{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6718709f",
   "metadata": {},
   "source": [
    "# Basis Change of the System (Spin operators and States)\n",
    "- Author: Vineeth Francis Thalakottoor\n",
    "- Email: vineeth.thalakottoor@ens.psl.eu or vineethfrancis.physics@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "27a57f94",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the source path\n",
    "SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/PyOR/Source_Doc'\n",
    "\n",
    "# Add source path\n",
    "import sys\n",
    "sys.path.append(SourcePath)\n",
    "import time\n",
    "%matplotlib ipympl\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\n",
    "from PyOR_HardPulse import HardPulse\n",
    "from PyOR_Basis import Basis\n",
    "from PyOR_Evolution import Evolutions\n",
    "from PyOR_Plotting import Plotting\n",
    "import PyOR_SignalProcessing as Spro\n",
    "from PyOR_Commutators import Commutators\n",
    "from PyOR_QuantumLibrary import QuantumLibrary\n",
    "from PyOR_Relaxation import RelaxationProcess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ab0e39a3",
   "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()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbf2e20a",
   "metadata": {},
   "source": [
    "### Spin Operators\n",
    "- After (first) QS.Initialize(), spin operators are always in Zeeman basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8e9435da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0.5\\\\0.5 & 0 & 0 & 0\\\\0 & 0.5 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0,   0, 0.5,   0],\n",
       "[  0,   0,   0, 0.5],\n",
       "[0.5,   0,   0,   0],\n",
       "[  0, 0.5,   0,   0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QS.Ax.matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3a59211f",
   "metadata": {},
   "source": [
    "### Set parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "275d8217",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor Frequency in MHz:  [-400.22802765 -400.22806765]\n"
     ]
    }
   ],
   "source": [
    "# Master Equation\n",
    "QS.PropagationSpace = \"Hilbert\"\n",
    "QS.MasterEquation = \"Redfield\"\n",
    "\n",
    "# Operator Basis\n",
    "#QS.Basis_SpinOperators_Hilbert = \"Singlet Triplet\" # or\n",
    "QS.Basis_SpinOperators_Hilbert = \"Zeeman\"\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",
    "# Define paris of spins coupled by dipolar interaction\n",
    "QS.Dipole_Pairs = [(\"A\",\"B\")]\n",
    "\n",
    "# Relaxation Process\n",
    "QS.Rprocess = \"Auto-correlated Dipolar Homonuclear\"\n",
    "QS.RelaxParDipole_tau = 10.0e-12\n",
    "QS.RelaxParDipole_bIS = [30.0e3]\n",
    "\n",
    "QS.Update()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0f7c0f44",
   "metadata": {},
   "source": [
    "### Generate Hamiltonians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b27e93bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor Frequency in MHz:  [-400.22802765 -400.22806765]\n"
     ]
    }
   ],
   "source": [
    "# generate Larmor Frequencies\n",
    "\n",
    "Ham = Hamiltonian(QS)\n",
    "COMM = Commutators(QS)\n",
    "\n",
    "# Zeeman Hamiltonian in rotating frame\n",
    "Hz = Ham.Zeeman_RotFrame()\n",
    "\n",
    "# J coupling Hamiltonian\n",
    "Hj = Ham.Jcoupling()\n",
    "\n",
    "# Generating the commutation superoperator\n",
    "QLib = QuantumLibrary(QS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fb63d498",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-30.0000000759161 & 0 & 0 & 0\\\\0 & 20.0000008601147 & 0 & 0\\\\0 & 0 & -20.0000008601147 & 0\\\\0 & 0 & 0 & 30.0000000759161\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-30.0000000759161,                0,                 0,                0],\n",
       "[                0, 20.0000008601147,                 0,                0],\n",
       "[                0,                0, -20.0000008601147,                0],\n",
       "[                0,                0,                 0, 30.0000000759161]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hz.Inverse2PI().matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7792fc79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.24999997786618 & 0 & 0 & 0\\\\0 & -1.24999997786618 & 2.49999995573235 & 0\\\\0 & 2.49999995573235 & -1.24999997786618 & 0\\\\0 & 0 & 0 & 1.24999997786618\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.24999997786618,                 0,                 0,                0],\n",
       "[               0, -1.24999997786618,  2.49999995573235,                0],\n",
       "[               0,  2.49999995573235, -1.24999997786618,                0],\n",
       "[               0,                 0,                 0, 1.24999997786618]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hj.Inverse2PI().Tolarence(1.0e-5).matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db7744d2",
   "metadata": {},
   "source": [
    "### Calling Hamiltonian class from QunautmSystem class\n",
    "- Alternate way of calling Hamiltonian class from QuantuSystem class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "74f01d80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.24999997786618 & 0 & 0 & 0\\\\0 & -1.24999997786618 & 2.49999995573235 & 0\\\\0 & 2.49999995573235 & -1.24999997786618 & 0\\\\0 & 0 & 0 & 1.24999997786618\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.24999997786618,                 0,                 0,                0],\n",
       "[               0, -1.24999997786618,  2.49999995573235,                0],\n",
       "[               0,  2.49999995573235, -1.24999997786618,                0],\n",
       "[               0,                 0,                 0, 1.24999997786618]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hj1 = QS.Class_hamiltonian.Jcoupling()\n",
    "Hj1.Inverse2PI().Tolarence(1.0e-5).matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6be770d3",
   "metadata": {},
   "source": [
    "### Spin operators\n",
    "- After QS.Update, all the spin operators will be in the new basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "24deaadc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0.5 & 0\\\\0 & 0 & 0 & 0.5\\\\0.5 & 0 & 0 & 0\\\\0 & 0.5 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0,   0, 0.5,   0],\n",
       "[  0,   0,   0, 0.5],\n",
       "[0.5,   0,   0,   0],\n",
       "[  0, 0.5,   0,   0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QS.Ax.matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5500951f",
   "metadata": {},
   "source": [
    "### Basis states\n",
    "- Singlet and triplet\n",
    "- Zeeman"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7c1c7bfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Singlet Triplet states\n",
    "ST_B, dic_ST = QS.Class_basis.SingletTriplet_Basis()\n",
    "\n",
    "# Zeeman states\n",
    "Z_B, dic_Z = QS.Class_basis.Zeeman_Basis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "80da9d16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['S0 ', 'Tp ', 'T0 ', 'Tm ']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Singlet triplet states dictionary\n",
    "dic_ST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d1794d8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['|1/2,1/2⟩|1/2,1/2⟩',\n",
       " '|1/2,1/2⟩|1/2,-1/2⟩',\n",
       " '|1/2,-1/2⟩|1/2,1/2⟩',\n",
       " '|1/2,-1/2⟩|1/2,-1/2⟩']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Zeeman states dictionary\n",
    "dic_Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "47a7c15e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0.707106781186547\\\\-0.707106781186547\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                 0],\n",
       "[ 0.707106781186547],\n",
       "[-0.707106781186547],\n",
       "[                 0]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ST_B[0].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8aa491c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\1.0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[1.0],\n",
       "[  0],\n",
       "[  0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_B[1].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "36bc4732",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ket State = 1.0 Tm \n"
     ]
    }
   ],
   "source": [
    "# Decompose the states in basis states\n",
    "QS.Class_basis.KetState_Components(Z_B[3],ST_B, dic_ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1513fc02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0],\n",
       "[  0],\n",
       "[  0],\n",
       "[1.0]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a stat with magnetic quantum number\n",
    "X1 = QS.State({\"A\": -1/2,\"B\": -1/2})\n",
    "X1.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "bf9780a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ket State = 1.0 Tm \n"
     ]
    }
   ],
   "source": [
    "QS.Class_basis.KetState_Components(X1, ST_B, dic_ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b0103a5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ket State = 1.0 |1/2,-1/2⟩|1/2,-1/2⟩\n"
     ]
    }
   ],
   "source": [
    "QS.Class_basis.KetState_Components(X1, Z_B, dic_Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3d6a8bf2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ket State = 0.70711 |1/2,1/2⟩|1/2,-1/2⟩ + -0.70711 |1/2,-1/2⟩|1/2,1/2⟩\n"
     ]
    }
   ],
   "source": [
    "QS.Class_basis.KetState_Components(ST_B[0], Z_B, dic_Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b82657e9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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