{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time dependence and PT-TEMPO\n",
    "\n",
    "A quick introduction on how to use the OQuPy package to compute the dynamics of a time dependent quantum system and how to employ the process tensor TEMPO method. We illustrate this by applying TEMPO and PT-TEMPO to a quantum dot driven by a time dependent laser pulse.\n",
    "\n",
    "- [launch binder](https://mybinder.org/v2/gh/tempoCollaboration/OQuPy/HEAD?labpath=tutorials%2Fpt_tempo.ipynb) (runs in browser),\n",
    "- [download the jupyter file](https://raw.githubusercontent.com/tempoCollaboration/OQuPy/main/tutorials/pt_tempo.ipynb), or\n",
    "- read through the text below and code along."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Contents:**\n",
    "\n",
    "* Example - Quantum dot driven by a laser pulse\n",
    "    * 1. Hamiltonian for driven quantum dot with bosonic environment\n",
    "    * 2. Laser pulse / time dependent system\n",
    "    * 3. Create time dependent system object\n",
    "    * 4. TEMPO computation\n",
    "    * 5. Using PT-TEMPO to explore many different laser pulses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's import OQuPy and some other packages we are going to use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.insert(0,'..')\n",
    "\n",
    "import oqupy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and check what version of tempo we are using."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.4.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oqupy.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also import some shorthands for the spin Pauli operators and density matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_x = oqupy.operators.sigma(\"x\")\n",
    "sigma_y = oqupy.operators.sigma(\"y\")\n",
    "sigma_z = oqupy.operators.sigma(\"z\")\n",
    "up_density_matrix = oqupy.operators.spin_dm(\"z+\")\n",
    "down_density_matrix = oqupy.operators.spin_dm(\"z-\")\n",
    "mixed_density_matrix = oqupy.operators.spin_dm(\"mixed\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------------------------------------------------\n",
    "## Example - Quantum Dot driven by a laser pulse\n",
    "\n",
    "As a first example let's try to reconstruct one of the lines in figure 3c of [Fux2021] ([Phys. Rev. Lett. 126, 200401 (2021)](https://link.aps.org/doi/10.1103/PhysRevLett.126.200401) / [arXiv:2101.03071](https://arxiv.org/abs/2101.03071)). In this example we compute the time evolution of a quantum dot which is driven with a $\\pi/2$ laser pulse and is strongly coupled to an ohmic bath (spin-boson model). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Hamiltonian for driven quantum dot with bosonic environment\n",
    "We consider a time dependent system Hamiltonian\n",
    "$$ H_{S}(t) = \\frac{\\Delta(t)}{2} \\hat{\\sigma}_z + \\frac{\\Omega(t)}{2} \\hat{\\sigma}_x \\mathrm{,}$$\n",
    "which may describe transitions between the ground and exciton state driven by a resonant laser pulse (in the rotating frame). Here, $\\Delta(t)$ is the detuning of the laser with respect to the transition and $\\Omega(t)$ is proportional to the electric field of the laser.\n",
    "We further include a bosonic environment\n",
    "$$ H_{B} = \\sum_k \\omega_k \\hat{b}^\\dagger_k \\hat{b}_k  \\mathrm{,}$$\n",
    "and an interaction Hamiltonian\n",
    "$$ H_{I} =  \\frac{1}{2} \\hat{\\sigma}_z \\sum_k \\left( g_k \\hat{b}^\\dagger_k + g^*_k \\hat{b}_k \\right) \\mathrm{,}$$\n",
    "where $\\hat{\\sigma}_i$ are the Pauli operators, and the $g_k$ and $\\omega_k$ are such that the spectral density $J(\\omega)$ is\n",
    "$$ J(\\omega) = \\sum_k |g_k|^2 \\delta(\\omega - \\omega_k) = 2 \\, \\alpha \\, \\frac{\\omega^3}{\\omega_\\mathrm{cutoff}^2} \\, \\exp\\left(-\\frac{\\omega^2}{\\omega_\\mathrm{cutoff}^2}\\right) \\mathrm{.} $$\n",
    "Also, let's assume the initial density matrix of the quantum dot is the ground state\n",
    "$$ \\rho_0 = \\begin{pmatrix} 0 & 0 \\\\ 0 & 1 \\end{pmatrix} $$\n",
    "and the bath is initially at temperature $T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We express all frequencies, temperatures and times in units of 1/ps and ps respectively.\n",
    "\n",
    "* $\\omega_c = 3.04 \\frac{1}{\\mathrm{ps}}$\n",
    "* $\\alpha = 0.126$\n",
    "* $T = 1 K = 0.1309 \\frac{1}{\\mathrm{ps}\\,\\mathrm{k}_B}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega_cutoff = 3.04 \n",
    "alpha = 0.126\n",
    "temperature = 0.1309\n",
    "initial_state=down_density_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Laser pulse / time dependent system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose a gaussian laser pulse shape with an adjustable pulse area and pulse width $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian_shape(t, area = 1.0, tau = 1.0, t_0 = 0.0):\n",
    "    return area/(tau*np.sqrt(np.pi)) * np.exp(-(t-t_0)**2/(tau**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choosing a pulse area of $\\pi/2$, a pulse width of 245 fs and no detuning, we can check the shape of the laser pulse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc555eaa170>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "detuning = lambda t: 0.0 * t\n",
    "\n",
    "t = np.linspace(-2,3,100)\n",
    "Omega_t = gaussian_shape(t, area = np.pi/2.0, tau = 0.245)\n",
    "Delta_t = detuning(t)\n",
    "\n",
    "plt.plot(t, Omega_t,label=r\"$\\Omega(t)$\")\n",
    "plt.plot(t, Delta_t,label=r\"$\\Delta(t)$\")\n",
    "plt.xlabel(r\"$t\\,/\\mathrm{ps}$\")\n",
    "plt.ylabel(r\"$\\mathrm{ps}^{-1}$\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Create time dependent system object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hamiltonian_t(t):\n",
    "    return detuning(t)/2.0 * sigma_z \\\n",
    "           + gaussian_shape(t, area = np.pi/2.0, tau = 0.245)/2.0 * sigma_x\n",
    "\n",
    "system = oqupy.TimeDependentSystem(hamiltonian_t)\n",
    "correlations = oqupy.PowerLawSD(alpha=alpha,\n",
    "                                zeta=3,\n",
    "                                cutoff=omega_cutoff,\n",
    "                                cutoff_type='gaussian',\n",
    "                                temperature=temperature)\n",
    "bath = oqupy.Bath(sigma_z/2.0, correlations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. TEMPO computation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all physical objects defined, we are now ready to compute the dynamics of the quantum dot using TEMPO (using quite rough convergence parameters):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--> TEMPO computation:\n",
      "100.0%   50 of   50 [########################################] 00:00:00\n",
      "Elapsed time: 0.7s\n"
     ]
    }
   ],
   "source": [
    "tempo_parameters = oqupy.TempoParameters(dt=0.1, tcut=2.0, epsrel=10**(-4))\n",
    "\n",
    "tempo_sys = oqupy.Tempo(system=system,\n",
    "                        bath=bath,\n",
    "                        initial_state=initial_state,\n",
    "                        start_time=-2.0,\n",
    "                        parameters=tempo_parameters)\n",
    "dynamics = tempo_sys.compute(end_time=3.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and extract the expectation values $\\langle\\sigma_{xy}\\rangle = \\sqrt{\\langle\\sigma_x\\rangle^2 + \\langle\\sigma_y\\rangle^2}$ for plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc553bb6e30>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, s_x = dynamics.expectations(sigma_x, real=True)\n",
    "t, s_y = dynamics.expectations(sigma_y, real=True)\n",
    "s_xy = np.sqrt(s_x**2 + s_y**2)\n",
    "plt.plot(t, s_xy, label=r'$\\Delta = 0.0$')\n",
    "plt.xlabel(r'$t\\,\\Omega$')\n",
    "plt.ylabel(r'$<\\sigma_{xy}>$')\n",
    "plt.ylim((0.0,1.0))\n",
    "plt.legend(loc=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Using PT-TEMPO to explore many different laser pulses\n",
    "If we want to do the same computation for a set of different laser pulses (and thus different time dependent system Hamiltonians), we could repeate the above procedure. However, for a large number of different system Hamiltonians this is impractical. In such cases one may instead use the process tensor approach (PT-TEMPO) wherein the bath influence tensors are computed separately from the rest of the network. This produces an object known as the process tensor which may then be used with many different system Hamiltonians at relatively little cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--> PT-TEMPO computation:\n",
      "100.0%   50 of   50 [########################################] 00:00:00\n",
      "Elapsed time: 0.3s\n"
     ]
    }
   ],
   "source": [
    "tempo_parameters = oqupy.TempoParameters(dt=0.1, tcut=2.0, epsrel=10**(-4))\n",
    "\n",
    "process_tensor = oqupy.pt_tempo_compute(bath=bath,\n",
    "                                        start_time=-2.0,\n",
    "                                        end_time=3.0,\n",
    "                                        parameters=tempo_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given we want to calculate $\\langle\\sigma_{xy}\\rangle(t)$ for 5 different laser pulse detunings, we define a seperate system object for each laser pulse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltas = [-10.0, -5.0, 0.0, 5.0, 10.0]\n",
    "systems = []\n",
    "for delta in deltas:\n",
    "    # NOTE: omitting \"delta=delta\" in the parameter definition below\n",
    "    #       would lead to all systems having the same detuning.\n",
    "    #       This is a common python pitfall. Check out \n",
    "    #       https://docs.python-guide.org/writing/gotchas/#late-binding-closures\n",
    "    #       for more information on this.\n",
    "    def hamiltonian_t(t, delta=delta): \n",
    "        return delta/2.0 * sigma_z \\\n",
    "            + gaussian_shape(t, area = np.pi/2.0, tau = 0.245)/2.0 * sigma_x \n",
    "    system = oqupy.TimeDependentSystem(hamiltonian_t)\n",
    "    systems.append(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use the process tensor to compute the dynamics for each laser pulse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "..... done.\n"
     ]
    }
   ],
   "source": [
    "s_xy_list = []\n",
    "t_list = []\n",
    "for system in systems:\n",
    "    dynamics = oqupy.compute_dynamics(\n",
    "        process_tensor=process_tensor,\n",
    "        system=system,\n",
    "        initial_state=initial_state,\n",
    "        start_time=-2.0,\n",
    "        progress_type=\"silent\")\n",
    "    t, s_x = dynamics.expectations(sigma_x, real=True)\n",
    "    _, s_y = dynamics.expectations(sigma_y, real=True)\n",
    "    s_xy = np.sqrt(s_x**2 + s_y**2)\n",
    "    s_xy_list.append(s_xy)\n",
    "    t_list.append(t)\n",
    "    print(\".\", end=\"\", flush=True)\n",
    "print(\" done.\", flush=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and plot $\\langle\\sigma_{xy}\\rangle(t)$ for each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc553b84bb0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for t, s_xy, delta in zip(t_list, s_xy_list, deltas):\n",
    "    plt.plot(t, s_xy, label=r\"$\\Delta = $\"+f\"{delta:0.1f}\")\n",
    "    plt.xlabel(r'$t/$ps')\n",
    "    plt.ylabel(r'$<\\sigma_{xy}>$')\n",
    "plt.ylim((0.0,1.0))\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "3306e98808c0871e8a1685f50cc307ae5b4a4a013844b10634a4efe89132c3fe"
  },
  "kernelspec": {
   "display_name": "oqupyPR",
   "language": "python",
   "name": "oqupypr"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.15"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 1,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}