{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyOR Quantum\n",
    "## Author: Vineeth Thalakottoor\n",
    "## Introduction to equlibrium density matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the source path\n",
    "SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumSystem import QuantumSystem as QunS\n",
    "from PyOR_Hamiltonian import Hamiltonian\n",
    "from PyOR_DensityMatrix import DensityMatrix\n",
    "from PyOR_QuantumObject import QunObj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the spin system\n",
    "Spin_list = {\"A\" : \"H1\", \"B\" : \"H1\"}\n",
    "QS = QunS(Spin_list,PrintDefault=False)\n",
    "\n",
    "# initialize the system\n",
    "QS.Initialize()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rotating frame frequencies: {'A': -2514706800.0, 'B': -2514706800.0}\n",
      "Offset frequencies: {'A': 10.0, 'B': 50.0}\n",
      "Initial spin temperatures: {'A': 300.0, 'B': 300.0}\n",
      "Final spin temperatures: {'A': 300.0, 'B': 300.0}\n",
      "Radiation damping gain: {'A': 0, 'B': 0}\n",
      "Radiation damping phase: {'A': 0, 'B': 0}\n",
      "\n",
      "Rprocess = No Relaxation\n",
      "RelaxParDipole_tau = 0.0\n",
      "DipolePairs = []\n",
      "RelaxParDipole_bIS = []\n"
     ]
    }
   ],
   "source": [
    "# Master Equation\n",
    "QS.PropagationSpace = \"Hilbert\"\n",
    "QS.MasterEquation = \"Redfield\"\n",
    "\n",
    "# B0 Field in Tesla, Static Magnetic field (B0) along Z\n",
    "QS.B0 = 9.4\n",
    "\n",
    "# Offset Frequency in rotating frame (Hz)\n",
    "QS.OFFSET[\"A\"] = 10.0\n",
    "QS.OFFSET[\"B\"] = 50.0\n",
    "\n",
    "# Define J coupling between Spins \n",
    "QS.JcoupleValue(\"A\",\"B\",5.0)\n",
    "\n",
    "# Define initial and final Spin Temperature\n",
    "QS.I_spintemp[\"A\"] = 300.0\n",
    "QS.I_spintemp[\"B\"] = 300.0\n",
    "QS.F_spintemp[\"A\"] = 300.0\n",
    "QS.F_spintemp[\"B\"] = 300.0\n",
    "\n",
    "QS.Update()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate Hamiltonians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor Frequency in MHz:  [-400.22802765 -400.22806765]\n"
     ]
    }
   ],
   "source": [
    "# generate Larmor Frequencies\n",
    "QS.print_Larmor = True\n",
    "Ham = Hamiltonian(QS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trace of density matrix =  1.0\n",
      "Trace of density matrix =  1.0\n"
     ]
    }
   ],
   "source": [
    "DM = DensityMatrix(QS,Ham)\n",
    "\n",
    "Thermal_DensMatrix = True\n",
    "\n",
    "if Thermal_DensMatrix:    \n",
    "    # High Temperature\n",
    "    HT_approx = False\n",
    "    \n",
    "    # Initial Density Matrix\n",
    "    rho_in = DM.EquilibriumDensityMatrix(QS.Ispintemp,HT_approx)\n",
    "    \n",
    "    # Equlibrium Density Matrix\n",
    "    rhoeq = DM.EquilibriumDensityMatrix(QS.Fspintemp,HT_approx)\n",
    "else:\n",
    "    rho_in = QunObj(QS.Az + QS.Bz)\n",
    "    rhoeq = QunObj(QS.Az + QS.Bz) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.250016003847122 & 0 & 0 & 0\\\\0 & 0.25 & 0 & 0\\\\0 & 0 & 0.25 & 0\\\\0 & 0 & 0 & 0.249983996152878\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.250016003847122,    0,    0,                 0],\n",
       "[                0, 0.25,    0,                 0],\n",
       "[                0,    0, 0.25,                 0],\n",
       "[                0,    0,    0, 0.249983996152878]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initial Density Matrix\n",
    "rho_in.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.250016003847122 & 0 & 0 & 0\\\\0 & 0.25 & 0 & 0\\\\0 & 0 & 0.25 & 0\\\\0 & 0 & 0 & 0.249983996152878\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.250016003847122,    0,    0,                 0],\n",
       "[                0, 0.25,    0,                 0],\n",
       "[                0,    0, 0.25,                 0],\n",
       "[                0,    0,    0, 0.249983996152878]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Final Density Matrix\n",
    "rhoeq.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "DM = DensityMatrix(QS,Ham)\n",
    "\n",
    "Thermal_DensMatrix = False\n",
    "\n",
    "if Thermal_DensMatrix:    \n",
    "    # High Temperature\n",
    "    HT_approx = False\n",
    "    \n",
    "    # Initial Density Matrix\n",
    "    rho_in = DM.EqulibriumDensityMatrix(QS.Ispintemp,HT_approx)\n",
    "    \n",
    "    # Equlibrium Density Matrix\n",
    "    rhoeq = DM.EqulibriumDensityMatrix(QS.Fspintemp,HT_approx)\n",
    "else:\n",
    "    rho_in = QS.Az + QS.Bz\n",
    "    rhoeq = QS.Az + QS.Bz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0, 0, 0,    0],\n",
       "[  0, 0, 0,    0],\n",
       "[  0, 0, 0,    0],\n",
       "[  0, 0, 0, -1.0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initial Density Matrix\n",
    "rho_in.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.0, 0, 0,    0],\n",
       "[  0, 0, 0,    0],\n",
       "[  0, 0, 0,    0],\n",
       "[  0, 0, 0, -1.0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Final Density Matrix\n",
    "rhoeq.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Individual density matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.500016005441018 & 0\\\\0 & 0.499983994558982\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.500016005441018,                 0],\n",
       "[                0, 0.499983994558982]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QS.Arho.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.500016005442617 & 0\\\\0 & 0.499983994557383\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.500016005442617,                 0],\n",
       "[                0, 0.499983994557383]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QS.Brho.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.250016005697992 & 0 & 0 & 0\\\\0 & 0.249999999743026 & 0 & 0\\\\0 & 0 & 0.249999999744626 & 0\\\\0 & 0 & 0 & 0.249983994814357\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.250016005697992,                 0,                 0,                 0],\n",
       "[                0, 0.249999999743026,                 0,                 0],\n",
       "[                0,                 0, 0.249999999744626,                 0],\n",
       "[                0,                 0,                 0, 0.249983994814357]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = QS.Arho.TensorProduct(QS.Brho)\n",
    "rho.matrix"
   ]
  }
 ],
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