3SVpfuerL4ozs7518uSR7G5t97yFvUkuz4b6b+D7wN2A/9wwK2KzJ2fmLZ5o3shJE72Ssf1BLmGxJyL+Je+VmFnqRg2u5sgxg1nw0iY++Y60q7H+JJew+IakG4B7gb2djRHxVN6qMrPUnDx5FHc9tYbW9g4qyz2taRm5hMWxwEeAs/nDMFQkn82syMyZMop/e+IVnl27lRMneCjKMnIJiw8AUyJiX76LMbP0dc5bLHhpk8PC3pDLOeazwPB8F2Jm/UPdkGqm1g3yzXn2R3I5sxgOPC9pIX88Z3Fx97uYWSGbM2UUP1+8jrb2Dio8b2HkFhY35L0KM+tXTp1ay08WrGLJmi2cNHFk2uVYP3DAsJBUDnwuInwRnVkJOf2IWsoED6/c4LAwoIc5i4hoBzokDTuYg0s6X9IKSU2Sruti+wRJD0p6WtJSSRcm7ZMk7Za0OHl952B+vpkdnGEDKzmhfjgPr2xJuxTrJ3IZhtoBPCPpPmBnZ2NE/M8D7ZScldwMnAOsARZKmh8Ry7O6/QNwR0T8q6SZwK+AScm2FyPihJy/iZkdUmccWcc37n+BzTv3MWJQVdrlWMpymbm6C/gM8AiwKOvVk9lAU0Q0J5fd3g5csl+fAIYm74cB63Ip2szy78wj64iAR5s2pF2K9QM9nllExI8kVQFHJk0rIqI1h2OPA1ZnfV4DnLxfn88B90r6FDAIeGfWtsmSnga2Af8QEY/u/wMkXQ1cDTBhwoQcSjKzXB03fjjDB1byyMoWLj7+8LTLsZTl8tTZs4AXyAwpfRtYKemMQ/TzrwB+GBHjgQuBf5NUBrwKTIiIE4G/Af5D0tD9d46IeRHREBENdXV1h6gkMwMoLxOnH1HLQyta6OiItMuxlOUyDPVPwLkRcWZEnAGcB3w9h/3WAvVZn8cnbdk+AdwBEBGPAzVAbUTsjYiNSfsi4EX+cGZjZn3knJlj2LBjL0+v3px2KZayXMKiMiJWdH6IiJVAZQ77LQSmJethVAGXA/uvg7EKmAsgaQaZsGiRVJdMkCNpCjANaM7hZ5rZIfSO6aOpLBf3LHs97VIsZbmERaOk70k6K3l9F2jsaaeIaAOuAe4BniNz1dMySTdK6rz7+2+BqyQtAW4DPhYRAZwBLJW0GLgT+POI8FqPZn1saE0lp06t5TfPvkbmP00rVerp/wCSqoFPAqcnTY8C346Ivd3v1fcaGhqisbHHDDOzXrrtyVVcf9cz/PrTb2fG2DdNHVqBk7QoIhp66tfjmUUyf/C1iHhv8vp6fwsKM8ufd84YgwT3LHst7VIsRblcDXWapPskrZTU3Pnqi+LMLH11Q6qZNWkkdy9Z56GoEpbLnMX3ga+RGYaalfUysxLx3hPH8WLLTpau2Zp2KZaSXMJia0T8OiLWR8TGzlfeKzOzfuPC48ZSVVHGXU+tSbsUS0kuYfGgpH+UdIqkt3W+8l6ZmfUbQ2sqOXfmGH6+ZB17WtvTLsdSkMuDBDsf0ZE9W+41uM1KzIfnTOQXS1/l54vX8sFZfrxOqcnl2VBey8LMOHnySKYfNoQfPPYylzXUIyntkqwPeb1EM8uJJD5+2iSef207D3mdi5LjsDCznL3nxPGMHzGAr9270pfRlhiHhZnlrKqijE/PncYza7dy99JX0y7H+lAuN+UNlPSZ5JlQSJom6V35L83M+qP3nDiOY8cN48a7l7F55760y7E+ksuZxQ+AvcApyee1wBfzVpGZ9WsV5WX8v/cdx5ZdrVx75xLavdZFScglLKZGxFeBVoCI2AX4MgizEjbz8KF85l0z+e1z6/nsz591YJSAXO6z2CdpAJl7K5A0lcyZhpmVsCtPncS6rbu55eFmVm3axQ3vPpojRg9OuyzLk1zC4nPAb4B6ST8BTgM+ns+izKwwXH/BDCaOHMSXfrmcc77+MMeNG8aRY4YwZmgNQ2oqGFRdwZCaCqYfNpRpowdTVuZBiULV43oWAJJGAXPIDD89EREb8l1Yb3k9C7P0bNyxl/9YsIqHV7awevMuWrbvZf+RqYmjBnLV26fwodkTHBr9SK7rWeSy+NH9ETG3p7a0OSzM+o+OjmB3azs797axeVcri1dv5j8XruapVVuYPXkk8z5yEsMHVqVdpnEIFj+SVCNpJFAraYSkkclrEjDu0JVqZsWmrEwMqq5g9NAajjpsCB+cNYGf/cWpfPX9x7F49RY+eMsTvuy2wBzoaqg/AxYB05N/O18/B76V/9LMrJhI4rKGen7wsVm8tHEn19z2FG3tHWmXZTnqNiwi4hsRMRn4u4iYEhGTk9fxEeGwMLODctoRtXzx0mN4rGkjNz/4YtrlWI5yWYP7m5KOkXSZpI92vnI5uKTzJa2Q1CTpui62T5D0oKSnJS2VdGHWtuuT/VZIOq93X8vM+rPLGuq5+PjDufnBJprWb0+7HMtBLo/7uAH4ZvJ6B/BV4OIc9isHbgYuAGYCV0iauV+3fwDuiIgTgcuBbyf7zkw+Hw2cD3w7OZ6ZFYnPvnsmA6rKuWH+srRLsRzkcgf3+4G5wGsR8XHgeGBYDvvNBpoiojki9gG3A5fs1yeAocn7YcC65P0lwO0RsTciXgKakuOZWZGoHVzNp84+gseaNvJYU7+7Gt/2k0tY7I6IDqBN0lBgPVCfw37jgNVZn9fw5quoPgd8WNIa4FfAp3qxL5KultQoqbGlxc/XNys0H54zkcOH1XDTvSv8yPN+LpewaJQ0HPgumauhngIeP0Q//wrghxExHrgQ+DdJOT82PSLmRURDRDTU1dUdopLMrK/UVJbzF+84gqdXbWHhy5vTLscOIJcJ7r+MiC0R8R3gHODKZDiqJ2v54zOQ8Ulbtk8AdyQ/53GgBqjNcV8zKwLvf9t4Rgys5LuPNqddih1ALhPc93e+j4iXI2JpdtsBLASmSZosqYrMhPX8/fqsIjMfgqQZZMKiJel3uaRqSZOBacCTuXwhMyssA6rK+cicifz2uddZtXFX2uVYN/J2B3dEtAHXAPcAz5G56mmZpBsldV5N9bfAVZKWALcBH4uMZWTOOJaTeYjhJyOi/eC/ppn1Z1ecPAEBP120use+lo5unw0l6dPAXwGHkxkC6nzy1zbgu/3txjw/G8qssH3sB0/y/Kvbeey6syn3gwb7zFt+NpTv4DazvvTBhnpe27aHR1b6ysb+KJcrj16TNARA0j9IukvS2/Jcl5mVmLkzxjBqUBX/udBDUf1RLmHxmYjYLul04J3A94F/zW9ZZlZqqirKeM+J47j/+dfZuqs17XJsP7mERefE8kXAvIj4JeAH0ZvZIffu4w+ntT24Z9lraZdi+8klLNZKugX4IPArSdU57mdm1ivHjR/GhJEDuXvpup47W5/K5Zf+ZWQufz0vIrYAI4Fr81qVmZUkSVx03Fh+/+JGNnlxpH4llzu4d0XEXRHxQvL51Yi4N/+lmVkpuujYsbR3BL951kNR/YmHk8ysXzn68KFMrh3EL5/xUFR/4rAws35FEucdfRgLmjexdbeviuovHBZm1u+cM3MMbR3BQyvWp12KJRwWZtbvnFA/nNrBVdy3/PW0S7GEw8LM+p3yMjF3+hgeXtHCvraOtMsxHBZm1k+dM3MM2/e2seCljWmXYjgszKyfOu2IWmoqyzwU1U84LMysXxpQVc7bp9Xx2+Wve33ufsBhYWb91jkzxrBu6x6WrduWdiklz2FhZv3WO6aPRoIHnvcltGlzWJhZv1U3pJrjxw/nfodF6hwWZtavzZ0+miWrt9CyfW/apZS0vIaFpPMlrZDUJOm6LrZ/XdLi5LVS0pasbe1Z2+bns04z67/OnjEagAd9N3eqKvJ1YEnlwM3AOcAaYKGk+RGxvLNPRPx1Vv9PASdmHWJ3RJyQr/rMrDDMHDuUscNquP+517msoT7tckpWPs8sZgNNEdEcEfuA24FLDtD/CuC2PNZjZgVIEmdPH82jL2xgb1t7zztYXuQzLMYB2Suvr0na3kTSRGAy8EBWc42kRklPSLo0f2WaWX83d8Zodu1rZ0HzprRLKVn9ZYL7cuDOiMj+s2FiRDQAHwL+WdLU/XeSdHUSKI0tLS19VauZ9bFTp2bu5vYltOnJZ1isBbIHGMcnbV25nP2GoCJibfJvM/AQfzyf0dlnXkQ0RERDXV3doajZzPqhmspyTptay/3P+27utOQzLBYC0yRNllRFJhDedFWTpOnACODxrLYRkqqT97XAacDy/fc1s9Jx9ozRrN60m6b1O9IupSTlLSwiog24BrgHeA64IyKWSbpR0sVZXS8Hbo8//nNhBtAoaQnwIPCV7KuozKz0zJ0+BoDfPuehqDSoWE7pGhoaorGxMe0yzCyPLvqXRxlYVc5P//zUtEspGpIWJfPDB9RfJrjNzHo0d/poFr2ymc0796VdSslxWJhZwTh7xhg6Ah5e6asf+5rDwswKxnHjhlE7uNoPFkyBw8LMCkZZmTh7eh0Pr1hPa7vX5u5LDgszKyhnTx/Dtj1tNL68Oe1SSorDwswKyunTaqkqL+OB5702d19yWJhZQRlcXcHJU0Z63qKPOSzMrODMnT6a5padvLRhZ9qllAyHhZkVnLkzMndz+8GCfcdhYWYFp37kQI4cM9jzFn3IYWFmBens6WNY0LyJ7Xta0y6lJDgszKwgzZ0xmraO4JGVG9IupSQ4LMysIJ1YP5zhAyu530NRfcJhYWYFqaK8jHccNZqHVrTQ3lEcT8/uzxwWZlaw5s4Yzaad+1j4stfmzjeHhZkVrLOnj2ZAZTnzl6xLu5Si57Aws4I1sKqCc2aO4dfPvOoHC+aZw8LMCtrFxx/O5l2t/K7JV0Xlk8PCzAra24+sZWhNBXcv9lBUPjkszKygVVeUc8ExY7ln2WvsaW1Pu5yildewkHS+pBWSmiRd18X2r0tanLxWStqSte1KSS8kryvzWaeZFbaLTzicnfva/ayoPKrI14EllQM3A+cAa4CFkuZHxPLOPhHx11n9PwWcmLwfCdwANAABLEr29WonZvYmc6aMYvSQau56ag0XHjs27XKKUj7PLGYDTRHRHBH7gNuBSw7Q/wrgtuT9ecB9EbEpCYj7gPPzWKuZFbDyMvG+k8bzwPPreW3rnrTLKUr5DItxwOqsz2uStjeRNBGYDDzQm30lXS2pUVJjS0vLISnazArT5bPq6Qi4c9Hqnjtbr/WXCe7LgTsjolezUxExLyIaIqKhrq4uT6WZWSGYOGoQp04dxX82rqbDj/845PIZFmuB+qzP45O2rlzOH4ageruvmRkAH5xVz+pNu3nsRd9zcajlMywWAtMkTZZURSYQ5u/fSdJ0YATweFbzPcC5kkZIGgGcm7SZmXXrvKMPo3ZwFT987OW0Syk6eQuLiGgDriHzS/454I6IWCbpRkkXZ3W9HLg9IiJr303AF8gEzkLgxqTNzKxbNZXlfHjORO5/fj1N63ekXU5RUdbv6ILW0NAQjY2NaZdhZinbuGMvp3zlAd5/0nj+73uOTbucfk/Sooho6Klff5ngNjM7JEYNruZ9bxvHzxatYeOOvWmXUzQcFmZWdD5x+hRa2zuY90hz2qUUDYeFmRWdI0YP5tITxvGjx19m/TbfpHcoOCzMrCh9+p3TaGsPvvVgU9qlFAWHhZkVpYmjBvGBhnpue3IVL7b4yqi3ymFhZkXrr8+ZRk1lOTf8fBnFcuVnWhwWZla0Rg+p4drzjuJ3TRv4xdJX0y6noDkszKyo/cnJEzl23DA+f/cyWrb7UtqD5bAws6JWXiZu+sDxbN/Txt/csdgPGTxIDgszK3pHHTaEG959NI++sIFvP+Srow6Gw8LMSsIVs+u55ITDuenelfzX02vSLqfg5G1ZVTOz/kQSX33/cby+bQ/X/nQpQ2sqmTtjTNplFQyfWZhZyajaOcAOAAAHA0lEQVSuKGfeRxuYPnYIV//bIn7a6FX1cuWwMLOSMrSmktuumsMpU0Zx7Z1L+eIvlrO3rVeLdJYkh4WZlZwhNZXc+rFZfPSUiXzvdy9xybce48mXvGTOgTgszKwkVVWUceMlx3DrxxrYsquVy255nP/xo4U80bzRd3t3wYsfmVnJ272vne//rpnv/e4ltuxqZUrdIM6deRjvnDGaY8cPo7qiPO0S8ybXxY8cFmZmid372rl7yTrmL1nHE80baesIKsvF9MOGcuSYIdSPHMD4EQMZM7SaYQMqGVpTydABlQyqLqeqvAxJaX+FXss1LHzprJlZYkBVOZfNqueyWfVs29PKYy9sYMmarSxds4XHmjbw+vY9HOjv6/IyUVkuKsvKqCgXFeVllEtI0Bkj2YHS+faNf5NeXfV/Y6+sbZ3bZ4wdyjevOPGtfPUeOSzMzLowtKaSC44dywXHjn2jbW9bO2s372bDjn1s293Ktj2tbNvdyo69bbS2B20dHbS2B63tHbQln9s74o2A6cyZCAj+uPEP2+KP+nW3LXtD/YgBh+x7dyevYSHpfOAbQDnwvYj4Shd9LgM+R+ZrL4mIDyXt7cAzSbdVEXFxPms1M+tJdUU5U+oGM6Uu7Ur6Xt7CQlI5cDNwDrAGWChpfkQsz+ozDbgeOC0iNksanXWI3RFxQr7qMzOz3OXz0tnZQFNENEfEPuB24JL9+lwF3BwRmwEiYn0e6zEzs4OUz7AYB2TfS78mact2JHCkpMckPZEMW3WqkdSYtF/a1Q+QdHXSp7GlpeXQVm9mZm9Ie4K7ApgGnAWMBx6RdGxEbAEmRsRaSVOAByQ9ExEvZu8cEfOAeZC5dLZvSzczKx35PLNYC9RnfR6ftGVbA8yPiNaIeAlYSSY8iIi1yb/NwENAfq8LMzOzbuUzLBYC0yRNllQFXA7M36/Pf5M5q0BSLZlhqWZJIyRVZ7WfBizHzMxSkbdhqIhok3QNcA+ZS2dvjYhlkm4EGiNifrLtXEnLgXbg2ojYKOlU4BZJHWQC7SvZV1GZmVnf8uM+zMxKWMk9G0pSC/DKWzhELbDhEJVTKErtO5fa9wV/51LxVr7zxIjo8TbDogmLt0pSYy7pWkxK7TuX2vcFf+dS0Rff2etZmJlZjxwWZmbWI4fFH8xLu4AUlNp3LrXvC/7OpSLv39lzFmZm1iOfWZiZWY8cFmZm1qOSDwtJ50taIalJ0nVp15Nvkm6VtF7Ss2nX0lck1Ut6UNJyScskfTrtmvJNUo2kJyUtSb7z59OuqS9IKpf0tKRfpF1LX5H0sqRnJC2WlLc7k0t6ziJZoGklWQs0AVcU86NFJJ0B7AB+HBHHpF1PX5A0FhgbEU9JGgIsAi4t8v+dBQyKiB2SKoHfAZ+OiCdSLi2vJP0N0AAMjYh3pV1PX5D0MtAQEXm9EbHUzyxyWaCpqETEI8CmtOvoSxHxakQ8lbzfDjzHm9dWKSqRsSP5WJm8ivovQ0njgYuA76VdSzEq9bDIZYEmKyKSJpF53P2CdCvJv2RIZjGwHrgvIor9O/8z8PdAR9qF9LEA7pW0SNLV+fohpR4WVkIkDQZ+BvxVRGxLu558i4j2ZB378cBsSUU77CjpXcD6iFiUdi0pOD0i3gZcAHwyGWo+5Eo9LHJZoMmKQDJu/zPgJxFxV9r19KVk5ckHgfN76lvATgMuTsbvbwfOlvTv6ZbUN7IWilsP/BeZ4fVDrtTDIpcFmqzAJZO93weei4ivpV1PX5BUJ2l48n4AmYs4nk+3qvyJiOsjYnxETCLz3/EDEfHhlMvKO0mDkos2kDQIOBfIy5WOJR0WEdEGdC7Q9BxwR0QsS7eq/JJ0G/A4cJSkNZI+kXZNfeA04CNk/tpcnLwuTLuoPBsLPChpKZk/iu6LiJK5nLSEjAF+J2kJ8CTwy4j4TT5+UElfOmtmZrkp6TMLMzPLjcPCzMx65LAwM7MeOSzMzKxHDgszM+uRw8LsIEkaLukvk/eHS7oz7ZrM8sWXzpodpOQ5U78olaf3WmmrSLsAswL2FWBq8rC+F4AZEXGMpI8BlwKDgGnATUAVmRsD9wIXRsQmSVOBm4E6YBdwVUQU7V3WVtg8DGV28K4DXkwe1nftftuOAd4LzAK+BOyKiBPJ3D3/0aTPPOBTEXES8HfAt/ukarOD4DMLs/x4MFk7Y7ukrcDdSfszwHHJE3BPBX6aeXQVANV9X6ZZbhwWZvmxN+t9R9bnDjL/3ZUBW5KzErN+z8NQZgdvOzDkYHZM1tN4SdIHIPNkXEnHH8rizA4lh4XZQYqIjcBjkp4F/vEgDvEnwCeSJ4Yuo8iX9LXC5ktnzcysRz6zMDOzHjkszMysRw4LMzPrkcPCzMx65LAwM7MeOSzMzKxHDgszM+vR/wcJJsWQ396olgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(guess_dynamics)\n", "plot_norm(guess_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now use all the information that we have gathered to initialize\n", "the optimization routine. That is: \n", "\n", "* The `objectives`: transferring population\n", "from $\\ket{1}$ to $\\ket{3}$ at $t_f$. \n", "\n", "* The `pulse_options`: initial pulses\n", "and their shapes restrictions. \n", "\n", "* The `propagator`: in our example we will\n", "choose a simple matrix exponential.\n", "\n", "* The `chi_constructor`: the optimization\n", "functional to use. \n", "\n", "* The `info_hook`: all processes taking place inbetween\n", "iterations, for example printing the fidelity in each step. \n", "\n", "* And the\n", "`iter_stop`: the number of iterations to perform the optimization." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "attributes": { "classes": [], "id": "", "n": "16" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " F = -0.023471\n", " F = 0.252768\n", " F = 0.482903\n", " F = 0.645458\n", " F = 0.747797\n", " F = 0.808008\n", " F = 0.842337\n", " F = 0.861818\n", " F = 0.873071\n", " F = 0.879836\n", " F = 0.884164\n", " F = 0.887167\n", " F = 0.889444\n", " F = 0.891316\n", " F = 0.892957\n", " F = 0.894460\n", " F = 0.895875\n", " F = 0.897230\n", " F = 0.898541\n", " F = 0.899817\n", " F = 0.901061\n" ] } ], "source": [ "oct_result = krotov.optimize_pulses(\n", " objectives, pulse_options, tlist,\n", " propagator=krotov.propagators.expm,\n", " chi_constructor=krotov.functionals.chis_re,\n", " info_hook=krotov.info_hooks.chain(\n", " #krotov.info_hooks.print_debug_information,\n", " print_fidelity),\n", " iter_stop=20\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that the algorithm takes into account the non Hermitian behaviour\n", "which leads to a non unitary final state. To improve the fidelity it is\n", "necessary to avoid these dissipative effects as much as possible." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "attributes": { "classes": [], "id": "", "n": "17" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pump pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Stokes pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_pulse_amplitude_and_phase(pulse_real, pulse_imaginary,tlist):\n", " ax1 = plt.subplot(211)\n", " ax2 = plt.subplot(212)\n", " amplitudes = [np.sqrt(x*x + y*y) for x,y in zip(pulse_real,pulse_imaginary)]\n", " phases = [np.arctan2(y,x)/np.pi for x,y in zip(pulse_real,pulse_imaginary)]\n", " ax1.plot(tlist,amplitudes)\n", " ax1.set_xlabel('time')\n", " ax1.set_ylabel('pulse amplitude')\n", " ax2.plot(tlist,phases)\n", " ax2.set_xlabel('time')\n", " ax2.set_ylabel('pulse phase (π)') \n", " plt.show()\n", " \n", "print(\"pump pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " oct_result.optimized_controls[0], oct_result.optimized_controls[1], tlist)\n", "print(\"Stokes pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " oct_result.optimized_controls[2], oct_result.optimized_controls[3], tlist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check the evolution of the population due to our optimized pulses." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "attributes": { "classes": [], "id": "", "n": "18" } }, "outputs": [], "source": [ "opt_dynamics = oct_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, e_ops=[proj1, proj2, proj3])\n", "opt_states = oct_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "attributes": { "classes": [], "id": "", "n": "19" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_population(opt_dynamics)\n", "plot_norm(opt_states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see the algorithm takes into account the decay in level $\\ket{2}$ and\n", "minimizes the population in this level during the process.\n", "\n", "However, convergence\n", "is relatively slow, and after 20 iterations, we have only\n", "achieved a 90%\n", "fidelity. As we can see from the population dynamics, we do not\n", "fully transfer\n", "the population in state $\\ket{3}$, and there is still non-\n", "negligible population\n", "in state $\\ket{2}$. If we were to continue up to iteration\n", "2000, the\n", "optimization converges much farther:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "attributes": { "classes": [], "id": "", "n": "20" } }, "outputs": [], "source": [ "oct_result = krotov.result.Result.load(\n", " './non_herm_oct_result.dump', objectives\n", ")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "attributes": { "classes": [], "id": "", "n": "21" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final fidelity: 0.986\n" ] } ], "source": [ "print(\"Final fidelity: %.3f\" % oct_result.info_vals[-1])" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "attributes": { "classes": [], "id": "", "n": "22" } }, "outputs": [], "source": [ "def plot_convergence(result):\n", " fig, ax = plt.subplots()\n", " ax.semilogy(result.iters, 1-np.array(result.info_vals))\n", " ax.set_xlabel('OCT iteration')\n", " ax.set_ylabel('error')\n", " plt.show(fig)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "attributes": { "classes": [], "id": "", "n": "23" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_convergence(oct_result)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dynamics now show a very good population transfer and negligible population\n", "in state $\\ket{2}$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "attributes": { "classes": [], "id": "", "n": "24" } }, "outputs": [], "source": [ "opt_dynamics = oct_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm, e_ops=[proj1, proj2, proj3])\n", "opt_states = oct_result.optimized_objectives[0].propagate(\n", " tlist, propagator=krotov.propagators.expm)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "attributes": { "classes": [], "id": "", "n": "25" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pump pulse amplitude and phase:\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(\"pump pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " oct_result.optimized_controls[0], oct_result.optimized_controls[1], tlist)\n", "print(\"Stokes pulse amplitude and phase:\")\n", "plot_pulse_amplitude_and_phase(\n", " oct_result.optimized_controls[2], oct_result.optimized_controls[3], tlist)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "attributes": { "classes": [], "id": "", "n": "26" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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