{
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  {
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   "id": "6718709f",
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   "source": [
    "# Spherical Tensors Product Operators (Spin One)\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\" : \"H2\"}\n",
    "QS = QunS(Spin_list,PrintDefault=False)\n",
    "\n",
    "# initialize the system\n",
    "QS.Initialize()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6f86d849",
   "metadata": {},
   "source": [
    "## Product Operator Basis: Spherical Tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "efb23439",
   "metadata": {},
   "outputs": [],
   "source": [
    "BS = Basis(QS)\n",
    "\n",
    "Basis_ST, coherence_ST, Dic_ST = BS.ProductOperators_SphericalTensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7cd39f7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, -1, 0, 1, -2, -1, 0, 1, 2]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coherence_ST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "73333478",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['T(0,0)',\n",
       " 'T(1,-1)',\n",
       " 'T(1,0)',\n",
       " 'T(1,1)',\n",
       " 'T(2,-2)',\n",
       " 'T(2,-1)',\n",
       " 'T(2,0)',\n",
       " 'T(2,1)',\n",
       " 'T(2,2)']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dic_ST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4f261213",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['T(0,0)', 'T(1,-1)', 'T(1,0)', 'T(1,1)', 'T(2,-2)', 'T(2,-1)', 'T(2,0)', 'T(2,1)', 'T(2,2)']\n"
     ]
    }
   ],
   "source": [
    "OpB_ST = BS.String_to_Matrix(Dic_ST, Basis_ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d0632fe6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.577350269189626 & 0 & 0\\\\0 & 0.577350269189626 & 0\\\\0 & 0 & 0.577350269189626\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0.577350269189626,                 0,                 0],\n",
       "[                0, 0.577350269189626,                 0],\n",
       "[                0,                 0, 0.577350269189626]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OpB_ST['T(0,0)'].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "41a46a96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0.707106781186548 & 0 & 0\\\\0 & 0.707106781186548 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                0,                 0, 0],\n",
       "[0.707106781186548,                 0, 0],\n",
       "[                0, 0.707106781186548, 0]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OpB_ST['T(1,-1)'].matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9a02a813",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\1.0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0, 0, 0],\n",
       "[  0, 0, 0],\n",
       "[1.0, 0, 0]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OpB_ST['T(2,-2)'].matrix"
   ]
  }
 ],
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