docs/notebooks/02_example_lambda_system_rwa_complex_pulse.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization of a State-to-State Transfer in a Lambda System in the RWA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.12.0\n",
      "IPython version      : 8.25.0\n",
      "\n",
      "krotov    : 1.3.0+dev\n",
      "matplotlib: 3.7.5\n",
      "scipy     : 1.12.0\n",
      "numpy     : 1.26.4\n",
      "qutip     : 4.7.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "%load_ext watermark\n",
    "import os\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",
    "%watermark -v --iversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{tr}[0]{\\operatorname{tr}}\n",
    "\\newcommand{diag}[0]{\\operatorname{diag}}\n",
    "\\newcommand{abs}[0]{\\operatorname{abs}}\n",
    "\\newcommand{pop}[0]{\\operatorname{pop}}\n",
    "\\newcommand{aux}[0]{\\text{aux}}\n",
    "\\newcommand{opt}[0]{\\text{opt}}\n",
    "\\newcommand{tgt}[0]{\\text{tgt}}\n",
    "\\newcommand{init}[0]{\\text{init}}\n",
    "\\newcommand{lab}[0]{\\text{lab}}\n",
    "\\newcommand{rwa}[0]{\\text{rwa}}\n",
    "\\newcommand{bra}[1]{\\langle#1\\vert}\n",
    "\\newcommand{ket}[1]{\\vert#1\\rangle}\n",
    "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n",
    "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n",
    "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2}\\mid{#2}\\vphantom{#1}\\right\\rangle}\n",
    "\\newcommand{ketbra}[2]{\\vert#1\\rangle\\!\\langle#2\\vert}\n",
    "\\newcommand{op}[1]{\\hat{#1}}\n",
    "\\newcommand{Op}[1]{\\hat{#1}}\n",
    "\\newcommand{dd}[0]{\\,\\text{d}}\n",
    "\\newcommand{Liouville}[0]{\\mathcal{L}}\n",
    "\\newcommand{DynMap}[0]{\\mathcal{E}}\n",
    "\\newcommand{identity}[0]{\\mathbf{1}}\n",
    "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n",
    "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n",
    "\\newcommand{avg}[1]{\\langle#1\\rangle}\n",
    "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n",
    "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n",
    "\\newcommand{Re}[0]{\\operatorname{Re}}\n",
    "\\newcommand{Im}[0]{\\operatorname{Im}}$\n",
    "\n",
    "This example is illustrates the use of complex-valued control fields. This is\n",
    "accomplished by rewriting the Hamiltonian as the sum of two independent\n",
    "controls (real and imaginary parts). We consider a 3-level system in a\n",
    "$\\Lambda$ configuration, and seek control pulses that implement a\n",
    "(phase-sensitive) state-to-state transition $\\ket{1} \\rightarrow \\ket{3}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The rotating wave Hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system consists of three levels $\\ket{1}$, $\\ket{2}$ and $\\ket{3}$ with\n",
    "energy levels $E_{1}, E_{2}$ and $E_{3}$ which interact with a pair of laser\n",
    "pulses $\\epsilon_{P}(t)$ (\"pump laser\") and $\\epsilon_{S}(t)$ (\"Stokes laser\"),\n",
    "respectively, see Chapter 15.4.2 in [\"Introduction to Quantum Mechanics: A\n",
    "Time-Dependent Perspective\" by David Tannor][Tannor] for details.\n",
    "\n",
    "[Tannor]: http://www.weizmann.ac.il/chemphys/tannor/Book/\n",
    "\n",
    "In the lab frame, the Hamiltonian reads\n",
    "\n",
    "$$\n",
    "\\Op{H}_{\\text{lab}} = \\begin{pmatrix}\n",
    "    E_1                     & -\\mu_{12} \\epsilon_P(t) & 0                          \\\\\n",
    "    -\\mu_{12} \\epsilon_P(t) & E_2                     & - \\mu_{23} \\epsilon_S(t) \\\\\n",
    "    0                       & -\\mu_{23} \\epsilon_S(t) &  E_2\n",
    "\\end{pmatrix}\\,.\n",
    "$$\n",
    "\n",
    "with the dipole values $\\mu_{12}$, $\\mu_{23}$ describing the coupling to the\n",
    "(real-valued) control fields $\\epsilon_P(t)$, $\\epsilon_S(t)$. The \"rotating\n",
    "frame\" is defined as\n",
    "\n",
    "$$\\ket{\\Psi_{\\text{rot}}} = \\Op{U}_0^\\dagger \\ket{\\Psi_{\\text{lab}}}$$\n",
    "\n",
    "with the transformation\n",
    "\n",
    "$$\\op{U}_{0} = \\ketbra{1}{1}\n",
    "e^{-i\\left(E_{2} - \\omega_{P} \\right)t} + \\ketbra{2}{2} e^{-iE_{2}t} +\n",
    "\\ketbra{3}{3} e^{-i\\left(E_{2}-\\omega_{S}\\right)t}\\,,$$\n",
    "\n",
    "where $\\omega_{P}$ and $\\omega_{S}$ are the two central frequencies defining\n",
    "the rotating frame.\n",
    "\n",
    "The condition of having to fulfill the Schrödinger equation in the rotating\n",
    "frame implies a rotating frame Hamiltonian defined as\n",
    "\n",
    "$$\\op{H}_{\\text{rot}}  = \\op{U}_{0}^{\\dagger} \\op{H}_{\\text{lab}} \\op{U}_{0}  - i \\op{U}_{0}^{\\dagger} \\dot{\\op{U}}_{0}\\,.$$\n",
    "\n",
    "Note that most textbooks use $\\Op{U}$ instead of $\\Op{U}^\\dagger$, and thus the\n",
    "adjoint of the above equation to define the rotating frame transformation, but\n",
    "we follow the example of Tannor's book here.\n",
    "\n",
    "The rotating frame Hamiltonian reads\n",
    "$$\n",
    "\\Op{H}_\\text{rot} = \\begin{pmatrix}\n",
    "    E_1 + \\omega_P - E_2                      & -\\mu_{12} \\epsilon_P(t) e^{-i \\omega_P t} & 0                          \\\\\n",
    "    -\\mu_{12} \\epsilon_P(t) e^{+i \\omega_P t} &  0                                        & - \\mu_{23} \\epsilon_S(t) e^{-i \\omega_S t}\\\\\n",
    "    0                                         & -\\mu_{23} \\epsilon_S(t) e^{+i \\omega_S t} &  E3 + \\omega_S -E_2\n",
    "\\end{pmatrix}\\,.\n",
    "$$\n",
    "\n",
    "We can now write the fields as\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\mu_{12} \\epsilon_{P}(t)\n",
    "    &= \\Omega_{P}^{(1)}(t) \\cos{(\\omega_P t)} - \\Omega_{P}^{(2)}(t) \\sin{(\\omega_P t)} \\\\\n",
    "    &= \\Omega_{P}^{(1)}(t) \\left( e^{i \\omega_P t} + e^{-i \\omega_P t}\\right)\n",
    "        + i \\Omega_{P}^{(2)}(t) \\left( e^{i \\omega_P t} - e^{-i \\omega_P t} \\right) \\,,\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "and similarly for $\\epsilon_{S}(t)$, where we have split each field into two\n",
    "arbitrary (real-valued) auxiliary fields $\\Omega_{P}^{(1)}(t),\n",
    "\\Omega_{P}^{(2)}(t)$, and $\\Omega_{S}^{(1)}(t), \\Omega_{S}^{(2)}(t)$. This\n",
    "rewriting is suggestive of controls being spectrally centered around $\\omega_P$\n",
    "and $\\omega_S$, respectively, in which case any oscillations in\n",
    "$\\Omega_{P,S}^{(1,2)}(t)$ are on a much slower time scale than $\\omega_{P, S}$.\n",
    "Mathematically, however, *any* control fields can written in the above form.\n",
    "Thus, we have not placed any restriction on the controls at this time.\n",
    "\n",
    "Plugging this into $\\Op{H}_\\text{rot}$ and invoking the rotating wave\n",
    "approximation that neglects all fast oscillating terms $\\propto e^{\\pm i 2\n",
    "\\omega_{P,S} t}$, we find\n",
    "\n",
    "$$\n",
    "\\Op{H}_\\text{RWA} = \\begin{pmatrix}\n",
    "    \\Delta_P                    & -\\frac{1}{2} \\Omega_P(t)   & 0                          \\\\\n",
    "    -\\frac{1}{2} \\Omega_P^*(t)  &  0                         &  -\\frac{1}{2} \\Omega_S(t)  \\\\\n",
    "    0                           & -\\frac{1}{2} \\Omega_S^*(t) & \\Delta_S\n",
    "\\end{pmatrix}\\,,\n",
    "$$\n",
    "\n",
    "with the detunings $\\Delta_P \\equiv E_1 + \\omega_P - E_2$, $\\Delta_S  \\equiv E3\n",
    "+ \\omega_S -E_2$ and the complex-valued control fields $\\Omega_P(t) \\equiv\n",
    "\\Omega_{P}^{(1)}(t) + i \\Omega_{P}^{(2)}(t)$ and $\\Omega_S(t) \\equiv\n",
    "\\Omega_{S}^{(1)}(t) + i \\Omega_{S}^{(2)}(t)$, illustrated in the following\n",
    "diagram:\n",
    "\n",
    "![Lambda system considered in this notebook](energylevels.png)\n",
    "\n",
    "Most textbooks (including Tannor's) only allow control fields of the form\n",
    "$\\epsilon_{P,S}(t) \\propto \\Omega_{P,S}(t) \\cos{(\\omega_{P,S} t)}$ with the\n",
    "pulse envelopes $\\Omega_{P,S}(t) \\in \\mathbb{R}^+$. This will result in the\n",
    "same $\\Op{H}_\\text{RWA}$ as above, but with the positive real-valued envelopes\n",
    "instead of the complex-valued $\\Omega_{P,S}(t)$. However, this restriction is\n",
    "unnecessary: complex-valued control fields in the RWA are more general and\n",
    "entirely physical, with the relation to the real-valued field in the lab\n",
    "frame as defined above. The spectra of the optimized pulses are free to deviate\n",
    "from the frequencies of the rotating frame, limited only by the numerical\n",
    "resolution of the time grid and the RWA.\n",
    "\n",
    "The `krotov` package requires that all control pulses are real-valued.\n",
    "Therefore, the real and imaginary parts of $\\Omega_{P}$ and $\\Omega_{S}$ are\n",
    "treated as independent Hamiltonians, and we write\n",
    "\n",
    "$$\n",
    "\\Op{H}_\\text{RWA}\n",
    "    = \\Op{H_0}\n",
    "    + \\Omega_{P}^{(1)}(t) \\Op{H}_{P,\\text{re}}\n",
    "    + \\Omega_{P}^{(2)}(t) \\Op{H}_{P,\\text{im}}\n",
    "    + \\Omega_{S}^{(1)}(t) \\Op{H}_{S,\\text{re}}\n",
    "    + \\Omega_{S}^{(2)}(t) \\Op{H}_{S,\\text{im}}\n",
    "$$\n",
    "\n",
    "for the purpose of the optimization, with\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\Op{H_0} &= \\Delta_P \\ketbra{1}{1} + \\Delta_S \\ketbra{3}{3}\\,, \\\\\n",
    "\\Op{H}_{P,\\text{re}} &= -\\frac{1}{2} \\left(\\ketbra{1}{2} + \\ketbra{2}{1}\\right)\\,, \\\\\n",
    "\\Op{H}_{P,\\text{im}} &= -\\frac{i}{2} \\left(\\ketbra{1}{2} - \\ketbra{2}{1}\\right)\\,, \\\\\n",
    "\\Op{H}_{S,\\text{re}} &= -\\frac{1}{2} \\left(\\ketbra{2}{3} + \\ketbra{3}{2}\\right)\\,, \\\\\n",
    "\\Op{H}_{S,\\text{im}} &= -\\frac{i}{2} \\left(\\ketbra{2}{3} - \\ketbra{3}{2}\\right)\\,.\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Guess controls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose the initial guess for the four control fields based on the intuition\n",
    "of the \"stimulated Raman adiabatic passage\" (STIRAP) scheme. STIRAP allows to\n",
    "transfer the population in $\\ket{1}$ $\\ket{3}$ without having to pass through\n",
    "$\\ket{2}$; it requires the Stokes-pulse to precede but overlap the pump-pulse.\n",
    "\n",
    "Here, we leave it up to Krotov's method to find appropriate pulses for a\n",
    "STIRAP-like transfer (without requiring that the $\\ket{2}$ level remains\n",
    "unpopulated).  We start from a low intensity real-valued $\\Omega_S(t)$ pulse\n",
    "with a Blackman shape, followed by an overlapping real-valued $\\Omega_P(t)$ of\n",
    "the same shape. The entire scheme is in the time interval [0, 5]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.829336Z",
     "start_time": "2019-02-12T04:40:55.819110Z"
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     "shell.execute_reply": "2024-06-03T14:29:07.960638Z"
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   },
   "outputs": [],
   "source": [
    "def Omega_P1(t, args):\n",
    "    \"\"\"Guess for the real part of the pump pulse\"\"\"\n",
    "    Ω0 = 5.0\n",
    "    return Ω0 * krotov.shapes.blackman(t, t_start=2.0, t_stop=5.0)\n",
    "\n",
    "\n",
    "def Omega_P2(t, args):\n",
    "    \"\"\"Guess for the imaginary part of the pump pulse\"\"\"\n",
    "    return 0.0\n",
    "\n",
    "\n",
    "def Omega_S1(t, args):\n",
    "    \"\"\"Guess for the real part of the Stokes pulse\"\"\"\n",
    "    Ω0 = 5.0\n",
    "    return Ω0 * krotov.shapes.blackman(t, t_start=0.0, t_stop=3.0)\n",
    "\n",
    "\n",
    "def Omega_S2(t, args):\n",
    "    \"\"\"Guess for the imaginary part of the Stokes pulse\"\"\"\n",
    "    return 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now instantiate the Hamiltonian including these guess controls:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2024-06-03T14:29:07.964936Z"
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   },
   "outputs": [],
   "source": [
    "def hamiltonian(E1=0.0, E2=10.0, E3=5.0, omega_P=9.5, omega_S=4.5):\n",
    "    \"\"\"Lambda-system Hamiltonian in the RWA\"\"\"\n",
    "\n",
    "    # detunings\n",
    "    ΔP = E1 + omega_P - E2\n",
    "    ΔS = E3 + omega_S - E2\n",
    "\n",
    "    H0 = Qobj([[ΔP, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, ΔS]])\n",
    "\n",
    "    HP_re = -0.5 * Qobj([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]])\n",
    "    HP_im = -0.5 * Qobj([[0.0, 1.0j, 0.0], [-1.0j, 0.0, 0.0], [0.0, 0.0, 0.0]])\n",
    "\n",
    "    HS_re = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]])\n",
    "    HS_im = -0.5 * Qobj([[0.0, 0.0, 0.0], [0.0, 0.0, 1.0j], [0.0, -1.0j, 0.0]])\n",
    "\n",
    "    return [\n",
    "        H0,\n",
    "        [HP_re, Omega_P1],\n",
    "        [HP_im, Omega_P2],\n",
    "        [HS_re, Omega_S1],\n",
    "        [HS_im, Omega_S2],\n",
    "    ]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2024-06-03T14:29:07.966349Z",
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     "shell.execute_reply": "2024-06-03T14:29:07.968658Z"
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   },
   "outputs": [],
   "source": [
    "H = hamiltonian()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Target state in the rotating frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basis states of the $\\Lambda$-system are defined as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2024-06-03T14:29:07.972392Z"
    }
   },
   "outputs": [],
   "source": [
    "ket1 = qutip.Qobj(np.array([1.0, 0.0, 0.0]))\n",
    "ket2 = qutip.Qobj(np.array([0.0, 1.0, 0.0]))\n",
    "ket3 = qutip.Qobj(np.array([0.0, 0.0, 1.0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We would like to implement a phase-sensitive transition $\\ket{1} \\rightarrow\n",
    "\\ket{3}$ *in the lab frame*. Since we are defining the dynamics in the RWA,\n",
    "this means we have to adjust the target state to be in the rotating frame as\n",
    "well (the initial state at $t=0$ is not affected by the RWA).\n",
    "\n",
    "As defined earlier, the states in the rotating frame are obtained from the\n",
    "states in the lab frame by the transformation $\\ket{\\Psi_{\\text{rot}}} =\n",
    "\\Op{U}_0^\\dagger \\ket{\\Psi_{\\text{lab}}}$. In our case, this means that we get\n",
    "$\\ket{3}$ with and additional phase factor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2024-06-03T14:29:07.973764Z",
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     "shell.execute_reply": "2024-06-03T14:29:07.975301Z"
    }
   },
   "outputs": [],
   "source": [
    "def rwa_target_state(ket3, E2=10.0, omega_S=4.5, T=5):\n",
    "    return np.exp(1j * (E2 - omega_S) * T) * ket3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:07.976763Z",
     "iopub.status.busy": "2024-06-03T14:29:07.976687Z",
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     "shell.execute_reply": "2024-06-03T14:29:07.978125Z"
    }
   },
   "outputs": [],
   "source": [
    "psi_target = rwa_target_state(ket3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now instantiate the control objective:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.816607Z",
     "start_time": "2019-02-12T04:40:55.813293Z"
    },
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     "classes": [],
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     "n": "5"
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    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Objective[|Ψ₀(3)⟩ to |Ψ₁(3)⟩ via [H₀[3,3], [H₁[3,3], u₁(t)], [H₂[3,3], u₂(t)], [H₃[3,3], u₃(t)], [H₄[3,3], u₄(t)]]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective = krotov.Objective(initial_state=ket1, target=psi_target, H=H)\n",
    "objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate dynamics under the guess field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a time grid with 500 steps between $t=0$ and $T=5$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.809020Z",
     "start_time": "2019-02-12T04:40:55.802160Z"
    },
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     "n": "4"
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     "shell.execute_reply": "2024-06-03T14:29:07.985694Z"
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   "outputs": [],
   "source": [
    "tlist = np.linspace(0, 5, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before propagating, we visually verify the guess pulses we defined earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.858312Z",
     "start_time": "2019-02-12T04:40:55.853316Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:07.987100Z",
     "iopub.status.busy": "2024-06-03T14:29:07.987022Z",
     "iopub.status.idle": "2024-06-03T14:29:07.988980Z",
     "shell.execute_reply": "2024-06-03T14:29:07.988755Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_pulse(pulse, tlist, label):\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('%s pulse amplitude' % label)\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:56.293915Z",
     "start_time": "2019-02-12T04:40:55.860421Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "11"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:07.990334Z",
     "iopub.status.busy": "2024-06-03T14:29:07.990246Z",
     "iopub.status.idle": "2024-06-03T14:29:08.191599Z",
     "shell.execute_reply": "2024-06-03T14:29:08.190621Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pulse(H[1][1], tlist, 'Ωₚ')\n",
    "plot_pulse(H[3][1], tlist, 'Ωₛ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The imaginary parts are zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:56.300681Z",
     "start_time": "2019-02-12T04:40:56.295922Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "12"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.197491Z",
     "iopub.status.busy": "2024-06-03T14:29:08.196869Z",
     "iopub.status.idle": "2024-06-03T14:29:08.202478Z",
     "shell.execute_reply": "2024-06-03T14:29:08.201756Z"
    }
   },
   "outputs": [],
   "source": [
    "assert np.all([H[2][1](t, None) == 0 for t in tlist])\n",
    "assert np.all([H[4][1](t, None) == 0 for t in tlist])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We introduce projectors $\\op{P}_{i} =\n",
    "\\ketbra{i}{i}$ for each of the three energy levels, allowing use to plot the population dynamics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.798666Z",
     "start_time": "2019-02-12T04:40:55.787265Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.206707Z",
     "iopub.status.busy": "2024-06-03T14:29:08.206571Z",
     "iopub.status.idle": "2024-06-03T14:29:08.209506Z",
     "shell.execute_reply": "2024-06-03T14:29:08.208887Z"
    }
   },
   "outputs": [],
   "source": [
    "proj1 = qutip.ket2dm(ket1)\n",
    "proj2 = qutip.ket2dm(ket2)\n",
    "proj3 = qutip.ket2dm(ket3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.224259Z",
     "start_time": "2019-02-12T04:40:56.304263Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "13"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.214148Z",
     "iopub.status.busy": "2024-06-03T14:29:08.213771Z",
     "iopub.status.idle": "2024-06-03T14:29:08.378228Z",
     "shell.execute_reply": "2024-06-03T14:29:08.377856Z"
    }
   },
   "outputs": [],
   "source": [
    "guess_dynamics = objective.mesolve(tlist, e_ops=[proj1,proj2,proj3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.232092Z",
     "start_time": "2019-02-12T04:40:57.226227Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "14"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.380028Z",
     "iopub.status.busy": "2024-06-03T14:29:08.379894Z",
     "iopub.status.idle": "2024-06-03T14:29:08.382566Z",
     "shell.execute_reply": "2024-06-03T14:29:08.382102Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_population(result):\n",
    "    fig, ax = plt.subplots()\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_xlabel('time')\n",
    "    ax.set_ylabel('population')\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.443794Z",
     "start_time": "2019-02-12T04:40:57.236490Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "15"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.384249Z",
     "iopub.status.busy": "2024-06-03T14:29:08.384131Z",
     "iopub.status.idle": "2024-06-03T14:29:08.453493Z",
     "shell.execute_reply": "2024-06-03T14:29:08.453209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Aws0HJdLxGQumZUJQKuCRJhhuiIgUNrcwFTGWMFS1dGP32QDpN5EDSOalyl0zgMJNS5cd247XAQBun5apcTXkK4YbIiKFWcKNuHWKtNLm/ZIAmJrqaQMaXTsrp09V7rpyuGkqlTb007G/Hq6GzeHEuNRoTEiP0boc8hHDDRGRCr47XZqa2nywCrZenR9BUH1IeozJBKKSlbtuRAIQ7zqXqepb5a6rArmR+LapnJIKBgw3REQqmJ2fiNQYM9q6e/HV6XqtyxletSt4ZCg4aiMLgKmpjp5efHFK+mc0f3KaxtWQEhhuiIhUYDAI7uMY5FEB3ZLDTfoU5a8dAOHmi5N1sPU6kZMYicI0TkkFA4YbIiKV3DRZCjd/PVIDh55XTclTRkr228jkAzirSpS/tkL+ergGAHDjxDROSQUJhhsiIpVcnp+I+MhwNHbYsLdUp6umem1A3THpuZrTUg2nAVuH8tf3kd3hxNZjtQCAGyZySipYMNwQEakk3GjAvEukH5i6nZqqPw44bIA5rq/5V0nRKUBUCgCxL0TpyN7SRrR02ZEYZcLMXG7cFywYboiIVHSTq+/m0yM1EEUdTk3J50mlT1FuZ+ILpV4iPdYcUef6Ptju2ttmbmEKwoz8kRgs+E+SiEhFc8YmwxRmQEVzF07VtmtdzsXkZeDpk9W7R+ok6bH2qHr38NL2E3K4SdW4ElISww0RkYoiTEYUjUkCAHx+vFbjagZR5wocqRPVu0ea69q1h9W7hxeqW7pxrLoNggBcPVbB/X1Icww3REQqu64wBQDw+bE6jSsZRK0fwo18bZ1NS+04Kf3zmJodj4Qok8bVkJIYboiIVCZPeewtbURbt13javrpagLaqqTnKYXq3SdlgvTYUQt06GdDQ3lK6trxKRpXQkpjuCEiUllechTGJEeh1yniy5P6+eGOWtfqpTgrYIlV7z7maCAhz3VPfYzeOPr9s2C4CT4MN0REfiCP3sgnT+uC3G8jj6yoSW4q1snU1MGKFrR02RFrCcO07DityyGFMdwQEfnB1eOlhtUvT9XrZ0m4u9/mEvXvJd9DJyM3O083AACuGJPEJeBBiP9EiYj84PK8RIQbBVQ0d6GssVPrciT+DDfuFVP6WA4uH2ZaVJCkcSWkBoYbIiI/iDKH4VKrtAPu3081aFyNiz/DjTz1VX8C0HjkytbrxL7SJgAMN8GK4YaIyE+uHCv9IP37aR00FbfXAZ31AAQgWcWVUrLEMdK9ups1XzH17flmdNkdSIwyYXwqTwEPRgw3RER+Mse1UdzO0w1wan1KuNxMnJAHmCLVv194BBCfIz2vP6H+/YbR12+TCIOBp4AHI4YbIiI/mZYdj0iTEY0dNhyrbtO2mLrj0qOa+9tcKHm89Kh1uDkjhRt552gKPgw3RER+Ygoz4PL8RAB9Da2aaTglPSaP89893eHmpP/ueQFbrxP7z0n9Nlcw3AQthhsiIj+anS/9QN1b2qhtIXLASPJnuHHdS8ORm0OVLejpdSIhMhxjU6M1q4PUxXBDRORH8sjN3tImbfe7kcONPJriDzqYltrvWiU1MzcRgsB+m2DFcENE5EdTsuJgCTegscOG03Xt2hRh7wJayqXnWkxLNZdJNWhAHjG7LC9Bk/uTfzDcEBH5kSnMgOnWeADAnrNN2hTRcBqACFjigUg/9p1EJUv3hOiqwb9EUXT328xiuAlqDDdERH52eZ48NaVR3408LZQ8DvDn1IwgaDo1VdrQiYYOG0xhBkzO4nlSwYzhhojIzy5z9d3sOatRuHGvlPJjv41MwxVT+1xhclp2HMxhRr/fn/yH4YaIyM9m5CTAaJDOmapo1qD3xL1Saqz/763hiil5SmpmbqLf703+pXm4efXVV5GXlweLxYLZs2djz549w75/9erVKCwsREREBKxWK370ox+hu7vbT9USEfkuyhyGSZmxAPp+4PpV/2kpf9NwWupAmRxu2G8T7DQNNxs2bEBxcTFWrFiBAwcOYNq0aZg/fz5qa2sHff/69evx1FNPYcWKFTh69CjefPNNbNiwAT/5yU/8XDkRkW9m5Eg/YL8u83O4EUV9TEs1nAKcTr/dtr2nFydrpdVpckM3BS9Nw82qVavw0EMPYcmSJZg4cSLWrl2LyMhIvPXWW4O+/6uvvsKcOXNwzz33IC8vDzfeeCPuvvvuYUd7enp60NraOuAXEZHWLs2JBwB8Xdbs3xu3VQO2dkAwAgn5/r03ACTkAoYwwN4JtFb47baHKlogikBmnAUpMWa/3Ze0oVm4sdls2L9/P+bNm9dXjMGAefPmYefOnYN+5sorr8T+/fvdYebMmTP46KOPcMsttwx5n5UrVyIuLs79y2q1KvuFEBF54VKrNHJzpLIVPb0O/91Yng5KyAXCTP67r8wY7johHH6dmvr2fDMAYGp2vN/uSdrRLNzU19fD4XAgLS1twOtpaWmorq4e9DP33HMPXnjhBVx11VUIDw9HQUEB5s6dO+y01PLly9HS0uL+VV5erujXQUTkDWtiBJKiTLA5nDhc6ccR5QYNdia+kAYrpr453wIAmGrlEvBQoHlD8Whs27YNv/jFL/Db3/4WBw4cwHvvvYfNmzfjpz/96ZCfMZvNiI2NHfCLiEhrgiC4p6YO+LOpuN7Vb6PFSimZfO9G/23k9015MwBgOkduQkKYVjdOTk6G0WhETU3NgNdramqQnp4+6GeeeeYZfO9738ODDz4IAJgyZQo6Ojrw8MMP49/+7d9gMARUViOiEHdpTgL+drQWX7t+8PqFliulZPK0lJ92KW5o78H5JmnJ/eRsjtyEAs3SgMlkwsyZM7F161b3a06nE1u3bkVRUdGgn+ns7LwowBiN0kZMmh5AR0TkBXnkpsSfTcUNGpwGfqGkAumx8YxfbvdthTQlNSYlCrGWcL/ck7Sl2cgNABQXF2Px4sWYNWsWLr/8cqxevRodHR1YsmQJAGDRokXIysrCypUrAQALFizAqlWrcOmll2L27Nk4deoUnnnmGSxYsMAdcoiIAsXU7HgIAlDR3IXatm6kxljUvaG9G2jW4MDMC8kjN81lgMMuNRmrSJ6SmsYpqZChabhZuHAh6urq8Oyzz6K6uhrTp0/Hli1b3E3GZWVlA0Zqnn76aQiCgKeffhoVFRVISUnBggUL8POf/1yrL4GIyGvR5jAUpETjVG07Dle0InWCyuGmqRSACJhjgagUde81nOh0ICwC6O2SAo48kqOSb+VmYk5JhQxNww0ALFu2DMuWLRv0z7Zt2zbg92FhYVixYgVWrFjhh8qIiNQ3JSsOp2rbcbCiBddNSFX3ZvI0UGK+fw/MvJDBII3e1B6WalIx3Iii6F4GPo2b94UMduASEWlIPp36oKsvRFXucDNG/XuNJNG1gaDKfTcVzV2ob7chzCBgYgZXy4YKhhsiIg1Ndp0xdSjkwo2rBpXDjTwlVZgeA0s4ezNDBcMNEZGGJmXFQRCAqpZu1Lf3qHszPYUbeSpK5eXg8ogY+21CC8MNEZGGos1hyE+OAuCH0Rt3uFG3gdcjfhq5OeLa/XliJsNNKGG4ISLS2BRX342q4abXBrS4loHrYeTGvRz8HODoVe02R6tc4SYjRrV7kP4w3BARaWyKP5qKm88BohMIjwKiVV6V5YmYTCDMAjh7gZYyVW5R396D2rYeCAJQmM5m4lDCcENEpLFJmfLIjYoHaPbvt9FyGbjMYAAS1F0xJY/a5CZGItqs+c4n5EcMN0REGpuUJY0qVDR3obHDps5N+u9xoxfuvpuzqlzePSWVyVGbUMNwQ0SksVhLuPpNxXpaKSVLUvcATbmZ+BJOSYUchhsiIh1QfTM/PYYblVdMHa1qA8CRm1DEcENEpANTslTezC/Ewk233YFTde0AgEu4M3HIYbghItIBualY7hNRlMMuHVAJ6CzcuPbbaSoFnA5FL32qth0Op4j4yHBkxKl8ICnpDsMNEZEOTEiX9mE519iJjh6F931pKZeWXIdFADEZyl7bF7FZgNEMOO19e/AopH+/jaCH1WHkVww3REQ6kBRtRkqMGaIInKhpU/bi/VdKGXT0177BACTkSc8VXjF1xDUCximp0KSjf8uJiEKbPHpzvFrpcOMKDnqakpLJ4aapVNHLHuEy8JDGcENEpBNyuDmmeLjR4R43MhXCjSiK7t6lS3jsQkhiuCEi0gn5iIBj1Qo3FcvhJiE0ws35pi60dfci3ChgXCrDTShiuCEi0on+IzeiKCp34RCblpJ7lsYkR8MUxh9zoYj/1ImIdGJsajSMBgHNnXbUtPYoc1FRlA7NBPqChJ6oEm6k/W3GpUUrdk0KLAw3REQ6YQk3uo9hUGxqqr0G6O0GBAMQl63MNZWUkCs9djcDXU2KXPJkrTRyMz6NU1KhiuGGiEhHFG8qlkdE4rIBY7gy11SSKQqISpWeN51T5JInXSM34zlyE7IYboiIdMQdbpTaqVgON3qckpIpODXldIo4VStPS3HkJlQx3BAR6cgE94oppUZudNxvI1Mw3Jxv6kKX3QGT0YDcxEifr0eBieGGiEhHJrj2ZTld1w5br9P3C8qBIT7X92upRcFw414plRKFMCN/xIUq/pMnItKRrPgIxJjDYHeIOFPf7vsFQ2xa6gSbiQkMN0REuiIIAgqVPIbBHW50uIGfTMFwc4rNxASGGyIi3SlUasWUvRtoq5KeB8LITUs54PDtRHR55IbNxKGN4YaISGfGpUqjDvKqH6+1lAMQAVM0EJnoe2FqickAjCbA2Qu0Vnh9mQErpVI5chPKGG6IiHRmrOs8pNO+hpv+/TaC4Nu11GQw9DU8+zA1Vd7UiW67E6YwA3KTopSpjQISww0Rkc7IxwaUNnSgp9fh/YUCoZlYpkDfjXzsQkGKdIwFhS6GGyIinUmNMSPGHAanCJTWd3p/oRALN33HLnBKKtQx3BAR6YwgCBjr+gEt/8D2SiDscSNTIty4V0qxmTjUMdwQEenQ2BQFmooDYXdimSLTUq6VUmwmDnkMN0REOjTOPXLjZbgRxZCalnI6RZyu45lSJGG4ISLSobGu0QevV0x1NgI215RWfI5CVakowTV11tUIdLeM+uNVrd3otjsRbhRgTYhQuDgKNAw3REQ6NM61HPxMXQd6HV6cMdVcKj3GZADhFuUKU4s5BohMlp7L02mjIIfA3CSeKUUMN0REupQVHwFLuAE2hxPlTV2jv0AgTUnJfJiaOuOakhqTzP1tiOGGiEiXDAYBBa6m4pM1XqyYCrVwU98BAChgMzGB4YaISLfcxzDUedF3E2Lh5jRHbqgfhhsiIp2Sm4rlk65HRe5bCYQ9bmQ+TUtJIzdjUjhyQww3RES6JZ8xFXojN2dH9bGOnl5UtXQDAApSOHJDDDdERLo1tt/p4E6n6PkHHXag5bz0PKDCjWuUqbkccHp+ptZZV79NUpQJ8ZEmNSqjAMNwQ0SkU7lJkQg3Cui0OVDZMooVUy3nAdEBhFmA6DT1ClRabBZgCAOcdqCtyuOPufttOGpDLgw3REQ6FW40IDdJ+oEt95R4pFnut8kBDAH017zBCMRZpeej6Ltx99sks9+GJAH0bz0RUejJd63+kadePBKI/TYyeWpqFBv5ceSGLsRwQ0SkY/IP7DOjaSoO6HCTJz02ex5u5JGbAq6UIheGGyIiHZP3bTkTKiM38tJ1D6elnE7RParFkRuSMdwQEemYvG/LqHpuAnGPG5l7ObhnIzdVrd3osjsQZhBgTYxUry4KKAw3REQ6JvfcVLZ0odvu4fLoQB65SRjdyI08XSetLOOPNJLw3wQiIh1LijIh1hIGUQTONXSO/IHuFqCrUXqeEIgjN/nSY3s1YB95+Tt3JqbBMNwQEemYIAjId09NedBULE/nRCYD5hgVK1NJRAJgctXdXDbi27lSigbDcENEpHMFo2kqdk9JBeCoDQAIwqiWg5e6RrN4YCb1x3BDRKRzct+NR03F8hLqQOy3kY1iOXipK/DJmx0SAQw3RES6l58ib+TnybRUqfQYyOHGw+Xgtl4nzjdJIzf5HLmhfhhuiIh0Tj5WYHTTUnmq1aM693Lw0mHfVtHcBacIWMINSI0xq14WBQ6GGyIinctLlvZvae60o6nDNvyb5UAQiHvcyDzsuSltkMJeXlIUBEFQuyoKIJqHm1dffRV5eXmwWCyYPXs29uzZM+z7m5ubsXTpUmRkZMBsNmP8+PH46KOP/FQtEZH/RZrCkBlnAQCcGW5qyunsW2EUDCM3zecAURzybX39Nty8jwbSNNxs2LABxcXFWLFiBQ4cOIBp06Zh/vz5qK2tHfT9NpsNN9xwA0pLS/HnP/8Zx48fxxtvvIGsrCw/V05E5F/5KR40FbdVAQ4bYAgDYgP478X4HOmxpxXoahrybfK+P3nst6ELhGl581WrVuGhhx7CkiVLAABr167F5s2b8dZbb+Gpp5666P1vvfUWGhsb8dVXXyE8PBwAkJeXN+w9enp60NPT4/59a2urcl8AEZGfjEmOxt9PNQx/Org8JRVnBYya/vXum/AIIDpd2sivqRSITBz0bf2npUKFw+GA3W7XugzVmEwmGAy+j7to9m+/zWbD/v37sXz5cvdrBoMB8+bNw86dOwf9zAcffICioiIsXboU77//PlJSUnDPPffgxz/+MYxG46CfWblyJZ5//nlVvgYiIn/xaDl4oO9x019CrhRums8BWTMGfYs8chMK01KiKKK6uhrNzc1al6Iqg8GA/Px8mEwmn66jWbipr6+Hw+FAWlragNfT0tJw7NixQT9z5swZfPbZZ7j33nvx0Ucf4dSpU/jhD38Iu92OFStWDPqZ5cuXo7i42P371tZWWK1W5b4QIiI/cE9LDddzEwx73Mjic4Hy3UOumOp1OFHeGDrLwOVgk5qaisjIyKBsoHY6naisrERVVRVycnJ8+hq9Cjc1NTV48sknsXXrVtTW1kK8oOHL4fDwcLdRcjqdSE1Nxeuvvw6j0YiZM2eioqICL7300pDhxmw2w2zmEkEiCmzyDrznGjrhdIowGAb5iz8YloHLRjgdvKK5C71OEeYwA9JiLP6rSwMOh8MdbJKSkrQuR1UpKSmorKxEb2+vu/3EG16Fm/vvvx9lZWV45plnkJGR4VW6Sk5OhtFoRE1NzYDXa2pqkJ6ePuhnMjIyEB4ePmAK6pJLLkF1dTVsNpvPw1hERHqVFR+BMIOAnl4natq6kREXcfGbgircDL+RX2m/KalBg14QkXtsIiODf/pN/jnucDj8H26+/PJLfPHFF5g+fbrXNzaZTJg5cya2bt2KO+64A4A0MrN161YsW7Zs0M/MmTMH69evh9PpdDccnThxAhkZGQw2RBTUwowGZCdEoLShE+caOocPN4G8x41shCMYzjWE3rELwTgVdSGlvkavWpKtVutFU1HeKC4uxhtvvIF33nkHR48exQ9+8AN0dHS4V08tWrRoQMPxD37wAzQ2NuLxxx/HiRMnsHnzZvziF7/A0qVLfa6FiEjvcpLkqalBmoptnUC7ayQ8GEZu5IDWXA44L251KK0PnX4bGj2vRm5Wr16Np556Cq+99tqIS7GHs3DhQtTV1eHZZ59FdXU1pk+fji1btribjMvKygYsCbNarfjkk0/wox/9CFOnTkVWVhYef/xx/PjHP/a6BiKiQJGXFIkd6JuSGUDevM8cB0Qk+LUuVcRmAoZwwGkHWiuB+IELQUobuIEfDc2rcLNw4UJ0dnaioKAAkZGRF82LNTY2enytZcuWDTkNtW3btoteKyoqwq5du0ZVLxFRMMgdbuSm/zLwYJi+MBilQNN4RpqaGiLchNIeN+Q5r0duiIjIv/JcoxTnBhu5CaZmYll8rhRumkqBvKvcLzuconsZOEdu9G3Hjh146aWXsH//flRVVWHjxo3uPls1eRVuFi9erHQdREQ0gr6Rm06Iojiw+TKYNvCTDbEcvLK5C3aHCFOYAZmDNVaTbnR0dGDatGl44IEHcOedd/rtvl5v4udwOLBp0yYcPXoUADBp0iTcfvvtQ+4UTEREvrEmRkAQgPaeXjR02JAc3W8Pr2DawE82xHJweUoqJzH4l4EPRRRFdNnV2VNuJBHhRo9XNd188824+eabVa7oYl6Fm1OnTuGWW25BRUUFCgsLAUjHHFitVmzevBkFBQWKFklERIA5zIjMuAhUNHfhXEPHwHATjNNSQywHlxuq80J4SqrL7sDEZz/R5N5HXpiPSJO+zy7zain4Y489hoKCApSXl+PAgQM4cOAAysrKkJ+fj8cee0zpGomIyEXuMZGXQgMARLFfuMn3f1FqkZeDXzAtda6ezcQ0PK+i1/bt27Fr1y4kJvad1JqUlIQXX3wRc+bMUaw4IiIaKDcpCl+dbsC5xn7hpqMOsHcCEKQTwYOFPHLTXg3Yu6TTwtFvd+IQ3uMmItyIIy/M1+zeeudVuDGbzWhra7vo9fb2du4UTESkolz3iql+y8HlUZu4bCAsiP4OjkgAzLFAT6u0j0+K1AbRtww8dKelBEHQ/dSQlryalrrtttvw8MMPY/fu3RBFEaIoYteuXXjkkUdw++23K10jERG5yD/QB2zkF0zHLvQnCP2mpkoBSMvAy9w9N6E7ckPD8yrc/OY3v0FBQQGKiopgsVhgsVgwZ84cjB07Fi+//LLSNRIRkcugG/k1BeFKKVnCwL6b6tZu2BxOhBsFZMZzGbjetbe3o6SkBCUlJQCAs2fPoqSkBGVlZare16sxrfj4eLz//vs4efIkjh07BkA6nXvs2LGKFkdERAPJ01LNnXa0dNoRFxkenCulZO69bkoB9DUTWxMiYQzRZeCBZN++fbjuuuvcvy8uLgYg7Ze3bt061e7r04TduHHjMG7cOKVqISKiEUSawpAaY0ZtWw/ONXZgamR8aIQb13Lw8iZpSsqaGLr9NoFk7ty5ihy0PVoeh5vi4mL89Kc/RVRUlDt5DWXVqlU+F0ZERIPLTYpEbVsPShs6MTU7PrjDzQXLwctcq8RyGG5oGB6Hm6+//hp2u939nIiItJGbFIW9pU3SFE1vD9BaIf1BMIab/tNSoojyxi4A0m7NREPxONx8/vnngz4nIiL/ch+g2dgJtJwHIALhkUBUsraFqSE+R3q0tQFdTX3TUgkcuaGhebVa6oEHHhh0n5uOjg488MADPhdFRERDG7Biqums9GJCnrR0OtiEW4CYDOl501n3aeDsuaHheBVu3nnnHXR1dV30eldXF373u9/5XBQREQ0tt/9eN8HcbyNz9d301J1FfbsNAMMNDW9Uq6VaW1vdm/a1tbXBYrG4/8zhcOCjjz5Camqq4kUSEVGf3ERp5KaurQe2+rMwAcEdbhJygfJdaK06CWAq4iLCERcRrnVVpGOjCjfx8fEQBAGCIGD8+PEX/bkgCHj++ecVK46IiC4WFxmOhMhwNHXa0V17OgTCTR4AaeQGmMpmYhrRqMLN559/DlEUcf311+N///d/BxycaTKZkJubi8zMTMWLJCKigXKTotDU2QwxmHcnlrmmpQTXXjdcBk4jGVW4ufbaawFI2ydbrVYYDF617BARkY/ykiJRUt4ES5trG/tgO1eqP1dwi+goB8CVUjQyr3Yozs2V/iPq7OxEWVkZbDbbgD+fOnWq75UREdGQchIjEYcOmB3t0gvykulg5DpfKranGgY4kc2RGxqBV+Gmrq4OS5YswccffzzonzscDp+KIiKi4VkTI5Ej1Eq/iU4HTEH8Az8mAzCaEOawIQMNnJYKICtXrsR7772HY8eOISIiAldeeSV++ctforCwUNX7ejWv9MQTT6C5uRm7d+9GREQEtmzZgnfeeQfjxo3DBx98oHSNRER0gZz+4SaY+20AwGCEGGcFAFgNdbAmsKE4UGzfvh1Lly7Frl278Omnn8Jut+PGG29ER0fHyB/2gVcjN5999hnef/99zJo1CwaDAbm5ubjhhhsQGxuLlStX4tZbb1W6TiIi6icnKRJWV7hxJuR693+qAcQea4Wp8TRyhFpkMdwAogjYO7W5d3ikxxtGbtmyZcDv161bh9TUVOzfvx/XXHONGtUB8DLcdHR0uPezSUhIQF1dHcaPH48pU6bgwIEDihZIREQXS4uxIM9QBwBoj8hGrMb1qK3FkoUUAJdYGmEOM2pdjvbsncAvNFqd/JNKwBTl1UdbWloAYMBqazV4FfYLCwtx/PhxAMC0adPw2muvoaKiAmvXrkVGRoaiBRIR0cUMBgFjTfUAgBpjmsbVqK/WmA4AGBveoHEl5C2n04knnngCc+bMweTJk1W9l1cjN48//jiqqqoAACtWrMBNN92E3//+9zCZTFi3bp2S9RER0RDknpsyMRXjNK5FbeViKiYB7qm4kBceKY2gaHVvLyxduhSHDh3Cl19+qXBBF/Mq3Nx3333u5zNnzsS5c+dw7Ngx5OTkIDk5CE+lJSLSG0cvknqlH/QnepLwHY3LUduJniTcBCClt1rrUvRBELyeGtLCsmXL8OGHH2LHjh3Izs5W/X5ehZsLRUZGYsaMGUpcioiIPNF6HkY40COG42h74PyQ89bBzngAQJS9AbB1BvfS9yAiiiIeffRRbNy4Edu2bUN+fr5f7utxuCkuLvb4oqtWrfKqGCIi8pDr2IVyMQXnmro1LkZ9x1qMaBUjESt0As1lQOoErUsiDyxduhTr16/H+++/j5iYGFRXSyNvcXFxiIhQb9Wbx+Hm66+/9uh9gofLw4iIyAdNpQCkfpvzjRotCfaTXocTlc3dKAtLxWShVPraGW4Cwpo1awAAc+fOHfD622+/jfvvv1+1+3ocbj7//HPViiAiolFyhZtyMQUNHTa09/Qi2qxIp4HuVLV0w+EUUYFUTEYp4DpAk/RPFEVN7hvs+z4REQWnprMAgPpwafuN8iAevSlzfW0tZte+Lk0MNzQ8r2L+ddddN+z002effeZ1QURE5IHGMwCArug8oEsKAJdkBOdWfnJw646xAo1wj1oRDcWrcDN9+vQBv7fb7SgpKcGhQ4ewePFiJeoiIqKhiCLQKI3cIDEfqAuNkRvE50rhhtNSNAKvws2vf/3rQV9/7rnn0N7e7lNBREQ0gs5GoKcVgICItALg+Pm+ABCEypu6AACWlALgDKSRG1H0+HwjCj2K9tzcd999eOutt5S8JBERXcg1JYXYLGQmJwAI7pEb+WuLzxwjvWBrlwIe0RAUDTc7d+6ExWJR8pJERHQhOdwk5iMnUdrMLqhHblxfW1ZKAhAjNxWXalcQ6Z5X01J33nnngN+Looiqqirs27cPzzzzjCKFERHREAYJN+VNXXA6RRgMwTVV09HTi4YOGwDAmhgJJOQCbZVAcymQPVPb4ki3vAo3cXFxA35vMBhQWFiIF154ATfeeKMihRER0RDc4WYMMuIsMBoE2HqdqG3rQXpccI2elze5pqQiwxFrCZeaist2cjk4DcurcPP2228rXQcREXmqSV4pNQZhRgOy4iNQ1tiJssbO4As3jVIzsTXBdZZUQp70yGkpGoZP21nu27cPR48eBQBMnDgRM2dyiJCISHX9Rm4AwJrYF24uz0/UsDDlyb1E1kTXOUQJudIjl4PTMLxqKD5//jyuvvpqXH755Xj88cfx+OOP47LLLsNVV12F8+fPK10jERHJupqBzgbpuWsUw913E4RNxeXucHPByI28zw/p2po1azB16lTExsYiNjYWRUVF+Pjjj1W/r1fh5sEHH4TdbsfRo0fR2NiIxsZGHD16FE6nEw8++KDSNRIRkUyekopKBcwxAPp+8Ad1uJGnpVyjVWgpB3ptGlVFnsrOzsaLL76I/fv3Y9++fbj++uvx3e9+F4cPH1b1vl5NS23fvh1fffUVCgsL3a8VFhbiP//zP3H11VcrVhwREV2gsa/fRhbMy8HlhmL5a0R0GhAeCdg7pYCTVKBhddoRRRFdvV2a3DsiLGLYI5j6W7BgwYDf//znP8eaNWuwa9cuTJo0SY3yAHgZbqxWK+x2+0WvOxwOZGZm+lwUEREN4YJ+GyB4w40oin0NxXK4EQTpa685BDScDtlw09XbhdnrZ2ty79337EZkeOSoP+dwOPCnP/0JHR0dKCoqUqGyPl5NS7300kt49NFHsW/fPvdr+/btw+OPP45f/epXihVHREQX6H+mlIscbmrbetBlc2hRlSrq223osjsgCEBWfETfH8hfuxz0SNcOHjyI6OhomM1mPPLII9i4cSMmTpyo6j29Grm5//770dnZidmzZyMsTLpEb28vwsLC8MADD+CBBx5wv7exkVtkExEpZpCRm7iIcMSYw9DW04vzTZ0YlxajUXHKkqekMmItMIX1+3/xRNdoTQiHm4iwCOy+Z7dm9x6NwsJClJSUoKWlBX/+85+xePFibN++XdWA41W4Wb16tcJlEBGRR/rtTiwTBAHWxEgcqWpFeTCFG9c0W3biBVMgcrBrPO3nivRDEASvpoa0YDKZMHbsWADAzJkzsXfvXrz88st47bXXVLunV+Fm8eLFStdBREQjsXUA7dXS834jN4A0NXWkqhVlDcHTdyOHm5whw03ojtwEMqfTiZ6eHlXv4fUmfg6HA5s2bXJv4jdp0iTcfvvtMBqNihVHRET9yLvyWuKBiIQBf5STJDcVa7OCRg1lFy4Dl8nhprkMcNgBY7ifKyNPLV++HDfffDNycnLQ1taG9evXY9u2bfjkk09Uva9X4ebUqVO45ZZbUFFR4V4OvnLlSlitVmzevBkFBaHZvU5EpKpB+m1k1iBcMSWvlMpJuqDHIyYDCIsAeruk5eCDfD9IH2pra7Fo0SJUVVUhLi4OU6dOxSeffIIbbrhB1ft6FW4ee+wxFBQUYNeuXUhMlLb6bmhowH333YfHHnsMmzdvVrRIIiLC8OEmQQoAwbSRn9xQfNHIjcEg9RzVHgEazjDc6Nibb76pyX293sSvf7ABgKSkJLz44ouYM2eOYsUREVE/g2zgJ+u/140oih5vsqZXdocTlc2ukZsLe24A6XtQe4R9NzQor/a5MZvNaGtru+j19vZ2mEwmn4siIqJBDLJSSpaVEAFBALrsDjR0BP6xBFXN3XCKgDnMgJQY88Vv4F43NAyvws1tt92Ghx9+GLt374YoihBFEbt27cIjjzyC22+/XekaiYgIGHbkxhxmREasBUBw9N3IX0N2whBb/XOvGxqGV+HmN7/5DQoKClBUVASLxQKLxYIrr7wSY8eOxcsvvzzq67366qvIy8uDxWLB7NmzsWfPHo8+9+6770IQBNxxxx2jvicRUUDp7ZGaZ4Ehe0yC6QDNi86UuhD3uqFheNVzEx8fj/fffx+nTp3CkSNHAAATJ050b9IzGhs2bEBxcTHWrl2L2bNnY/Xq1Zg/fz6OHz+O1NTUIT9XWlqKJ598kgd1ElFoaDoHQATCo4ColEHfYk2MxO6zjUGx1417GfhI4abpHODoBYxe72wSMJxOp9YlqE4URUWu4/W/DW+++SZ+/etf4+TJkwCAcePG4YknnsCDDz44quusWrUKDz30EJYsWQIAWLt2LTZv3oy33noLTz311KCfcTgcuPfee/H888/jiy++QHNzs7dfBhFRYGg4JT0mFUiHRw5CHuWQRz0C2ZAb+MliswCjGXD0AK3ngYQ8/xXnZyaTCQaDAZWVlUhJSYHJZAr4hvHBiKKIuro6CIKA8HDf9i7yKtw8++yzWLVqFR599FH3yZ47d+7Ej370I5SVleGFF17w6Do2mw379+/H8uXL3a8ZDAbMmzcPO3fuHPJzL7zwAlJTU/H9738fX3zxxbD36OnpGbATYmtrq0e1ERHpijvcDD1CHkyng7uPXrhwGbhMXg5ed0w6HTyIw43BYEB+fj6qqqpQWVmpdTmqEgQB2dnZPm8I7FW4WbNmDd544w3cfffd7tduv/12TJ06FY8++qjH4aa+vh4OhwNpaWkDXk9LS8OxY8cG/cyXX36JN998EyUlJR7dY+XKlXj++ec9ei8RkW41SKPkSB435Fv6em4Cf5fi8qZhloHLEsdI4abxDIDv+KcwjZhMJuTk5KC3txcOR/Cc/H6h8PBwRU468Crc2O12zJo166LXZ86cid7eXp+LGkpbWxu+973v4Y033kBycrJHn1m+fDmKi4vdv29tbYXValWrRCIidTS4GmeHGbmxJkob+VW2dMHW6xx4knYAae/pRaNrObv8NQ3K3VR81g9VaU+ervF1yiYUeBVuvve972HNmjVYtWrVgNdff/113HvvvR5fJzk5GUajETU1NQNer6mpQXp6+kXvP336NEpLS7FgwQL3a3KDVVhYGI4fP37R0Q9msxlm8yB7JBARBZL+PTdDSIk2wxJuQLdd2gAvLznKT8UpS56Sio8MR4xlmB/k3OuGhuBTQ/Ff//pXXHHFFQCA3bt3o6ysDIsWLRowUnJhAOrPZDJh5syZ2Lp1q3s5t9PpxNatW7Fs2bKL3j9hwgQcPHhwwGtPP/002tra8PLLL3NEhoiCU3cr0O76n8BhRm4EQUBOYiRO1LSjrLEz4MPNsFNSAJeD05C8CjeHDh3CjBkzAEijKYA0CpOcnIxDhw653+dJN3dxcTEWL16MWbNm4fLLL8fq1avR0dHhXj21aNEiZGVlYeXKlbBYLJg8efKAz8fHxwPARa8TEQUNedQmKhWwxA371v7hJlANeRr4heSN/JpKAacDMPjeq0HBwatw8/nnnytWwMKFC1FXV4dnn30W1dXVmD59OrZs2eJuMi4rK4PBEJjzxkREipDDzTDNxDJ5dVEgb+R33tVMPOQeN7K4bMAQDjhsQGsFEJ/jh+ooEOhi16Nly5YNOg0FANu2bRv2s+vWrVO+ICIiPfGg30YWDHvd9G3gN0wzMSCN1CTkSSvJGs8w3JAbh0SIiPSu3rUMPGnkkZtg2OvG454boK/vpoF9N9SH4YaISO882MBPlpPkCjcBegSDKIruUacRe26AvtEshhvqh+GGiEjPRLHvB7dHPTfSVE5rdy9aOu1qVqaKuvYedNudEAQgM36EaSmg73sib3JIBIYbIiJ9a6sC7B2AYATic0d8e6QpDMnR0t5egdh3I++unBkX4dkmhPJUXf0JFauiQMNwQ0SkZ/KUVEIuEGby6CM5rkbcQOy76TtTyoNRG6Bv5Ka5DOjtGf69FDIYboiI9GwUzcSyQG4qHlUzMQBEpwHmWEB0cqdicmO4ISLSMw/OlLpQIIebvmXgHoYbQej73tSz74YkDDdERHrmPg3c83CTnRi4G/m5V0qNtMdNf8nsu6GBGG6IiPRsFMvAZTmBHG5cDcUeT0sB/VZMnVKhIgpEDDdERHpl75bOTQK86rk539QFh1NUoTB12B1OVLW4jl7wZI8bmXvFFKelSMJwQ0SkV42npUZZcxwQk+7xx9JiLTAZDeh1iu6wEAgqm7vgFAFzmAEpMWbPP5jcL9yIgRPmSD0MN0REelV3THpMKZQaZz1kNAjIci2llqd5AkH/ZmJhFF+vdDq4APS0AB116hRHAYXhhohIr+pcDbIp40f9UWsA9t2UjXYZuCzc0ndoJqemCAw3RET65R65mTDqjwbiRn5ehxsASHYFQB7DQGC4ISLSr7rj0qNX4Sbw9ropH+0eN/0ls6mY+jDcEBHpkaO3b2lzshfTUq7VRoF0vpRPIzfcyI/6YbghItKjprOA0w6ERwJx1lF/PCB7bho4LUXKYLghItIjeUoqeRxgGP1f1TlJUkCob7eho6dXycpU0dJpR2u3VOeodieWydNSTaU8QJMYboiIdMmHZmIAiLWEIz4yHEBgTE3JU1LJ0WZEmsJGfwEeoEn9MNwQEemRfE6SF/02MnffTQDsdSOHm9wkL6akAGkfIPl7JQdDClkMN0REeuTjyA0QWCumfGomlsnfq1qGm1DHcENEpDdOZ9+qn5RCry8TSE3FZb4sA5elusINR25CHsMNEZHetJQD9k7AEA4k5Ht9mUAauSlXZOTmEumR4SbkMdwQEemN3G+TNBYwetFc65ITgCM3PoUbeeSm4RTQa1OgKgpUDDdERHrT/8BMH1j7HcEg6vi07F6HExXNUtOzT+EmNktaMeXslU5Up5DFcENEpDcKhZvM+AgYBKCn14m6Nv3u/VLV0g2HU4QpzIDUGLP3FxKEvu9Z7VFliqOAxHBDRKQ3NUekx9SJPl0m3GhAZrz+D9B0NxMnRMBgEHy7mBxu2HcT0hhuiIj0xOnoG3VIm+Tz5dx9NzreyE+RfhuZ3FTMkZuQxnBDRKQnTaVAbxcQZgESx/h8OXkjv7IG/W7kp2i44XJwAsMNEZG+1BySHlMvAQxGny8nnzEVENNSSo7cNJzmGVMhjOGGiEhPag5Lj6m+T0kBgbGRnyJ73MhiM11nTDmkJeEUkhhuiIj0RA43CvTbAAHWc+PtuVL9ccUUgeGGiEhfFA431gRptVR1aze67Q5Frqmkli47mjvtAPr6g3wmnzFVd1yZ61HAYbghItKLnnapoRhQLNwkRpkQZTJCFOHeKE9P5Cmp5GgTosze78Y8QKp8DANHbkIVww0RkV7UHQMgAtFpQFSyIpcUBMHdd6PHpuJyJZuJZe7TwRluQhXDDRGRXrhXSvm2ed+F3AdoNugv3Ci6DFwmj3o1ngFs+vuaSX0MN0REeiHvTKzQlJQsPzkKAFDa0KHodZWgSriJTgMikwHRydGbEMVwQ0SkF+5m4smKXjY3SQo353Q8cqPotJQgAOlTpOc1B5W7LgUMhhsiIj0QRaBWDjfKTkvluZZY63Hkxt1zo9RKKVm6KyBWM9yEIoYbIiI9aKsCupoAwQgk+3Ya+IVyXdNS5Y2dcDhFRa/ti16HE+ebpBVceclKh5up0mP1IWWvSwGB4YaISA/kKankcUC4RdFLZ8RaYAozwO4QUamj5eAVzV3odYowhxmQFqPs1+ye2qs5BDidyl6bdI/hhohID6pKpEeF+20AwGAQ3A27euq7KXXVkpcUBYNBUPbiyeMAowmwtQPNpcpem3SP4YaISA8qS6THzOmqXF7uuzmro76b0nqpllwljl24kDG8bzM/9t2EHIYbIiI9qPpGesyYrsrl3Sum6nUUblxBK8/VE6S4NNeKKfbdhByGGyIirXU0AC3l0vOMqarcom/FlH6mpc71m5ZShbwcnCM3IYfhhohIa3K/TWIBYIlT5RZ9e93oaOTGNYqUp8a0FNC3HLyGIzehhuGGiEhrcrhRqd8G6BsdOdfYCacOloP3Opwob5JGbnJVm5ZyhZuWcmmZPYUMhhsiIq3JzcQZ01S7RWa8BWEGAbZeJ6pbu1W7j6cqm7thd4gwhRmQEavwMnBZRDwQlyM9Z99NSGG4ISLSmjxyo1IzMQCEGQ3uIw70sFOxXENuYqTyy8D7cx/DwHATShhuiIi01NkINJdJz1UcuQH6llzrYa8bufcnV61mYpncdyOvRqOQwHBDRKQl+YduQr40jaIiue9GDyM3Z+vllVIqNRPLMi+VHiu/Vvc+pCsMN0REWvJDM7HMvRxcB3vdnFN7jxtZ5gzpse440NOm7r1INxhuiIi05G4mnq76reRVSXqYlnJv4Kf2tFRMGhCbDUDk1FQIYbghItKSu5lY3X4bYOC0lChqtxzc4RRR3igd4KnK0QsXynJNTVXsV/9epAsMN0REWulsBJpKped+CDfZCREwGgR027VdDl7Z3AWbwwmT0YDM+Aj1byhPTVUcUP9epAsMN0REWpFHEpLGApGJqt8u3Ghwnw5+pk67vht5WsyaKIUt1WXNlB4rGW5ChS7Czauvvoq8vDxYLBbMnj0be/bsGfK9b7zxBq6++mokJCQgISEB8+bNG/b9RES6dX6v9Jh9md9uOcbVd3Omrt1v97zQWX/128jkZu3mMqCj3j/3JE1pHm42bNiA4uJirFixAgcOHMC0adMwf/581NbWDvr+bdu24e6778bnn3+OnTt3wmq14sYbb0RFRYWfKyci8pE73Mzy2y0LUqMBAKe1HLmp99MeNzJLHJA0TnrOJeEhQfNws2rVKjz00ENYsmQJJk6ciLVr1yIyMhJvvfXWoO///e9/jx/+8IeYPn06JkyYgP/6r/+C0+nE1q1b/Vw5EZEPnE7gvGtaSoORm9MajtyccYWb/BQ/hRugb2qKTcUhQdNwY7PZsH//fsybN8/9msFgwLx587Bz506PrtHZ2Qm73Y7ExMHnq3t6etDa2jrgFxGR5hpOAj0tQFgEkDrJb7eVR2607LmRg9XYlGj/3TSLTcWhRNNwU19fD4fDgbS0tAGvp6Wlobq62qNr/PjHP0ZmZuaAgNTfypUrERcX5/5ltVp9rpuIyGflrl7BrBmAMcxvt5VHbipbutBtd/jtvrJuuwPljVJDcUGqH0du5BVTlQcADZfBk39oPi3lixdffBHvvvsuNm7cCItl8FNlly9fjpaWFvev8vJyP1dJRDQIDZqJASAxyoS4iHCIInBWg52KzzV0wikCMZYwpESb/Xfj9CmAIQzoqANazvvvvqQJTcNNcnIyjEYjampqBrxeU1OD9PT0YT/7q1/9Ci+++CL++te/YurUqUO+z2w2IzY2dsAvIiLNadBMDACCIKAgRbu+G/meBSnREAQ/LAOXhVuANNf0X8U+/92XNKFpuDGZTJg5c+aAZmC5ObioqGjIz/37v/87fvrTn2LLli2YNcu/fzEQEfmssxGoPSI9t872++3HpGjXd3O6ti/c+J38vS7b7f97k19pPi1VXFyMN954A++88w6OHj2KH/zgB+jo6MCSJUsAAIsWLcLy5cvd7//lL3+JZ555Bm+99Rby8vJQXV2N6upqtLdr1/lPRDQq5a4frknjgOhUv99+TIp2e93IIzdj/LlSSiaHm/Jd/r83+ZX/utiGsHDhQtTV1eHZZ59FdXU1pk+fji1btribjMvKymAw9GWwNWvWwGaz4a677hpwnRUrVuC5557zZ+lERN4595X0mDv0CLWa5FETLfa6kZeBazJyk3OF9Fj1LdDTDpg1qIH8QvNwAwDLli3DsmXLBv2zbdu2Dfh9aWmp+gUREampzLXVRc6Vmty+oN/IjSiKfut9EUXRPS011p8rpWRx2dIJ4a3npf1uxlzr/xrILzSfliIiCim2zr5dcjUauclJjILRIKDD5kBtW4/f7lvT2oMOmwNGg4CcRA3CDQDkyFNT7LsJZgw3RET+VLEPcPYCsVlAfK4mJZjC+g7QlEdS/EHut8lNjIQpTKMfP1bX1FSZZxvFUmBiuCEi8ie53yanCPDnUugLuI9h8ONeN33NxBr2urhHbvYCTv9vYkj+wXBDRORPpV9KjxpNScm0WDHlXgauRb+NLG0yYIoBbG1A9UHt6iBVMdwQEfmLrbOv1yN/rpaVaLJiSr6XJiulZAZjX7As/UK7OkhVDDdERP5Svgtw2KR+m6QCTUsZ6zpA81RNm9/u2X93Yk3lXS09nmW4CVYMN0RE/nJmu/SYf62m/TYAMC4tBgBQ2dKNtm676vdr7+lFVUs3gL6l6JrJd4Wbc18Bjl5tayFVMNwQEfnLWVe40cH+KnER4UiPlQ4cPlGjft/NWdeUVHK0CfGRJtXvN6z0qYAlTuq7qfpG21pIFQw3RET+0NUEVJZIz/O1DzcAMC5Nmh466YepqZO10j00XSklMxiB3Kuk56U7tK2FVMFwQ0TkD6VfAhCB5PFAbIbW1QAACl1TU8f9EG6OV0v3mJAeo/q9PJLPvptgxnBDROQPp7ZKj2PmalpGf+Nd4eaEP8KN6x7yPTWXf430WLYT6PXfLs3kHww3RERqE0Xg5KfS83E3altLP+PT5XCjfs+N7kZuUicC0WmAvZO7FQchhhsiIrXVHpEOawyzAHlXaV2N2zjXcvC6th40ddhUu09Lp929Umq8XsKNIAAF35Gey6NqFDQYboiI1Hbyr9Jj/jVAeIS2tfQTZQ5DdoJUj5pTUydczcSZcRbEWsJVu8+ojWW4CVYMN0REatPhlJTMH303x1xTUoV6GbWRFVwPQABqDwOtlVpXQwpiuCEiUlNXM1C2S3o+7gZNSxmMHG7kAKKG49Wt0r30Fm4iE4GsGdJzjt4EFYYbIiI1nfobIDqkJeAJeVpXc5FLMqTAcaSqVbV7nKiWGpZ100zc39h50uOpT7WtgxTFcENEpKajf5EeJ9ymbR1DmJQZBwA4VtUGh1NU/PqiKOKYa+SmMC1W8ev7TJ4qPLWVS8KDCMMNEZFa7F19/TaXLNC2liHkJ0chItyILrsDZ+uVPyG8qqUbrd29MBoEjNH6TKnBZM4AotMBWzs39AsiDDdERGo5/Tlg7wBis4HMS7WuZlBGg4AJKk5NHa6UrjkuNRqWcKPi1/eZwQAU3iw9P/ahtrWQYhhuiIjUIk9JXbJA81PAhzMxQ5ouOlzZovi1D1ZI15Snv3RJnjI8/jHgdGpbCymC4YaISA0OO3D8I+m5TqekZHLwOFKpwsiNK9xMztJhv40s/2rAFAO0VwOVB7SuhhTAcENEpIZTW4HuZiAqFci5QutqhjUxUwoeRypbIYrKNhUfco0GTcnS8chNmBkY51o1dfQDbWshRTDcEBGp4eAfpccpdwEGHfaa9DMhPQZGg4CGDhtqWpVbMVTb1o2a1h4IAnBJho5HbgBg4nelx0MbpbPAKKAx3BARKa27FTi2WXo+5Z+0rcUDlnAjClwrmZTsu5GbicckRyHKHKbYdVUx/ibAFA20lAHle7SuhnzEcENEpLRjHwK93UDSON2ukrrQZFffzbfnFQw3FQEwJSULjwAm3Co9P/RnbWshnzHcEBEp7VvXlNTU/6PrVVL9XZoTDwD4urxZsWsedDcTB0C4AYDJd0mPhzcCjl5tayGfMNwQESmp6RxwZpv0PACmpGTTrQkAgG/Km+FUaKfiQxXStJSul4H3V3AdEJEIdNQBZ7drXQ35gOGGiEhJB34HQATGzAUS87WuxmMTMmJgDjOgpcuOsw2+71Rc09qNiuYuGARgSnaAhBtjODD5Tun51/+jbS3kE4YbIiKlOOx9PxRnLtG2llEKNxow1RVCvi5r9vl6+881AQAmpMciWu/NxP3NWCQ9HvsQ6GzUthbyGsMNEZFSTmyRNoKLSgEKb9G6mlG7NEeamiopb/L5WnK4mZmb4PO1/CpjmvTLYQO+3aB1NeQlhhsiIqXs/S/pcfq9QJhJ21q8MN0aD0CZkZt9gRpugL7RmwO/4543AYrhhohICdUHpUZiwQjMekDrarwir5g6Vt2GLpvD6+t02x3uZeABGW4m3wWERQC1R4CyXVpXQ15guCEiUsJXr0iPE78LJORqW4uXMuIikBFngcMp4usy76emvj3fgl6niNQYM7ITIhSs0E8i4qVl/ACw67ealkLeYbghIvJVS0Xfxm9XPqptLT66YkwSAOCr0w1eX2PfOakRd1ZeAoQA2efnIlf8QHo89iHQVKppKTR6DDdERL7a+Srg7AVy5wBZM7SuxidFBXK4qff6GvtKpVGfGTkBOCUlS70EKLgeEJ3A7te1roZGieGGiMgXrVXAvjel51cXa1uLAuaMTQYAfHO+BW3d9lF/3tbrxK4z0qiPHJQC1hU/lB4P/I7LwgMMww0RkS++XCWdI2W9Aij4jtbV+CwrPgJ5SZFwOEXsOTv6H+j7zjWi0+ZAcrQZl6Tr/CTwkRR8B0ibAtja2HsTYBhuiIi81VwO7F8nPb/uJwFzjtRIigqk0Zu/nxp9382OE9J01jXjkmEwBPj3w2AA5v5Yer5rLUdvAgjDDRGRt/62QtrsLe9qYMy1WlejmDljve+72XGiDgBwzfgURWvSTOGtfaM3O1/RuhryEMMNEZE3zn0FHPpfAAIw/xdaV6OoojFJEARpv5uK5i6PP1fb1o0jVdJhmVeNS1arPP8yGIC5T0nPd/5WWhlHusdwQ0Q0Wo5e4GPXdMXMxUDGVG3rUVhStBmX5SYCALYcqvb4c1+4pqQmZcYiOdqsSm2amHArkHMl0NsF/O05rashDzDcEBGN1s5XgOpvAUsccP0zWlejipunpAMAPj5Y5fFnPj1SAwCYWxgkU1IyQQBuWglAAA7+ESjfq3VFNAKGGyKi0ag7Dnzumoaa/wsgKkimXy5w02Qp3Ow714Tqlu4R39/R04vPj9cCAG6enKFqbZrInA5ceq/0/C+PA702Tcuh4THcEBF5qtcGbHwEcPQAY2+QDsgMUhlxEe5zoT45PPLU1N+O1qCn14ncpEhMygzwJeBDmfc8EJkE1B6WtgAg3WK4ISLy1KfPAJUHpOmoBS8HzdLvodzsGr35yzeVI773z/vPAwBun5YZuEcujCQqGbjlJen5jpeAqm+0rYeGxHBDROSJQ+8Bu9dKz//hNSAuS9t6/GDBtEwYDQL2nWvCserWId9X3tiJL05KzcT/Z5bVX+VpY9KdwITbpOM2/rgY6G7RuiIaBMMNEdFIynYDm1wHKc55Aii8WdNy/CUt1oIbJ6YBAN75qnTI9739d+nPrhqbDGtipB8q05AgALf/JxBnBZrOAu8vBURR66roAgw3RETDqTsO/GGhdMTC+JuCdnXUUJbMyQcgTTudb+q86M8b2nvwhz1lAICHrxnj19o0E5kI/NM7gCEcOPoX4LOfaV0RXYDhhohoKDVHgHW3Al1NQNZM4K63AGOY1lX51eX5ibiyIAl2h4h/33L8oj//1V+Po8vuwJSsOFwdLBv3eSJ7JnCbq6n4i18Be9/Uth4agOGGiGgw5XuBd24DOuqA9CnAPX8CTFFaV6WJH980AQYB+OCbSnz4bV9z8WfHavDu3nIAwLMLJgZvI/FQZiwCrnXtXrz5X4B9b2tbD7mF1v+CEBF54psNwAePSku+My8F7ntPmooIUdOs8Xj4mgKs3X4axRu+wbmGToQZBKz+20mIIvC9K3JxWV6Ifn/mPiWN7O15DfjwCaCnFbjysaBfSad3giiGVidUa2sr4uLi0NLSgtjYIN2LgYi809MGfPwUUPI/0u8LbwHufAMwR2tblw44nCIe+8PX2HzBjsVzC1Pw+vdmwRQWwhMBoigdovr3l6XfT7sHuO3XQLhF27qCzGh+fjPcEBGJInD8IynYtJQBEICr/wW47t+kgxMJAOB0ivjjvnJ88E0lep0ibpmcju8V5cFo4CgFRFHaKuCTfwNEB5A6UdoyIMjOHdMSw80wGG6IyE0UgbM7pA3ZSr+QXouzAv+wFsi7StvaKDCd/hx47yGpV8sQBsx+BLjm/wER8VpXFvAYbobBcENE6GmXlvDuexM47zoE0RAOXPkocM2TIds4TArpqJf6b47+Rfp9RAJw2YPA5Q8D0amalhbIRvPzWxfjra+++iry8vJgsVgwe/Zs7NmzZ9j3/+lPf8KECRNgsVgwZcoUfPTRR36qlIgCVnut1Cj8vw8CvxoHbHpECjZGs/RD57GvgXkrGGzId1HJwML/Ae79M5A8Xmo43vES8OvJwP8+BBz7CLCPfBgpeU/zkZsNGzZg0aJFWLt2LWbPno3Vq1fjT3/6E44fP47U1IsT7ldffYVrrrkGK1euxG233Yb169fjl7/8JQ4cOIDJkyePeD+O3BAFOUcv0FYJNJ4Bqr4Fqr+VzgCqPzHwfYkFwLR/lpbzxqRrUysFP6dDGsHZ+UrfKCEAmGKAvDlAzhWA9QogpTCkV+R5IqCmpWbPno3LLrsMr7zyCgDA6XTCarXi0UcfxVNPPXXR+xcuXIiOjg58+OGH7teuuOIKTJ8+HWvXrh3xfmqFG1tPG+oajg39hhG/zcP8uS+f9ejz3l/a27pFiF5/1iPDft7X75eK/6wG+fO+S6pY94jU/HdshM867UBvT98vh+vR3imd69PVLD12NwPtNUBbNSA6B79WSiGQeyWQP9fV6BnajbCiT/9OhB6fv1/VB4ETnwCntkr/rl4oIgFIyANiM6WgE5EoPYZHAGGRQJhZWoFlNAEQAMHQt+RcMGDgv89O6b8t0fV3rSi6/rsQpf+c5ee48D3yc2e//zadF7yOwa+LvuuaI5KQPuF2375fFxjNz29N97mx2WzYv38/li9f7n7NYDBg3rx52Llz56Cf2blzJ4qLiwe8Nn/+fGzatGnQ9/f09KCnp8f9+9bWoQ9/88XRk5tx3/6fq3JtIvKAEUAcgLjhRmHagJpPpF9EWkkwAgmZQ/xhDdBRA3T4tSLFTXOG438UDjejoWm4qa+vh8PhQFpa2oDX09LScOzY4KMg1dXVg76/urp60PevXLkSzz//vDIFD8MgGGFxBvn/BSn8P7nCaL9dof0/2SoLhG+u0O9Bfi64ngt9zwUBgqCLdsKAEHK7CvtIUO2/FdcIiNOJQUdd3CMjavycEXz4K2DwD0aYtN0bKuh3KF6+fPmAkZ7W1lZYrVbF7zNl0j9h76R/Uvy6RERENDqahpvk5GQYjUbU1Ayce6ypqUF6+uBDy+np6aN6v9lshtlsVqZgIiIi0j1Nx25NJhNmzpyJrVu3ul9zOp3YunUrioqKBv1MUVHRgPcDwKeffjrk+4mIiCi0aD4tVVxcjMWLF2PWrFm4/PLLsXr1anR0dGDJkiUAgEWLFiErKwsrV64EADz++OO49tpr8R//8R+49dZb8e6772Lfvn14/fXXtfwyiIiISCc0DzcLFy5EXV0dnn32WVRXV2P69OnYsmWLu2m4rKwMhn5nu1x55ZVYv349nn76afzkJz/BuHHjsGnTJo/2uCEiIqLgp/k+N/7GTfyIiIgCT8Adv0BERESkFIYbIiIiCioMN0RERBRUGG6IiIgoqDDcEBERUVBhuCEiIqKgwnBDREREQYXhhoiIiIIKww0REREFFc2PX/A3eUPm1tZWjSshIiIiT8k/tz05WCHkwk1bWxsAwGq1alwJERERjVZbWxvi4uKGfU/InS3ldDpRWVmJmJgYCIKg6LVbW1thtVpRXl7Oc6tUxO+zf/D77B/8PvsPv9f+odb3WRRFtLW1ITMzc8CB2oMJuZEbg8GA7OxsVe8RGxvL/3D8gN9n/+D32T/4ffYffq/9Q43v80gjNjI2FBMREVFQYbghIiKioMJwoyCz2YwVK1bAbDZrXUpQ4/fZP/h99g9+n/2H32v/0MP3OeQaiomIiCi4ceSGiIiIggrDDREREQUVhhsiIiIKKgw3REREFFQYbhTy6quvIi8vDxaLBbNnz8aePXu0Lino7NixAwsWLEBmZiYEQcCmTZu0LikorVy5EpdddhliYmKQmpqKO+64A8ePH9e6rKCzZs0aTJ061b3RWVFRET7++GOtywp6L774IgRBwBNPPKF1KUHlueeegyAIA35NmDBBs3oYbhSwYcMGFBcXY8WKFThw4ACmTZuG+fPno7a2VuvSgkpHRwemTZuGV199VetSgtr27duxdOlS7Nq1C59++insdjtuvPFGdHR0aF1aUMnOzsaLL76I/fv3Y9++fbj++uvx3e9+F4cPH9a6tKC1d+9evPbaa5g6darWpQSlSZMmoaqqyv3ryy+/1KwWLgVXwOzZs3HZZZfhlVdeASCdX2W1WvHoo4/iqaee0ri64CQIAjZu3Ig77rhD61KCXl1dHVJTU7F9+3Zcc801WpcT1BITE/HSSy/h+9//vtalBJ329nbMmDEDv/3tb/Gzn/0M06dPx+rVq7UuK2g899xz2LRpE0pKSrQuBQBHbnxms9mwf/9+zJs3z/2awWDAvHnzsHPnTg0rI1JGS0sLAOkHL6nD4XDg3XffRUdHB4qKirQuJygtXboUt95664C/q0lZJ0+eRGZmJsaMGYN7770XZWVlmtUScgdnKq2+vh4OhwNpaWkDXk9LS8OxY8c0qopIGU6nE0888QTmzJmDyZMna11O0Dl48CCKiorQ3d2N6OhobNy4ERMnTtS6rKDz7rvv4sCBA9i7d6/WpQSt2bNnY926dSgsLERVVRWef/55XH311Th06BBiYmL8Xg/DDRENaenSpTh06JCmc+fBrLCwECUlJWhpacGf//xnLF68GNu3b2fAUVB5eTkef/xxfPrpp7BYLFqXE7Ruvvlm9/OpU6di9uzZyM3NxR//+EdNplkZbnyUnJwMo9GImpqaAa/X1NQgPT1do6qIfLds2TJ8+OGH2LFjB7Kzs7UuJyiZTCaMHTsWADBz5kzs3bsXL7/8Ml577TWNKwse+/fvR21tLWbMmOF+zeFwYMeOHXjllVfQ09MDo9GoYYXBKT4+HuPHj8epU6c0uT97bnxkMpkwc+ZMbN261f2a0+nE1q1bOXdOAUkURSxbtgwbN27EZ599hvz8fK1LChlOpxM9PT1alxFUvvOd7+DgwYMoKSlx/5o1axbuvfdelJSUMNiopL29HadPn0ZGRoYm9+fIjQKKi4uxePFizJo1C5dffjlWr16Njo4OLFmyROvSgkp7e/uA/ws4e/YsSkpKkJiYiJycHA0rCy5Lly7F+vXr8f777yMmJgbV1dUAgLi4OERERGhcXfBYvnw5br75ZuTk5KCtrQ3r16/Htm3b8Mknn2hdWlCJiYm5qF8sKioKSUlJ7CNT0JNPPokFCxYgNzcXlZWVWLFiBYxGI+6++25N6mG4UcDChQtRV1eHZ599FtXV1Zg+fTq2bNlyUZMx+Wbfvn247rrr3L8vLi4GACxevBjr1q3TqKrgs2bNGgDA3LlzB7z+9ttv4/777/d/QUGqtrYWixYtQlVVFeLi4jB16lR88sknuOGGG7QujWjUzp8/j7vvvhsNDQ1ISUnBVVddhV27diElJUWTerjPDREREQUV9twQERFRUGG4ISIioqDCcENERERBheGGiIiIggrDDREREQUVhhsiIiIKKgw3REREFFQYboiIiCioMNwQUUDYtm0bBEFAc3Oz1qUQkc5xh2Ii0qW5c+di+vTpWL16NQDAZrOhsbERaWlpEARB2+KISNd4thQRBQSTyYT09HStyyCiAMBpKSLSnfvvvx/bt2/Hyy+/DEEQIAgC1q1bN2Baat26dYiPj8eHH36IwsJCREZG4q677kJnZyfeeecd5OXlISEhAY899hgcDof72j09PXjyySeRlZWFqKgozJ49G9u2bdPmCyUiVXDkhoh05+WXX8aJEycwefJkvPDCCwCAw4cPX/S+zs5O/OY3v8G7776LtrY23HnnnfiHf/gHxMfH46OPPsKZM2fwj//4j5gzZw4WLlwIAFi2bBmOHDmCd999F5mZmdi4cSNuuukmHDx4EOPGjfPr10lE6mC4ISLdiYuLg8lkQmRkpHsq6tixYxe9z263Y82aNSgoKAAA3HXXXfjv//5v1NTUIDo6GhMnTsR1112Hzz//HAsXLkRZWRnefvttlJWVITMzEwDw5JNPYsuWLXj77bfxi1/8wn9fJBGphuGGiAJWZGSkO9gAQFpaGvLy8hAdHT3gtdraWgDAwYMH4XA4MH78+AHX6enpQVJSkn+KJiLVMdwQUcAKDw8f8HtBEAZ9zel0AgDa29thNBqxf/9+GI3GAe/rH4iIKLAx3BCRLplMpgGNwEq49NJL4XA4UFtbi6uvvlrRaxORfnC1FBHpUl5eHnbv3o3S0lLU19e7R198MX78eNx7771YtGgR3nvvPZw9exZ79uzBypUrsXnzZgWqJiI9YLghIl168sknYTQaMXHiRKSkpKCsrEyR67799ttYtGgR/uVf/gWFhYW44447sHfvXuTk5ChyfSLSHncoJiIioqDCkRsiIiIKKgw3REREFFQYboiIiCioMNwQERFRUGG4ISIioqDCcENERERBheGGiIiIggrDDREREQUVhhsiIiIKKgw3REREFFQYboiIiCio/H+f8zG6L4N+wQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(guess_dynamics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that our guess pulses are too disjoint to implement the STIRAP scheme.\n",
    "Thus, the Stokes pulse has no effect, whilst the pump pulse merely transfers\n",
    "population out of $\\ket{1}$ into $\\ket{2}$ and back again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to invoke `optimize_pulses`, we must define the required parameters\n",
    "for each control, a pulse shape (used to ensure that the controls remain 0 at\n",
    "$t=0$ and $t=T$), and the parameter $\\lambda_a$ that determines the overall\n",
    "magnitude of the pulse updates in each iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.455244Z",
     "iopub.status.busy": "2024-06-03T14:29:08.455137Z",
     "iopub.status.idle": "2024-06-03T14:29:08.457235Z",
     "shell.execute_reply": "2024-06-03T14:29:08.456924Z"
    }
   },
   "outputs": [],
   "source": [
    "def S(t):\n",
    "    \"\"\"Scales the Krotov methods update of the pulse value at the time t\"\"\"\n",
    "    return krotov.shapes.flattop(\n",
    "        t, t_start=0.0, t_stop=5.0, t_rise=0.3, func='sinsq'\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.458641Z",
     "iopub.status.busy": "2024-06-03T14:29:08.458539Z",
     "iopub.status.idle": "2024-06-03T14:29:08.460482Z",
     "shell.execute_reply": "2024-06-03T14:29:08.460170Z"
    }
   },
   "outputs": [],
   "source": [
    "pulse_options = {\n",
    "    H[1][1]: dict(lambda_a=0.5, update_shape=S),\n",
    "    H[2][1]: dict(lambda_a=0.5, update_shape=S),\n",
    "    H[3][1]: dict(lambda_a=0.5, update_shape=S),\n",
    "    H[4][1]: dict(lambda_a=0.5, update_shape=S)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now run the optimization, using the phase-sensitive functional $J_{T,\n",
    "\\text{re}} = 1 - \\Re\\Braket{\\Psi(t)}{\\Psi_{\\tgt}}$, printing the integrated\n",
    "pulse update for each control in each iteration. The optimization stops when\n",
    "$J_T$ falls below $10^{-3}$, changes by less than $10^{-5}$, or after at most\n",
    "15 iterations. We also check for monotonic convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "16"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:08.461832Z",
     "iopub.status.busy": "2024-06-03T14:29:08.461726Z",
     "iopub.status.idle": "2024-06-03T14:29:29.129548Z",
     "shell.execute_reply": "2024-06-03T14:29:29.129125Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter.      J_T   g_a_int_1   g_a_int_2   g_a_int_3   g_a_int_4    g_a_int          J  Delta J_T    Delta J  secs\n",
      "0     1.01e+00    0.00e+00    0.00e+00    0.00e+00    0.00e+00   0.00e+00   1.01e+00        n/a        n/a     0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1     6.72e-01    8.60e-02    2.87e-04    8.17e-02    3.72e-04   1.68e-01   8.40e-01  -3.37e-01  -1.68e-01     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2     4.02e-01    7.20e-02    4.21e-04    6.22e-02    4.20e-04   1.35e-01   5.37e-01  -2.70e-01  -1.35e-01     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3     2.22e-01    4.91e-02    4.64e-04    3.99e-02    3.88e-04   8.98e-02   3.12e-01  -1.80e-01  -8.98e-02     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4     1.17e-01    2.89e-02    3.87e-04    2.29e-02    3.01e-04   5.25e-02   1.69e-01  -1.05e-01  -5.25e-02     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5     6.00e-02    1.56e-02    2.69e-04    1.23e-02    2.10e-04   2.84e-02   8.84e-02  -5.69e-02  -2.84e-02     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6     3.05e-02    8.08e-03    1.71e-04    6.37e-03    1.39e-04   1.48e-02   4.52e-02  -2.95e-02  -1.48e-02     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7     1.54e-02    4.08e-03    1.06e-04    3.24e-03    9.10e-05   7.51e-03   2.30e-02  -1.50e-02  -7.51e-03     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8     7.85e-03    2.04e-03    6.65e-05    1.63e-03    5.99e-05   3.79e-03   1.16e-02  -7.59e-03  -3.79e-03     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9     4.02e-03    1.02e-03    4.31e-05    8.14e-04    4.01e-05   1.91e-03   5.94e-03  -3.83e-03  -1.91e-03     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10    2.09e-03    5.05e-04    2.88e-05    4.07e-04    2.73e-05   9.68e-04   3.05e-03  -1.94e-03  -9.68e-04     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11    1.10e-03    2.52e-04    1.99e-05    2.03e-04    1.88e-05   4.94e-04   1.59e-03  -9.87e-04  -4.94e-04     1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12    5.90e-04    1.26e-04    1.40e-05    1.02e-04    1.31e-05   2.54e-04   8.45e-04  -5.09e-04  -2.54e-04     1\n"
     ]
    }
   ],
   "source": [
    "opt_result = krotov.optimize_pulses(\n",
    "    [objective],\n",
    "    pulse_options,\n",
    "    tlist,\n",
    "    propagator=krotov.propagators.expm,\n",
    "    chi_constructor=krotov.functionals.chis_re,\n",
    "    info_hook=krotov.info_hooks.print_table(\n",
    "        J_T=krotov.functionals.J_T_re,\n",
    "        show_g_a_int_per_pulse=True,\n",
    "        unicode=False,\n",
    "    ),\n",
    "    check_convergence=krotov.convergence.Or(\n",
    "        krotov.convergence.value_below(1e-3, name='J_T'),\n",
    "        krotov.convergence.delta_below(1e-5),\n",
    "        krotov.convergence.check_monotonic_error,\n",
    "    ),\n",
    "    iter_stop=15,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "17"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.131611Z",
     "iopub.status.busy": "2024-06-03T14:29:29.131435Z",
     "iopub.status.idle": "2024-06-03T14:29:29.134135Z",
     "shell.execute_reply": "2024-06-03T14:29:29.133861Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2024-06-03 10:29:08\n",
       "- Number of objectives: 1\n",
       "- Number of iterations: 12\n",
       "- Reason for termination: Reached convergence: J_T < 0.001\n",
       "- Ended at 2024-06-03 10:29:29 (0:00:21)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We dump the result of the optimization to disk for later use in the [Ensemble\n",
    "Optimization for Robust Pulses](08_example_ensemble.ipynb).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.136014Z",
     "iopub.status.busy": "2024-06-03T14:29:29.135896Z",
     "iopub.status.idle": "2024-06-03T14:29:29.137898Z",
     "shell.execute_reply": "2024-06-03T14:29:29.137629Z"
    }
   },
   "outputs": [],
   "source": [
    "if not os.path.isfile('lambda_rwa_opt_result.dump'):\n",
    "    opt_result.dump('lambda_rwa_opt_result.dump')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimized complex pulses look as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "18"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.139511Z",
     "iopub.status.busy": "2024-06-03T14:29:29.139395Z",
     "iopub.status.idle": "2024-06-03T14:29:29.327709Z",
     "shell.execute_reply": "2024-06-03T14:29:29.327446Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pump pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stokes pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "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",
    "    opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist)\n",
    "print(\"Stokes pulse amplitude and phase:\")\n",
    "plot_pulse_amplitude_and_phase(\n",
    "    opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the complex controls in the rotating frame back into the\n",
    "real-valued pulses in the lab frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.329382Z",
     "iopub.status.busy": "2024-06-03T14:29:29.329269Z",
     "iopub.status.idle": "2024-06-03T14:29:29.504967Z",
     "shell.execute_reply": "2024-06-03T14:29:29.504672Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Physical electric pump pulse in the lab frame:\n"
     ]
    },
    {
     "data": {
      "image/png": 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CQgKOHDmCI0eO4PTp03Z3jShw27bJG1PdukC/ftXfR1Vyliyxrl8UGrxevapixlCU0yo2x45JGxUFJCQEfh01FHXkiFRDyTVCKti89NJLKCgowNChQ9G8efPyjw8++MDurhEFbs0aafv3B6Kjq7/PZZdJu3MncPSoNf2i0FBYKMuygfCo2Kif/8aNAztOQUlOlsn6Xq8+tEWuEFLBRtO0aj8mVFweSxRq1q6VdsCAmu+TlCS7EQPA6tXm94lCh5pfExcnH0ZxasWmYrAJRmSkPvmYw1GuElLBhsiVVMWmtmADAJdcIi2DDVVkxsRhIDQqNsHiBGJXYrAhslNxMbB9u9zu37/2+w4cKO3335vbJwotZgUbt1dsAE4gdikGGyI77dghY/xNm+ovsjVRFZ2NG515fg/ZI9wqNmrysBHBhscquBKDDZGdtm2Ttpbds8t16iTb3J88CRw4YGq3KISwYhM4VmxcicGGyE7+BJvoaP1+GRmmdYlCjAo2tZyZFxCnVmyMDDbcfdiVGGyI7ORPsAGAnj2lZbAhhRWbwHHysCsx2BDZicGGghVuc2xUsGnUKPhrcSjKlRhsiOxy/Lj+gtqli2+P6dFDWgYbUswONqdPA6Wlxl47GGYMRR0/Ln9PcgUGGyK7qGXe6emAr4ezqmCTlaWfD0ThzaxgU/Fn0ilVG00zNtg0aKBvanj4cPDXI0dgsCGyi7/DUID8Fq0Of9282fg+UegxK9hERQH16sltp8yzKS4GSkrkthHBxuPhkm8XYrAhsksgwQbgPBuqzKxgA+gTiJ1SsVF72MTGyqGxRuA8G9dhsCGyS6DBhvNsqCIzg40ajiosNP7agTDqAMyKGGxch8GGyC4//iitrxOHFRWE1OMpfHm9+jBRuAUbo3AoynUYbIjsUFAA5OfL7fbt/Xts587S7twpkykpfJ08qR+vwWATGFZsXIfBhsgOe/dKm5wMJCT499h27YDISHlT42+Z4U0NQ8XF6at7jBQOwYYVG9dhsCGyw5490rZr5/9jY2KAtm3lNoejwpuZ82sA5wYbIzbnU1ixcR0GGyI7qIpNIMEGqDwcReErXIONGUNR2dkc2nUJBhsiO6iKjaq8+EsFG1ZswpvapDFcgo1a7m1GsDl92jnL2ikoDDZEdghmKAoAOnWSlsHGONnZwD33yD5Bd90F5OXZ3aMLM7tio45VcEqwMWMoqk4dfb8e7j7sClF2d4AoLAUbbFixMdb+/cDQoUBmpvx582bgm2+AH36QCd5OZdVQlFMqGapCZWSwAaRqc+KEzLNR/7coZLFiQ2S1U6f0iYrBVmxyc/U3NwpMWRkwbpyEmg4dgFdfBdq0kbDzm9/Y3bvahdscGxVskpKMvS4nELsKgw2R1fbtk7Zhw8BfoOvX15epcgJxcF59FVi9Wr6nX38NTJwIfPKJnJX0ySfAd9/Z3cOaMdgYg8HGVRhsiKwW7MRhhfNsgnf6NPDYY3L78cflpHVA5tlMmCC3n3rKjp75JpyCTWmpHIIJGP/3ZbBxFQYbIqsFO79GUcFm9+7grhPO5syRCaPp6TJxuKKHHpL2s8+AQ4es75svwinYqL+rx6NPajYKg42rMNhQaDp1CvjnP4Fhw4Bf/hJYt87uHvnOqGCjjmL46afgrhOuNA147jm5/fvfy4nRFXXqBAweLPf78EPr++cL9WZv9NCM4sRgk5goO28bicHGVRhsKPScOAFcfjkwdSqwdCnwwQfAwIHA/Pl298w3+/dL26ZNcNdhsAnOqlUyjFe3rj7sVNXYsdK+955l3fKLVRWb0lKgpMSc5/CVWfNrAAYbl2GwodCiacDttwNr18oL3NNPAyNHysqWsWP1HX2dTC0pbtkyuOuoYLNnj34QIvnu3XelHTOm5qGNW26RoY/16525x4nZwabiOWZ2V22sCjbcfTjkMdhQaHnzTeCLL2TYYMkSGUL49FOp4Jw5A/z2t3b3sHaaBmRlye1gg02rVlKSP33amW+6TlZaqg8v/epXNd8vORno3Vtuf/21+f3yh9cr1UvAvGATGQnUqye37Q42Zoa4Zs2kLS3VAxSFLAYbCh0nTwJ/+YvcfvxxoFcvuR0VBbz8srQLFzp7vs2JE/rKjtTU4K4VHS3hBuBwlL8WL5Y3sKZNJRTX5uqrpf3qK/P75Y+TJ/VKnVnBBnDOPBszKzaxsfoxDRyOCnkMNhQ6XnpJtrlv1w743e8qf61DB30+xMyZ1vfNV2oYqnFjID4++Otxnk1g1DDUrbdKIK7N8OHSLl3qrGEKVcGIi5MPszhl92Gzh904z8Y1GGwoNJw9C8yaJbf/8hcgJub8+6jlufPm6YflOY1Rw1BKxXk25JszZ4AFC+R2bcNQSv/+8vOWl+es77PZb/RKOFRsAAYbF2GwodAwb57sJZKcrFdmqurRQ4anzp6VlVJOpCo2aWnGXE8tGWfFxncrV8pwYEqKhJYLiYsD+vWT26tWmds3f4RbsGHFhnzEYEOh4ZlnpL3vvtrL7nfcIa0aanAasyo2DDa+W7RI2quvlhVPvhg8WNpvvzWnT4EIt2DDig35iMGGnG/TJjnLJzoauP/+2u97003Srl4N5Oeb3zd/GV2x4ZJv/y1cKO011/j+mEsukXbtWuP7EygGG2Mx2LgGgw0539y50o4apS/LrEnLlnLOj9cLfPml6V3zm9EVm1atZPLrmTN8QfbFgQNyaGhkpOxa7au+faX98UegqMiUrvkt3IINh6LIRww25GxlZfqw0u23+/aYkSOl/e9/zelTMFSwMapiExXFJd/+UNWagQOBBg18f1xKinx4vUBGhhk981+4BRtWbMhHDDbkbMuWAUeOyIuZ2k/kQtTy3GXLnDU8U1amH6ZoVMUG4DwbfwQyDKX06SPthg3G9ScYVgUbtSuzncFG06yr2Bw+7KzXDfIbgw052zvvSPuLX1S/xLs6/fvL+T/HjgFbt5rXN3/l5gLnzskwSPPmxl2XS759U1IiYRcILNio4ahwCzZOqNgUFcn/HcC8ik3TpjKZvKzMmfPzyGcMNuRcZ84An3wit2+7zffHxcQAQ4bI7aVLje9XoNTE4ZQUY08n5pJv33z7rSzzbtZM5mH5q3t3abdtM7RbAVNDM+EQbNTfNTbWmI0tqxMVJeEG4HBUiGOwIedaskR+U2vRQuZE+GPoUGm//97wbgXM6InDCoeifKOGofxZ5l3RRRdJ++OP8lu93ayu2Ni583DFv2sg/3a+4jwbV2CwIeeaN0/a0aOBCD9/VC++WNoffjC0S0ExeuKwooLN3r2cG1AbtX9NIMNQANCmjeyhdOYMsG+fcf0KVDgNRZk9cVhhsHEFBhtyprIy4LPP5PaNN/r/+D59ZLgnO1ufsGs3NRRldMUmPV1f8u2Uv6vTZGYCO3ZIQL7qqsCuERkJdOokt7dvN65vgQqnYGPV35XBxhUYbMiZvvsOOHpUXsjUfBl/1K0LdO0qt9esMbZvgTKrYhMVBbRuLbc5gbh6ahjq4ouDe3NUP1N2BxuvV06KB8Ij2LBiQ35gsCFnUsNQ118vOw4HQg1HOSXYmFWxAbgy6kKCWeZdkZpnY3ewOXlSH3a0KticOQOUlpr7XDVRFRsGG/IBgw05j6YB8+fL7UCGoZQBA6R1yjwbsyo2gL4yisHmfKWl+uo4o4KN3Suj1Bt9XJx5q4SUhAT99smT5j5XTaxaAcZg4woMNuQ8mzfL1vfx8cCIEYFfR1VsNmzQ98CwS0mJ7GMDmBNsuDKqZqtWyeq65GQ5/T0YKtjs2mXvz5RVc04AqZiq8GTXcJT6+/qzW3QgGGxcgcGGnEcNQ40YAdSpE/h1OnaUXVNPnbL/N2w1qTc+HmjUyPjrs2JTs4rLvP1dXVdVq1byM1laau/32spgA9i/+7BV84lUsFGbaVJIYrAh51HDUKNHB3ediAigXz+5vW5dcNcKVsVhKDP24VDBhku+zxfsMu+KIiKALl3ktp3zbKwONnZPILYq2DRpIqvfNE2vsFLIYbAhZ9m3D9iyRV5c1GGWwVA7zG7ZEvy1gmHmxGFAP+X79GmW0SvKypJqXTDLvKtSwWbHDmOuFwi7go1dm/SpYGP2UFREhH7cCf8fhSwGG3IWNQx12WXGrIBQ2+DbHWzMnDgMVD7lm8NROlWt6d/fuCHAihsi2sWqybSKUyo2ZgcbgPNsXIDBhpyl4m7DRqgYbDTNmGsGwuyKDcAzo6pj1DLvipwwn8mq5c8Kg42znDghqz03bpQqLVXCYEPOkZurn+1kVLDp3FmqGSdO6FUTO5hdsQG4l01VpaVy3hhgbLBxwvc5nObYaBqDjbJ3L3DTTVJ9HDhQdlhv3Bi4+25n9tcmAQWbJUuWYNCgQRg4cCAee+wxnD171uh+UThasEBexPr2NS4AxMRIuAHsHY5SFRszg40TKglO8v33su9KkybyBmCUtm2lzc21b1+XcAo2FTcGDOdgs2QJ0Lu3VLW9XnktadxYVn2+8QbQoQMwa5a9lWmHCCjYTJo0CX/6058wa9YsHDhwAH//+9+N7heFIzUMFcymfNXp0UNaO4ONWSd7V+TEoSivF3j1VdlTqHlz+S3zpZcAK34Z+vxzaY1Y5l1RgwbyhgLYN88mnIKNqtZERAD16pn/fE4MNmvWADfcIN//QYNkQnxmJpCXB6xcKZuRFhcDv/sdMGFC2A9PBfS/vU6dOhg1ahT69u2LV199FUtUuZcoUAUF+u6wRgcbNc9m82Zjr+urggL9DcGqoSgn/NZWXCyh4t575YX5yBGZF/Cb3wCXXmr+G4cKNjfcYPy17a6OWXV2kuKEYNOggTlbJVTltGBz/Dhwyy0SVq69Fli2TN8o0uOR/0vffw88/bSsJv3Pf+R+RUX29ttGAQWb/Px8fPTRR9iyZQvOnTuHUrvODyH3+PJL+S2+Y0d96Mgodq+MUtWapCQ5nNMs6enywnb6NHD4sHnP44uyMpkLsHix/J1nzpS9hP7v/+QNas0aYOhQCTtm2LVLKlfR0cDw4cZf3+5gE04b9Fk5vwZwXrD5wx9kg88OHYD335fh9aoiIoDf/15WASYkAMuXy7wyOw8utVFAweahhx7CokWLMHHiRCQnJ2PHjh34xS9+gcceewzz1eZqRP4waxgK0Ieidu+2p0RrxcRhQF7w0tPltt3DUf/4B/D117JL75IlwEMPydypBx8E1q+Xfv70EzBmjDnDUp99Ju3ll+vVBiPZPewXjkNRVgebo0flKBQ7rVsHzJ4tt996q/K5XdUZNkx+mUhMlKNEhg/Xv39hJKBg8/vf/x5vvPEG1qxZg4KCAvz444+4/fbbERUVhY8//tjoPpLbnTmjL8s1I9g0bSpzIrxe4Mcfjb/+hVix1Ftxwoqd3buBxx+X2y+/rJ/ZpbRtK6Gnfn158Z02zfg+mDkMBdhbsfF6rduJVwmnYJOUpFdFzKoo+urRR6W9/XaZn+aLAQNkuCopSSqjI0bYt7GiTfwKNsOGDcNC9QZUQXp6OkaOHIlp06Zh7ty5hnWOwsTixTIe3KKF/FZvNI9H3y3WjmBjVcUGsL+SAEjpvLRUSuG33Vb9fTp0kN9AAeDf/9Y30jPC0aPAd9/J7euvN+66FdkZIAsK9DlU4bDzsNXBxuNxxnDUxo3AF1/IMNP/+3/+PbZ3bwk3jRoBa9dK5SaMwo1fwWb9+vVo9b/dTQ8ePFj++ddffx233367oR2jMPLee9Lecouxq1cqUvN23B5s7K7YrF0r1ZKICJlPU9tkzxtvlFUcAHDffcZNdvz4Y6lq9OqlD80ZTQXInByZJG0lNQxVpw4QG2vNc9pZsbHqZO+KnBBsVNXzl7+UXwT81aOHDAMnJcn/yzCq3Pj1LlJaWoqE/43xdevWDfv27QMAXHLJJViqVrQQ+aO4WPavAYCxY817HjuDjZVDUXZPav3Xv6S9/XaZCH4hTzwh4ePgQeBvfzOmD++/L62ZP09JSXq1xOol31bPrwHCaygKsD/YHDigzzv8618Dv07PnhJuGjaUYanhw6Wi6XJ+BZv27dtj7dq1KCgoQHFxMQr+l/4SEhJwXC0/JPLH55/LBlNt2sh5PmYJl4pNxWBj9ZLvQ4f0k9n/8AffHlOvnszDAYDnnpPyezCys2VfDwC49dbgrnUhaqO+/fvNfZ6q7Aw2p04B585Z97yAvcEmO9u656xIDdNeeaU+jB6oXr1kKw1VuRk0yPqfWYv5FWx++9vfYuLEibjiiivQvXt3vPHGGwCAb7/9Fk2bNjWlg2SwEyekVP+3vwHjxkmZ8667gGeflTcVq98M331X2rFjzd2jQgWbn36yZnM4xeu1ZnM+pXVrGQYqLrZ+4uOrr8oy7yFDgK5dfX/c1VfLv7/XK3vceL2B9+GDD+RnePBg87/f6tDRAwfMfZ6q7Ag2FVfjWL3bsh3BJjVV2kOHrHtOxevVV0L9+tfGXLNXL5mo37KlTO7v1w/46itjru1AfgWbu+++G6+99hrGjBmDJUuWYNeuXWjTpg0mTpyIX/ziF2b18TwvvPACWrVqhbi4OAwYMABr16617LlD1rffAtddJ9vLjxkj47fvvitvBG++Kctw+/SR/wBz5gT35uKrY8f0SaO/+pW5z5WaKtWBc+esHTrIz5eJtBUnJJqp4pJvK4ejSkuB116T25Mm+f/4mTPlzXPNGvl5DJSar/XLXwZ+DV/ZFWysPtkbkLk8aj6P1cNRVq8AA/Tqqh3nyy1bJsPXiYnGrhLt3Fk28uvTR157r7lGtmFw4UZ+fs/UvOmmmzB16lQ0atQICxcuxD//+U+8/vrrePLJJ83o33k++OADTJkyBdOnT8fGjRvRo0cPjBgxAnl5eZY8v180TX5ocnKAnTtl59t9+6z9QVq+XPbyGDJENsE7d05+wO++G3jqKanUTJ8uq0diY6WPEyYAl1xi/k69//mPVE969Qq+3HohHg/QqZPctnI4Ss2vSUmRzeKsYMfKqM8+kwpRs2aBvRinpADqaJapU+WF118bNsgeOdHREt7NpoJNhYUUlrD6ZG/Frnk2dlRs7Aw2qlrzq18B8fHGXrtFC6nc3HOPvD89/bTsYvzqq7LthktEBfXgqCiMseIFpIKnn34aEydOxJ133gkAePnll/Hf//4Xb775JqZOnXre/UtKSlBSYZOlQrP+U958s1QCTp2Sj6IieQGoaWinRQtJzlddBYwaZez8C02T1P/oo/p8g+ho4M47ZXdK9QZf1fHj8gP+xBPym/PFFwMvviiPM5qmAa+8Irfvucf461enc2d549uxw5z9cqpj5fwapX17WUJvZcVGVUrGjw88wP32t/KivnWr7G3z6qv+PX7WLGnHjAGSkwPrgz9UZSwchqIAqSDk54dXsDl0SKrXZq3WrOr0aX0xxfjx5jxHXJy89o4aJUO/Bw/KsSd//SswerRMMO7VS4at1H4+mibB59gxeZ+orq36uWXLZA8xO2ghpKSkRIuMjNTmzZtX6fN33HGHdsMNN1T7mOnTp2sAzvsoKCgwtnOdO2ua/POf/xEZqWkNG2pas2aaVrfu+V/3eDTtqqs07b33NO3MmcD74PVq2ldfadqgQfq1Y2I07Te/0bSDB32/Tna2pl17rX6NKVM0raws8H5VZ8UKuXbduppm9L9FTf7xD3nOceOseT5N07RnnpHnHDPGuud8+ml5zltuseb5Cgo0LTZWnjMjI7hrffut/n/ihx98f1xent6H1auD64Ovtm6V52vY0JrnUyZOlOd99FFrn7d3b3neL7+09nmbNJHn3brVuuc8e1bTIiLkeXNyrHveBQvkOdPS5PXcbMXF8hqVmlr9e1edOvr/K38/TPj3Kigo8On9O6iKjdWOHj2KsrKy8yYqN23aFDt37qz2MdOmTcOUKVPK/1xYWIg0M357fvFFmWdQp46UDxMSpHRbv778ueLE2BMngO3bZd7Ll19Ku3ixfDRpAkycKAna18mPZ8/KapSnn5ZDBgEZVrrnHuBPf9InwvkqJUVWKz3xBPDww3LdY8eA118Hogz6kVHVmrFjzdnyvjp2rIyycqm3YvVQ1IIFsvV8p076uVyBGjxYflOdM0d+m1y7Vs6/upDXXpM+9O0rO69aQVVsfv5Z9gdR5ymZzY45NoA9m/Rpmj0Vm6goOY0+O1uqrs2bW/O8aon36NHWHPhZpw7wwAPyf23lSnn+NWukalpSIqMPFUVFyaZ/SUnnt1U/p4Zq7RBocjp16pR26NCh8z6/bdu2QC95QdnZ2RoA7fvvv6/0+T/+8Y9a//79fbqGr4nPUnv3atrf/qZpLVroaTciQtNGjdK0zz+XVF2V1yuJ+JFHKqftuDhNe/BBqboYYc4cqTipSse5c8FfMzNT06Kj5Zrr1gV/PV/t3Kn/FmLFb0OaJpUaQH4rssru3fKc8fHGV9qqc9118nyPPGLM9XJzNS0x0ffvW2Gh/lv9nDnG9MFXjRrJ827ebN1zXnGFPOc771j3nJqmaTfcIM/7yivWPWdxsf7advKkdc+raZp28cXyvB9/bM3znT2r/zwtW2bNc9akrEzTjh/XtH37pNp/5Ij8P7PqdbMGvr5/BzRw+PHHH6N9+/a47rrr0L17d6xZs6b8a2buQNy4cWNERkYiNze30udzc3PRrFkz057XdG3ayHyYAweATz4BrrhCxnUXLABGjpT0O2CAVDfGjZPlsc2aAd26AY88IuPAyclSXdm/X3Z8NWoFzh13yPLwqCjgnXdkh9hgl4Q/9ZRUmYYONecIhZq0aSO//Z86Zd3GW3ZUbFq3lnkup0/rz2+W48f1ZaNG7RuTnAzMmCG3//xnICOj9vv/+98y96NdO3M35auOHSuj7JpjY8fkYVWtiYyUU+KtZPUE4m+/lcp4o0bApZda85w1iYiQn6/WreW1q2lTGYWwoopkgICCzeOPP44NGzYgIyMDs2fPxl133YV3/7cfiWbiPigxMTHo06dPpV2OvV4vli5dioG+HhDmZFFRwE03yWZK27fLZMq0NJm0tXat7Kj67rvyRpKXJ8NN118PvP22vIH9/e8SeIw2ejQwd678sL/+uiwND/Tf+cgRfVmwv+efBCs6Wv6jAtYN09gxeTgqSj9aoYYhWsN89ZWstOvateZJ6YG47z752S4pkcBU094pu3bpIeiJJ6xbeaYw2Jir4jCU1W+q6pcRq4KN2tzyhhuMG/IPUwF9986ePVs+z6VPnz5YuXIlbrzxRuzZswcek3/4pkyZgvHjx6Nv377o378/nnnmGRQXF5evknKNLl1kJ9Znn5U3px075MUzIkL2Y+nWTc4CMXo5YE1uvVUC1oQJ0q86dYB//MP/F5uZM+U6F18slSmrdeggq4V275aKkZlKS4HDh+W2lRUbQELGjh3ys3P11eY9jzoU97rrjL2uxyO7r/bsKf9WN98sFcyKP+9FRbICqrRU/o4Wr9AEoM+zsXLJd7gGG6tZXbFR/5dGjrTm+VwsoGCTnJyMLVu2oPv/JgomJSVh8eLFGD9+PLZs2WJoB6u69dZbkZ+fj4cffhhHjhxBz549sWjRIvfufOzxyKRXNfHVTuPHyzDOb34DPPmklIcfe8z3cLN7t4QiQIbN7ChrqkrG7t3mP1dOjlS2YmNlUriVVPXEzIqN16tvsHjNNcZfv1Ej4NNPZR+mxYslCM+eLX+3Awdk2GnrVimTv/66PT9PVldsysr0ybsMNuayMtjs3y9V5MhIe37hc5mAgs3bb7+NqCqlspiYGLz33nuYPHmyIR2rzeTJky15HqrG/ffLb8gPPiilf49H5gdd6E3F65XhhbNn5bdrM6sItVGn5FoxFKVeEFNTrX/TVUHYzGCzYYPMbalfXzZ0NEO/frJycNQoWfHXubN8P3Ny5GeqYUPZHLBFC3Oe/0KsDjbqjR5gsDGblcHm66+lHTjQutV1LhbQHJvU1NQaJ+tWDTzkQg88IBOUATma4Y9/lN8ka/PPfwLffCNDWLNm2TcJTQUbKyo2dkwcVqyo2KjS+VVXmTu3ZcgQOcfshhvk50ZtmnbFFcDq1eYennohVgcbNQxVr57184nUG66VwUb9fe0MNocPm3/wp5qAP2KEuc8TJgzfTtHqnYjJJg8+KPvbALIq5cYb9Rehqt5+W3a1BIBnntH3WbGDGorau/fCYSxYdkwcVjp2lDY3t+Z/l2B9+aW0ZgxDVdW6tcyxOXxYKjeHDskke/X3tIuaY3P8uDWHQ9o1vwawZx8bOys2yckSHr1ec1dRnj0rP8sAg41BAiqv1HTgpaZpOK42jyL3+/3vZX7DXXfJhn4dOsicm9tvl6WZR4/KBGNV3Zk8WTYftFNamsx5KSmRCZ9t2pj3XHZWbBISZHgmO1tWDl18sbHXP3pUVuoB1g4rNm1q3zbt1alfXyoZBQUSZM0+88yuzfmA8BuKioiQYc/9++Xf1qz/x2vWyPe0USOgd29zniPMBBRslixZgrfffhv16tWr9HlN07BSnU1E4eFXv5IqyJ13yhL1+++XZepNm+qTZwEJQTNn2ttXQF6s2rWTvu7ebW6wsbNiA8hwVHa2DEcZHWy++kr+bXv0sG9+i1OkpVkXbJxQsQmXYANImNm/X35JGTTInOdYskTaYcN822WbLiigoaihQ4ciISEBl112WaWPoUOHlq+UojDSrx+waZMsTW/dWsajs7Plja9PH+CLL2TYyqqD5C7EqgnEKtjYUbEBzD3NXM2vsWIYyunUv6/ZmyEC9p3sDdgbbOwIcoA+h2r/fvOeY/lyabkayjABVWw+/fTTGr+2ePHigDtDISw6Gvjd76Rak5kpQxUpKdadseIPqyYQqzc6uyo2qnqwfbux1y0r0yc7MthYu3rGzoqNmjxcVCQ/A1ZUF+yu2KgNPc0KNmfO6Of7mb2vVhjx61foLKs2KqLQ5fHIhMo+fZwZagB9ArGZFZuiIv1NyK5g062btFu3Gnvd9esluNavL8tTw124BJuKh9VaMVEacH+wWbNG5vs1b66/LlHQ/KrYpKenIykpCT169EDPnj3LP0pLS/Hcc89hzpw5ZvWTyDhWVGzUm1xionWnl1elgk1mprxBGPXmoIahhg+3fsmxE1kZbOycPBwbq0+8Lyy0Jmy4PdioYaihQ0PmHKZQ4Few2b9/PzZt2oSMjAxs2rQJH374IXL+twyuvl0v3kT+Ur8ZHTwoL9KxscY/h90ThwF5M0hLk75s2wYMHmzMdTm/pjI7KjZ2zLEBJKTn51u35NspwSYzU+YOGr1Pmwo2l11m7HXDnF9DUenp6Rg9ejQeeeQRLFiwAFlZWVi1ahXatm2Ll156yaw+EhlLnVTr9QL79pnzHHYu9a5ITeY36qiT/Hxg3Tq5bdfu0U5TMdiYeAgwAHuHogBrJxBrmv3BJiUFiImRUHPokLHXPnNGNpgEOL/GYEEvUxk4cCCeffZZzHTCUl4iX3g85g9HOaFiAxg/z6biMu+UFGOuGepSU6U9fVofKjKL3cHGyt2HT53Sd/y1K9hEROibMBo9HKXm1zRrpr8ekSH8CjalpaXVfr59+/bYbvTKCyIzmT2B2O6l3orRFRs1DHXttcZczw3i4vRDTs0ejrJzjg1g7e7DqloTFSVHsdjFrHk2nF9jGr8GDOvVq4cuXbqgV69e6NmzJ3r16oWUlBTMmjULw4YNM6uPRMYzu2Jj91JvRQWbrVul0hLMC2hZmbmneYeytDQZpsvKAnr2NO95VLCxc44NYE3FpuIwlJ1v/GoTTzODDRnKr4rNsmXLMHHiRERHR+Odd97B1VdfjQ4dOmDWrFkoKyvDww8/jI8++gg7zTx4j8gIVlVs7A42HTrIyqWTJ2WydDDWrZM31sRELvOuSlXmzKzYlJQAxcVyu1Ej856nNlYORdk9v0Yxo2LD+TWm8qtiM3jwYAyusLLC6/Vi165dyMjIQEZGBtauXYvXXnsNeXl5KDP7gEGiYJhZsdE050wejo6Wjfo2b5bhKLWTaiAqLvM2enVIqFMB1szdh48dkzYiQg8YVrNjKMqNwWbtWgmqTZtyfo0Jgnp1ioiIQOfOndG5c2eMHTu2/PO5ublBd4zIVKpik5Mjm+lVOfcsKHl58huZx6NPLLVTjx4SbDZuBG64IfDrWHmad6ixYsl3xWEou44nsWsoyk5mBBt1puJll3F+jQlM+d/R1Emn7xJVp2FDoHFjub1nj7HXVkM+aqmo3fr3l3bNmsCvkZcnOw4DXOZdHSuCjarY2DUMBVg7FKVWgDkl2Bw+LCvfjLBihbRDhhhzParEIacSEtnArOEoFWzUMlG7DRgg7Zo1ge+zos6G6tnTuUdl2Clcgk04DkUlJel/byOqNmfPAt9/L7cZbEzBYEPhy6wJxGqehVOCTffusrvyzz8H/nf94gtpucy7eirYZGfLxo9mcFKwCaehqIr7Xu3aFfz1Nm6UPXqSkoCLLgr+enQeBhsKX0a+WFXktIpNTIwcSgoENhxVWqpPHB450rh+uUlKisx7OXsWMGuOoROCjR2rouzas6eiTp2kNWLFr5pfc+ml9s2Vcjl+Vyl8deworduHooDKw1H+WrlSlosnJ+vzdaiyqCh9iM6s4SgVbOzawwYIz6EowNhgw/k1pmOwofBVsWJj5Bk/bgs2n38u7fXX8zfM2pg9z8YJFZtwHIoCjAs2ZWXAqlVym8HGNHyVovDVrp2Mn584ARw9atx1VbCxew+bilSw2bxZlqL7StP0YMNhqNqZvUmfE4JNOG7QB1QONsH8ErR1q1S7EhLM3aE6zDHYUPiKj9ffjIwajios1F+QnVSxSU+XzcDOntWXbftixw5ZCRIbC1x1lXn9c4NwqticOiU/S2ZyUrBp106qlYWFwJEjgV9Hza8ZNIibXJqIwYbCm9ETiFW1JinJ2E3/guXx6KXvZct8f9yHH0o7bBhQt67x/XKTcAo2gMy7MpOTgk1srH5mVDDDUZxfYwkGGwpvRk8gduL8GuXKK6X1NdhoGvDee3L7l780p09uYvaxCmrnYTuDTXS0VDoBc4ejNM1ZwQbQXysCDTaapldsGGxMxWBD4c2sio0Tg80VV0i7erV+mGJtNm6UfW/i4oBRo8ztmxuoYHPokPHX1jRnBBvAmpVRxcUy0RZwTrBR82wCfa3YuVPm8sXFAf36GdcvOg+DDYU3o3cfdnKwaddODsEsLQWWLr3w/d99V9qRI2WyI9VOBZvDh4Fz54y9dmGhfk2nBBszKzaqWlOxQmS3YFdGqWrNwIHOOGrFxRhsKLyp8vKePfpviMFwcrDxePRDMBcsqP2+Xi/wwQdyu8IBt1SL5GR5I/Z65XBVI6n5NXXqyG/8drJiZVTFYSinHBKpgs2PPwb2eM6vsQyDDYW3tDSZGFhaqoeSYKizZFq1Cv5aZlDB5vPPa68qfP21HA+QmMjTvH0VEQG0aCG3jZ5A7ISJw4oVQ1FOm18DAF26SJuZ6f/fXdOAb76R25ddZmy/6DwMNhTeIiP1M6OMGI7au1fatm2Dv5YZhgyRN8f8fGDx4prv9+KL0k6YYH+FIJSYNc/GicHGqoqNUyQl6f++W7b499jt22WZeHw8cMklxveNKmGwITJqAvGJE/oET7U01Gmio4Ff/Upuz55d/X127tQPvbz/fmv65RZmLfl2UrCxYijq55+ldVKwAfRN9TIy/Huc+iViyBCpEJOpGGyIjJpAvG+ftMnJztrDpqoJE6SdP7/6N+B//ENK56NG6XOQyDepqdK6OdiE61AUAPToIe3mzf49bskSabnJpSUYbIjUm3ewFRunD0MpvXsDQ4fKzrH/+lflr61bB8ydK7f/3/+zvGshLxwqNuE6FAXoFZtNm3x/TGmpPnF42DDDu0TnY7AhMqpiEyrBBtBDy0svSZgBZCfZX/9aqjW33w707Wtf/0KV2XNs7DzZW7FyVVTDhuY9RyD69JF2yxbg9GnfHvPDD7IvT3Iy0K2beX2jcgw2RKpik5Xl28Z1NQmlYHPllbKMu6wMuO464OmnpUy+bRvQrBnw1FN29zA0mVWxccrmfEB4D0Wlp0tAOXfO96rN119Le+WVsnKOTMfvMlGjRvpvwnv2BH6dUAo2APDCC0CvXrJC6qGHgDVr5E1r/nw5MJP8p4JNbq4MQRhFnT7vpGATjkNRHg9w8cVye80a3x7z2WfSXn21OX2i8zDYEAF61SbQzbcAffJwqASbhg2B5cuBhx+WOTf33iuTIgcMsLtnoatxY1n1ommyD5BR8vOlTU427pqBsnqDPqdR/z9Wr77wfffuBbZulW0lrr/e3H5ROZ6bTgQAF10kL1Tbtwf2+NJSffghVIINIL99//3vdvfCPTweWRm1d6/Ms2nd2pjrqmDTpIkx1wtGOA9FAcCgQdJ++60E2Np2Rp43T9qhQ50xPypMsGJDBEiwAQIPNgcOyFb6des647dqso/R82w0DcjLk9tO+NkK56EoQIai4uJkw70LVXjnz5d29Gize0UVMNgQAcEHGzW/pk0b55xtQ/YwOtgUFMjSfMAZFZtwH4qKjQUGD5bbtR0mm5sLfP+93GawsRSDDRGgB5s9e4AzZ/x/fKhNHCbzGB1s1DBUQoIzjrdQFZszZ4ydIK1omrODDSArnABg0aKa7/PJJ/J36dtX37iRLMFgQwQAzZvLi6jXG9hGfT/9JC2DDak3MaP2snHSMBQgAUsxo2pTVCT/DwHnBpuRI6VdsqTm78Gbb0o7bpw1faJyDDZEgAwfBTMcpcba1QnAFL7Mqtg4YRgKAKKiZC4ZYE6wUedExcQ4o0JVnS5dgE6dpGKlzlWrKCMD2LBBzmZjsLEcgw2R0rWrtIEEG/UYBhsyOtg4rWIDmLsyquKuw06dr+bxALfcIrerO0z23/+W9sYbnRNIwwiDDZESaMXmxAkgJ0dud+5saJcoBKlgk58f2HytqlSwcdIbpJkro5x6sndVd90lOwkvWVL5NeOnn4D33pPbf/qTPX0Lcww2REqgwUYNQ6Wm6itGKHw1bAjEx8ttI+bZOGlzPsXMlVEq2DjtnKiqWrUCRo2S23/+s0wU9nqByZPlqJJrrtHPliJLMdgQKSrY7N0LnDrl++N27JCWw1AEyDCFkYdhhutQlNMrNgDwxBMyj+a//wV+9ztgwgQ5GyomBnj2Wbt7F7YYbIiU5GT50DTZBt1XDDZUlZHzbJw2eRhgxUbp3BmYMUNuP/888Pbbcvu114D27e3rV5hjsCFSPB69dLxhg++PY7ChqowMNk6u2JgRbCpOHg4FDz0EzJ0LXHopcPnlskrqjjvs7lVY41lRRBX16QMsXAisX+/7Y7giiqoyI9g4qWJj5lBUqEwermjcOC7rdhBWbIgq6ttXWl8rNoWF+psXV0SRYtQmfV4vcPSo3HZSxYZDUeRgDDZEFamhqO3bgdOnL3z/nTulbdaMp/eSzqiKzc8/ywobAGjcOLhrGcmKoahQqtiQozDYEFXUooX8ZlxWBmzefOH7b9kiLYehqCKjgo2aONyggay0cQorhqJYsaEAMdgQVeTx+Dccpe7D/SqoIhVsjh/3b+uAqpw4cRjgUBQ5GoMNUVUqpPgygZjBhqqTmKgfFhnMPBsnThwGOBRFjsZgQ1SVr8GmtFQfilJVHiJFTSAOZjjKibsOAxyKIkdjsCGqasAAabdv119kq7N9O1BSIr9ZtmljSdcohKjhqMzMwK/h1IqNWUNRJSX6pH1WbChADDZEVTVrBnToIDsQr1pV8/3U1/r3d+4pxGSf9HRpgwk2R45I27Rp8P0xkllDUWoYyuPhuWsUMAYboupcdpm0K1bUfJ9vv5V2yBDz+0Ohp1UraQ8cCPwa6tT4Fi2C7Y2xVLApLZUqi1FUhTQxUU7OJgoAf3KIqqOCzTffVP91TQNWrpTbl15qTZ8otBgZbFJSgu2NsdTEaMDYeTacOEwGYLAhqs6VV0q7cSNw+PD5X9+1C8jNlb1F+ve3tm8UGtwcbCIi9HBj5HAUJw6TAUIm2Bw4cAB33XUXWrdujfj4eLRt2xbTp09HaWmp3V0jN2rWTF/ptHDh+V//4gtpL7sMiIuzrl8UOtQcm6ws4Nw5/x9fVqbPsXFasAHMmWfDig0ZIGSCzc6dO+H1evHKK69g+/bt+L//+z+8/PLL+Mtf/mJ318itrrtO2gULzv/a559LO3Kkdf2h0NK8ORAdLQElO9v/x+flyVlRERHOW+4N6JN7jRyKYsWGDBAywebqq6/G7NmzMXz4cLRp0wY33HAD/vCHP+DTTz+1u2vkVrfcIu2XX+r7iQDyW/R338nt66+3vl8UGiIi9KrNwYP+P14NQzVrBkRGGtcvo5hRsWGwIQOETLCpTkFBAZIucPBgSUkJCgsLK30Q+aRrVxmOOncOmDtX//wbb8hv4QMHAq1b29c/cr5g5tmoKo8Th6EADkWRY4VssNmzZw9mzZqFe++9t9b7zZgxA4mJieUfaWrTLCJf3H23tE89JWf+FBcDL78sn7v/fvv6RaFBVWwCCTZOnTisqKEoFUaMwIoNGcD2YDN16lR4PJ5aP3bu3FnpMdnZ2bj66qsxZswYTJw4sdbrT5s2DQUFBeUfWcGetkvhZcIE+a378GEJOffcI2f/pKXpQ1VENQmmYuPUPWwUVVXhcm9ymCi7O/DQQw9hwoQJtd6nTYXt6nNycnD55ZfjkksuwauvvnrB68fGxiI2NjbYblK4io0Fnn0WGD0aeO89/fMvvgjEx9vWLQoRRgQbp1ZsVPhgxYYcxvZg06RJEzTx8RyU7OxsXH755ejTpw9mz56NCO5MSVa44QbgnXeA6dNlp9V//IOThsk34RBsajtPzV8MNmQA24ONr7KzszF06FCkp6dj5syZyK+wSqVZs2Y29ozCwtix8kHkDxVssrJkwrk/q5ucHmxU+DCyYsOhKDJAyASbxYsXY8+ePdizZw9SU1MrfU3TNJt6RURUi+bNgagoWVmXk6Of+O0LpwcbDkWRQ4XMWM6ECROgaVq1H0REjhQZqa+M2rvX98eVlup7J4VLsPF69YnIrNhQEEIm2BARhaR27aT96SffH6OOUoiOBho1Mr5PRjA62BQWyuGyACs2FBQGGyIiM7VvL60/wabiMJTHY3yfjGB0sFHDUPHxshqRKEAMNkREZlLBZs8e3x+jdh1u3tz4/hilYrDxeoO/HicOk0EYbIiIzBRIxSYzU1o1P8eJ1HCR1wsUFQV/PU4cJoMw2BARmalixcbXyoba98bJwSYuTh8yMmI4ihUbMgiDDRGRmVq1kiXfZ87oQ0wXooKN2gfHqYycZ8OKDRmEwYaIyExRUfop8L4ORx08KC2DDZHfGGyIiMzm7zybUBiKAowNNhyKIoMw2BARmc2fYHPihL5RXagEGyPOi2LFhgzCYENEZDZ/go0ahmrcGKhb17w+GYEVG3IgBhsiIrP5E2zU0Qtt2pjXH6MYeRAmKzZkEAYbIiKzqWCzd6+c8l0bFX7UY5zMjMnDrNhQkBhsiIjM1rKlHBVQWnrhwzB375Y23ILN8ePSJiUFfy0Kaww2RERmi4wELrpIbm/bVvt9w7Vio4KNUw/9pJDBYENEZIWuXaW9ULBRFZsOHcztjxGMWhXl9TLYkGEYbIiIrOBLsCksBHJz5XY4VWwKCvTjJjgURUFisCEisoIKNlu31nyfnTulTU4GEhPN71OwjFoVpao1devq508RBYjBhojICt27S7t7N1BcXP19VOhR93U6oyo2x45Jy2EoMgCDDRGRFZo3B1JSZMglI6P6+2zZIm23bpZ1Kygq2BQW+n5yeXW4IooMxGBDRGSVvn2lXb+++q+HWsVGDZdpmoSbQLFiQwZisCEiskqfPtJWF2w0Ta/YhEqwiY2V/XmA4FZGMdiQgRhsiIisoio2P/xw/tcyM+UNPioK6NzZ2n4Fw4gl3xyKIgMx2BARWeWSS4CICGDPHiA7u/LXvvtO2l699CpIKFAro1ixIYdgsCEiskqDBhJcAGDFispfW7VK2kGDLO1S0FQYUVWXQDDYkIEYbIiIrDR0qLTLllX+vKrYhGqwUeEkEByKIgMx2BARWemqq6T9/HP9pO9Dh/SJw4MH29OvQKkwEkywYcWGDMRgQ0RkpSuukDCQl6cPR336qbSDBgHNmtnXt0AYWbFhsCEDMNgQEVkpOhq46Sa5/cYbssz7nXfkz7fcYl+/AmXkHBsORZEBGGyIiKx2773Svvce8JvfAGvXAnFxwC9+YW+/AhFsxebcOTkEs+K1iILAYENEZLW+fSXEaBrw8svyuYcekiMXQk2wc2wqLhNXe+IQBSHK7g4QEYWll14CSkqAL74A7rgD+Otf7e5RYIKt2KjHNWggmxMSBYk/RUREdkhKAubPB0pLgZgYu3sTuGDn2HBFFBmMQ1FERHYK5VAD6ENRx48HdsI397AhgzHYEBFR4FSlxevVJwH7gxUbMhiDDRERBS42FqhbV24HMs+Ge9iQwRhsiIgoOMHMs+EeNmQwBhsiIgpOMEu+ORRFBmOwISKi4ASz5Ds/X9rkZOP6Q2GNwYaIiIITzFBUXp60TZoY1x8Kaww2REQUnGCGolSwYcWGDMJgQ0REwQlmKIrBhgzGYENERMEJNNiUlgInTshtBhsyCIMNEREFJ9A5NmricFQUD8AkwzDYEBFRcAKdY1Nx4nAE347IGPxJIiKi4AQ6FMX5NWQCBhsiIgoOgw05CIMNEREFRwWbkydlQrCvGGzIBAw2REQUnIYN9TkyR4/6/jgGGzIBgw0REQUnIkLfOViFFV8w2JAJGGyIiCh4Kpww2JDNGGyIiCh4DDbkEAw2REQUPBVO1KZ7vmCwIRMw2BARUfD8rdhoGoMNmYLBhoiIgudvsCkqAs6ckdtq4jGRARhsiIgoeP4GG3W/unXlg8ggDDZERBS8QIMNh6HIYAw2REQUvECDDYehyGAMNkREFDwVbI4ckYnBF8KKDZmEwYaIiILXvLm0Z84ABQUXvn9OTuXHERmEwYaIiIIXHw8kJsrtw4cvfH8VbFJSzOsThSUGGyIiMoYKKQw2ZCMGGyIiMoYaVvIn2LRoYV5/KCwx2BARkTECCTas2JDBQjLYlJSUoGfPnvB4PMjIyLC7O0REBOjBRoWWmpw9C+Tmym0GGzJYSAabP/3pT0jhfwYiImfxtWKTmytLwiMjuY8NGS7kgs3ChQvx9ddfY+bMmXZ3hYiIKvI12FRc6h0Rcm9D5HBRdnfAH7m5uZg4cSLmz5+POnXq+PSYkpISlJSUlP+5sLDQrO4REYU3VUm/0FBUdnbl+xMZKGSisqZpmDBhAu677z707dvX58fNmDEDiYmJ5R9paWkm9pKIKIy1bCltVlbtuw9nZla+P5GBbA82U6dOhcfjqfVj586dmDVrFk6ePIlp06b5df1p06ahoKCg/CMrK8ukvwkRUZhr0QLweGT34aNHa77fwYPSMtiQCWwfinrooYcwYcKEWu/Tpk0bLFu2DKtXr0ZsbGylr/Xt2xfjxo3DnDlzqn1sbGzseY8hIiITxMQAzZrJHJvMzJonBquKTXq6dX2jsGF7sGnSpAma+DAr/rnnnsPjjz9e/uecnByMGDECH3zwAQYMGGBmF4mIyFctW+rBpk+f6u+jKjYMNmQC24ONr1pWKVnWq1cPANC2bVukpqba0SUiIqoqLQ1Ys0avylSHc2zIRLbPsSEiIhepOIG4OqdPA3l5cpsVGzJByFRsqmrVqhW02mbdExGR9VSwqaliowJP3bpAw4bW9InCCis2RERkHFWF2bev+q/v3Stt69aygorIYAw2RERknHbtpN2zp/q9bH76Sdr27a3rE4UVBhsiIjJO27bSFhRUv5fN7t3SduhgXZ8orDDYEBGRceLjZWUUoFdnKmLFhkzGYENERMaqOBxVlQo2rNiQSRhsiIjIWKoaU7ViU1Kib87HYEMmYbAhIiJjqdCyc2flz+/aBXi9QP36QHKy9f2isMBgQ0RExureXdqMjMqf37RJ2p49udSbTMNgQ0RExurVS9o9e4DCQv3zKtiorxOZgMGGiIiM1bgxoM7w27xZ/zyDDVmAwYaIiIzXs6e0Ksx4vfrQFIMNmYjBhoiIjNevn7Tffivtpk0yLJWQAHTubF+/yPUYbIiIyHgjRki7eDFw7hywaJH8edgwIDravn6R6zHYEBGR8fr2BRo1kqMVVq8GvvxSPn/11fb2i1yPwYaIiIwXGQlce63cHjIE+P57ICICuOYae/tFrsdgQ0RE5pg6VQKOctdd+jlSRCZhsCEiInN06QI8+ijQoIGsknr0Ubt7RGHAo2maZncnrFRYWIjExEQUFBSgfv36dneHiIiIfODr+zcrNkREROQaDDZERETkGgw2RERE5BoMNkREROQaDDZERETkGgw2RERE5BoMNkREROQaDDZERETkGgw2RERE5BoMNkREROQaDDZERETkGgw2RERE5BoMNkREROQaDDZERETkGlF2d8BqmqYBkOPPiYiIKDSo9231Pl6TsAs2J0+eBACkpaXZ3BMiIiLy18mTJ5GYmFjj1z3ahaKPy3i9XuTk5CAhIQEej8ew6xYWFiItLQ1ZWVmoX7++Ydelyvh9tg6/19bg99ka/D5bw8zvs6ZpOHnyJFJSUhARUfNMmrCr2ERERCA1NdW069evX5//aSzA77N1+L22Br/P1uD32RpmfZ9rq9QonDxMRERErsFgQ0RERK7BYGOQ2NhYTJ8+HbGxsXZ3xdX4fbYOv9fW4PfZGvw+W8MJ3+ewmzxMRERE7sWKDREREbkGgw0RERG5BoMNERERuQaDDREREbkGg41BXnjhBbRq1QpxcXEYMGAA1q5da3eXXGflypUYOXIkUlJS4PF4MH/+fLu75DozZsxAv379kJCQgOTkZIwePRq7du2yu1uu89JLL6F79+7lm5gNHDgQCxcutLtbrvfkk0/C4/HgwQcftLsrrvPII4/A4/FU+ujUqZMtfWGwMcAHH3yAKVOmYPr06di4cSN69OiBESNGIC8vz+6uuUpxcTF69OiBF154we6uuNaKFSswadIk/PDDD1i8eDHOnj2L4cOHo7i42O6uuUpqaiqefPJJbNiwAevXr8cVV1yBUaNGYfv27XZ3zbXWrVuHV155Bd27d7e7K6510UUX4fDhw+Ufq1atsqUfXO5tgAEDBqBfv354/vnnAch5VGlpafjtb3+LqVOn2tw7d/J4PJg3bx5Gjx5td1dcLT8/H8nJyVixYgWGDBlid3dcLSkpCU899RTuuusuu7viOkVFRejduzdefPFFPP744+jZsyeeeeYZu7vlKo888gjmz5+PjIwMu7vCik2wSktLsWHDBgwbNqz8cxERERg2bBhWr15tY8+IgldQUABA3nTJHGVlZXj//fdRXFyMgQMH2t0dV5o0aRKuu+66Sq/TZLyffvoJKSkpaNOmDcaNG4fMzExb+hF2h2Aa7ejRoygrK0PTpk0rfb5p06bYuXOnTb0iCp7X68WDDz6IQYMGoWvXrnZ3x3W2bt2KgQMH4syZM6hXrx7mzZuHLl262N0t13n//fexceNGrFu3zu6uuNqAAQPw1ltvoWPHjjh8+DD+/ve/49JLL8W2bduQkJBgaV8YbIioWpMmTcK2bdtsGyd3u44dOyIjIwMFBQX4+OOPMX78eKxYsYLhxkBZWVl44IEHsHjxYsTFxdndHVe75pprym93794dAwYMQHp6Oj788EPLh1cZbILUuHFjREZGIjc3t9Lnc3Nz0axZM5t6RRScyZMn44svvsDKlSuRmppqd3dcKSYmBu3atQMA9OnTB+vWrcOzzz6LV155xeaeuceGDRuQl5eH3r17l3+urKwMK1euxPPPP4+SkhJERkba2EP3atCgATp06IA9e/ZY/tycYxOkmJgY9OnTB0uXLi3/nNfrxdKlSzleTiFH0zRMnjwZ8+bNw7Jly9C6dWu7uxQ2vF4vSkpK7O6Gq1x55ZXYunUrMjIyyj/69u2LcePGISMjg6HGREVFRdi7dy+aN29u+XOzYmOAKVOmYPz48ejbty/69++PZ555BsXFxbjzzjvt7pqrFBUVVUr/+/fvR0ZGBpKSktCyZUsbe+YekyZNwrvvvosFCxYgISEBR44cAQAkJiYiPj7e5t65x7Rp03DNNdegZcuWOHnyJN59910sX74cX331ld1dc5WEhITz5ofVrVsXjRo14rwxg/3hD3/AyJEjkZ6ejpycHEyfPh2RkZEYO3as5X1hsDHArbfeivz8fDz88MM4cuQIevbsiUWLFp03oZiCs379elx++eXlf54yZQoAYPz48Xjrrbds6pW7vPTSSwCAoUOHVvr87NmzMWHCBOs75FJ5eXm44447cPjwYSQmJqJ79+746quvcNVVV9ndNaKAHDp0CGPHjsWxY8fQpEkTDB48GD/88AOaNGlieV+4jw0RERG5BufYEBERkWsw2BAREZFrMNgQERGRazDYEBERkWsw2BAREZFrMNgQERGRazDYEBERkWsw2BAREZFrMNgQkaMcOHAAHo8HrVq1srsrRBSCGGyIyHKtWrWCx+PBgQMH7O4KEbkMz4oiIkdp0aIFfvzxR0RHR9vdFSIKQQw2ROQo0dHR6NSpk93dIKIQxaEoIrLMW2+9BY/Hg4MHDwIAWrduDY/HU/6xfPnyWufYqPsBwNy5c9G/f3/Uq1cPTZo0wdixY5GZmQkA0DQNzz//PHr27Im6deuicePGmDBhAvLy8mrs2+7du3Hvvfeibdu2iIuLQ2JiIoYMGYK5c+ca/40gItPwdG8issyqVavw+uuv4+OPP0ZxcTFuvvlm1KtXr/zrU6dORVxcHFq3bo309PTz5uCoUDN16lTMnDkTQ4YMQVJSEtauXYvMzEykpaVh8+bNuO+++/DZZ59h6NChiI+Px3fffYe8vDx0794d69atQ0xMTKXrfvTRR7jjjjtw5swZdOrUCZ07d0ZBQQHWrFmD4uJi3HnnnXjzzTdN//4QkQE0IiKLpaenawC0/fv3n/e1/fv3awC09PT0874GQAOgNWrUSMvIyCj//KlTp7TBgwdrALRu3bppbdu21Q4cOFD+9fz8fK1du3YaAG3u3LmVrrllyxYtNjZWi4uL0z755JNKXztw4IDWrVs3DYA2Z86c4P7SRGQJDkURUch59NFH0aNHj/I/x8fHY8qUKQCArVu34rnnnkN6enr51xs3boz7778fALB06dJK13riiSdQUlKCxx9/HDfddFOlr6Wnp+ONN94AADz33HOm/F2IyFgMNkQUcq699trzPte+fXsAQFRUFIYPH17j13Nycso/5/V6sXDhQgDArbfeWu1z9e3bF/Xq1cOmTZtw5syZoPtOROZisCGikNOyZcvzPqfm6jRv3hxRUecv+ExISACASuHk2LFjKCwsBACkpaVVmsisPiIiIlBUVASv14tjx46Z8dchIgNxuTcRhZyIiJp/J6vta1V5vd7y2+PHj7/g/WNjY32+NhHZg8GGiMJW48aNER8fj9OnT2PmzJlo3Lix3V0ioiBxKIqILKeWW587d87WfkRGRuKqq64CAHz44Ye29oWIjMFgQ0SWS01NBQBs377d5p4A06dPR0xMDP74xz9izpw5lYanlG3btuHTTz+1oXdE5C8GGyKy3M033wwAuO2223DzzTfj7rvvxt13341du3ZZ3pfevXuX7y48YcIEpKenY8SIEbjttttw7bXXIi0tDd26dWNFhyhEcI4NEVnu/vvvx8mTJzF37lx8+eWX5SuVbrvttmqPUjDbmDFj0K9fPzz33HNYvHgxvvvuO5SVlaFp06Zo164dJk+ejFtuucXyfhGR/3ikAhEREbkGh6KIiIjINRhsiIiIyDUYbIiIiMg1GGyIiIjINRhsiIiIyDUYbIiIiMg1GGyIiIjINRhsiIiIyDUYbIiIiMg1GGyIiIjINRhsiIiIyDUYbIiIiMg1/j+8VTEEmSL17gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Physical electric Stokes pulse in the lab frame:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_physical_field(pulse_re, pulse_im, tlist, case=None):\n",
    "\n",
    "    if case == 'pump':\n",
    "        w = 9.5\n",
    "    elif case == 'stokes':\n",
    "        w = 4.5\n",
    "    else:\n",
    "        print('Error: selected case is not a valid option')\n",
    "        return\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    ax.plot(tlist,pulse_re*np.cos(w*tlist)-pulse_im*np.sin(w*tlist), 'r')\n",
    "    ax.set_xlabel('time', fontsize = 16)\n",
    "    if case == 'pump':\n",
    "        ax.set_ylabel(r'$\\mu_{12}\\,\\epsilon_{P}$')\n",
    "    elif case == 'stokes':\n",
    "        ax.set_ylabel(r'$ \\mu_{23}\\,\\epsilon_{S}$')\n",
    "    plt.show()\n",
    "\n",
    "print('Physical electric pump pulse in the lab frame:')\n",
    "plot_physical_field(\n",
    "    opt_result.optimized_controls[0], opt_result.optimized_controls[1], tlist, case = 'pump')\n",
    "\n",
    "\n",
    "print('Physical electric Stokes pulse in the lab frame:')\n",
    "plot_physical_field(\n",
    "    opt_result.optimized_controls[2], opt_result.optimized_controls[3], tlist, case = 'stokes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, we check the population dynamics to verify that we indeed implement the\n",
    "desired state-to-state transfer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "19"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.506506Z",
     "iopub.status.busy": "2024-06-03T14:29:29.506353Z",
     "iopub.status.idle": "2024-06-03T14:29:29.575616Z",
     "shell.execute_reply": "2024-06-03T14:29:29.575302Z"
    }
   },
   "outputs": [],
   "source": [
    "opt_dynamics = opt_result.optimized_objectives[0].mesolve(\n",
    "    tlist, e_ops=[proj1, proj2, proj3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:23.853468Z",
     "start_time": "2019-02-12T04:41:23.633866Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "20"
    },
    "execution": {
     "iopub.execute_input": "2024-06-03T14:29:29.577145Z",
     "iopub.status.busy": "2024-06-03T14:29:29.577053Z",
     "iopub.status.idle": "2024-06-03T14:29:29.647757Z",
     "shell.execute_reply": "2024-06-03T14:29:29.647509Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(opt_dynamics)"
   ]
  }
 ],
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  "kernelspec": {
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  "language_info": {
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   "kernels_config": {
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     "varRefreshCmd": "print(var_dic_list())"
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   "types_to_exclude": [
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