{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyOR Quantum\n",
    "## Author: Vineeth Thalakottoor\n",
    "## Introduction to CSA Hamiltonians"
   ]
  },
  {
   "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 numpy as np\n",
    "# Import PyOR package\n",
    "from PyOR_QuantumSystem import QuantumSystem as QunS\n",
    "from PyOR_Hamiltonian import Hamiltonian\n",
    "from PyOR_QuantumLibrary import QuantumLibrary\n",
    "import PyOR_SphericalTensors as ST\n",
    "import PyOR_Rotation as Rot\n",
    "QLib = QuantumLibrary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the spin system\n",
    "Spin_list = {\"A\" : \"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': -628541601.39}\n",
      "Offset frequencies: {'A': 0.0}\n",
      "Initial spin temperatures: {'A': 300.0}\n",
      "Final spin temperatures: {'A': 300.0}\n",
      "Radiation damping gain: {'A': 0}\n",
      "Radiation damping phase: {'A': 0}\n",
      "\n",
      "Rprocess = Phenomenological\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 = QS.L100\n",
    "\n",
    "# Offset Frequency in rotating frame (Hz)\n",
    "QS.OFFSET[\"A\"] = 0.0\n",
    "\n",
    "\n",
    "# Define initial and final Spin Temperature\n",
    "QS.I_spintemp[\"A\"] = 300.0\n",
    "QS.F_spintemp[\"A\"] = 300.0\n",
    "\n",
    "# Relaxation Process\n",
    "QS.Rprocess = \"Phenomenological\"\n",
    "QS.R1 = 1\n",
    "QS.R2 = 2\n",
    "\n",
    "QS.Update()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zeeman Hamiltonians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor Frequency in MHz:  [-100.0355028]\n"
     ]
    }
   ],
   "source": [
    "# generate Larmor Frequencies\n",
    "QS.print_Larmor = True\n",
    "Ham = Hamiltonian(QS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-50017753.8359235 & 0\\\\0 & 50017753.8359235\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-50017753.8359235,                0],\n",
       "[                0, 50017753.8359235]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lab Frame Hamiltonian\n",
    "Hz_lab = Ham.Zeeman()\n",
    "Hz_lab.Inverse2PI().matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0],\n",
       "[0, 0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rotating Frame Hamiltonian\n",
    "Hz = Ham.Zeeman_RotFrame()\n",
    "Hz.Inverse2PI().matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA tensor PAF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}15.0 & 0 & 0\\\\0 & 5.0 & 0\\\\0 & 0 & -5.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[15.0,   0,    0],\n",
       "[   0, 5.0,    0],\n",
       "[   0,   0, -5.0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_iso = 5.0 # Hz\n",
    "delta_aniso = -10.0 # Hz\n",
    "\n",
    "IT_PAF = Ham.InteractionTensor_PAF_CSA(Iso=delta_iso,Aniso=delta_aniso,Asymmetry=1.0)\n",
    "IT_PAF.Inverse2PI().matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Isotropic': 4.999999999999999,\n",
       " 'Anisotropy': -10.0,\n",
       " 'Asymmetry': 0.9999999999999999}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PAF_Decom = Ham.InteractionTensor_PAF_Decomposition(IT_PAF)\n",
    "PAF_Decom"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA tensor LAB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}41.05 & 3.507 & -58.146\\\\3.507 & 32.692 & -21.163\\\\-58.146 & -21.163 & 20.505\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  41.05,   3.507, -58.146],\n",
       "[  3.507,  32.692, -21.163],\n",
       "[-58.146, -21.163,  20.505]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi,theta = 20.0,40.0\n",
    "\n",
    "IT_LAB = Ham.InteractionTensor_LAB(IT_PAF,phi,theta,0)\n",
    "IT_LAB.Round(3).matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}31.4159265358979 & 0 & 0\\\\0 & 31.4159265358979 & 0\\\\0 & 0 & 31.4159265358979\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[31.4159265358979,                0,                0],\n",
       "[               0, 31.4159265358979,                0],\n",
       "[               0,                0, 31.4159265358979]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LAB_Decom = Ham.InteractionTensor_LAB_Decomposition(IT_LAB)\n",
    "LAB_Decom['Isotropic'].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}6.533 & 0.558 & -9.254\\\\0.558 & 5.203 & -3.368\\\\-9.254 & -3.368 & 3.264\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 6.533,  0.558, -9.254],\n",
       "[ 0.558,  5.203, -3.368],\n",
       "[-9.254, -3.368,  3.264]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LAB_Decom[\"Symmetric\"].Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 0],\n",
       "[0, 0, 0],\n",
       "[0, 0, 0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LAB_Decom[\"Antisymmetric\"].Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA Hamiltonian in Lab frame (Secular)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & 0\\\\0 & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.39,     0],\n",
       "[   0, -1.39]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = \"A\"\n",
    "B = \"\"\n",
    "\n",
    "Hcsa_LAB_Truncates = Ham.Interaction_Hamiltonian_LAB_CSA_Secular(A,IT_PAF,theta,phi)\n",
    "Hcsa_LAB_Truncates.Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA Hamiltonian in Lab frame (Cartesian, Euler rotation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & -4.636 + 1.033 i\\\\-4.636 - 1.033 i & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[            1.39, -4.636 + 1.033*I],\n",
       "[-4.636 - 1.033*I,            -1.39]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hcsa_LAB_Euler = Ham.Interaction_Hamiltonian_Catesian_Euler(A,IT_PAF,B,0,theta,phi)\n",
    "Hcsa_LAB_Euler.Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA Hamiltonian in Lab frame (Cartesian, Wigner rotation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & -4.636 + 1.033 i\\\\-4.636 - 1.033 i & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[            1.39, -4.636 + 1.033*I],\n",
       "[-4.636 - 1.033*I,            -1.39]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hcsa_LAB_Wig = Ham.Interaction_Hamiltonian_Catesian_Wigner(A,IT_PAF,B,0,theta,phi)\n",
    "Hcsa_LAB_Wig.Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CSA Hamiltonian in Lab frame (Spherical Tensors, Wigner Rotation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & -4.636 - 1.033 i\\\\-4.636 + 1.033 i & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[            1.39, -4.636 - 1.033*I],\n",
       "[-4.636 + 1.033*I,            -1.39]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,\"spin-field\",\"all\", 0,theta,phi)\n",
    "Hcsa_LAB_ST.Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & 0\\\\0 & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.39,     0],\n",
       "[   0, -1.39]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,\"spin-field\",\"secular\", 0,theta,phi)\n",
    "Hcsa_LAB_ST.Inverse2PI().Round(3).matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.39 & 0\\\\0 & -1.39\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1.39,     0],\n",
       "[   0, -1.39]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,\"spin-field\",\"secular + pseudosecular\", 0,theta,phi)\n",
    "Hcsa_LAB_ST.Inverse2PI().Round(3).matrix"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}