Spherical Tensors Product Operators (Two Spin Half)

[1]:

# Define the source path
SourcePath = '/media/HD2/Vineeth/PostDoc_Simulations/Github/PyOR_V1/PyOR_Combined/PyOR/Source_Doc'

# Add source path
import sys
sys.path.append(SourcePath)
import time
%matplotlib ipympl

# Import PyOR package
from PyOR_QuantumSystem import QuantumSystem as QunS
from PyOR_Hamiltonian import Hamiltonian
from PyOR_DensityMatrix import DensityMatrix
from PyOR_QuantumObject import QunObj
from PyOR_HardPulse import HardPulse
from PyOR_Basis import Basis
from PyOR_Evolution import Evolutions
from PyOR_Plotting import Plotting
import PyOR_SignalProcessing as Spro
from PyOR_Commutators import Commutators
from PyOR_QuantumLibrary import QuantumLibrary
from PyOR_Relaxation import RelaxationProcess

[2]:

# Define the spin system
Spin_list = {"A" : "H1","B" : "H1"}
QS = QunS(Spin_list,PrintDefault=False)

# initialize the system
QS.Initialize()

Product Operator Basis: Spherical Tensors

[3]:

BS = Basis(QS)

Basis_ST, coherence_ST, Dic_ST = BS.ProductOperators_SphericalTensor()

[4]:

coherence_ST

[4]:

[-2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2]

[5]:

Dic_ST

[5]:

['T(1,-1)T(1,-1)',
 'T(0,0)T(1,-1)',
 'T(1,-1)T(0,0)',
 'T(1,-1)T(1,0)',
 'T(1,0)T(1,-1)',
 'T(0,0)T(0,0)',
 'T(0,0)T(1,0)',
 'T(1,-1)T(1,1)',
 'T(1,0)T(0,0)',
 'T(1,0)T(1,0)',
 'T(1,1)T(1,-1)',
 'T(0,0)T(1,1)',
 'T(1,0)T(1,1)',
 'T(1,1)T(0,0)',
 'T(1,1)T(1,0)',
 'T(1,1)T(1,1)']

[6]:

Basis_ST[0].matrix

[6]:
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\1.0 & 0 & 0 & 0\end{matrix}\right]$
[7]:

Basis_ST[1].matrix

[7]:
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 0\\0.707106781186547 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0.707106781186547 & 0\end{matrix}\right]$
[8]:

Basis_ST[2].matrix

[8]:
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0.707106781186547 & 0 & 0 & 0\\0 & 0.707106781186547 & 0 & 0\end{matrix}\right]$
[9]:

Basis_ST[3].matrix

[9]:
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0.707106781186547 & 0 & 0 & 0\\0 & -0.707106781186547 & 0 & 0\end{matrix}\right]$

String Index

[10]:

B_ST = BS.String_to_Matrix(Dic_ST, Basis_ST)

['T(1,-1)T(1,-1)', 'T(0,0)T(1,-1)', 'T(1,-1)T(0,0)', 'T(1,-1)T(1,0)', 'T(1,0)T(1,-1)', 'T(0,0)T(0,0)', 'T(0,0)T(1,0)', 'T(1,-1)T(1,1)', 'T(1,0)T(0,0)', 'T(1,0)T(1,0)', 'T(1,1)T(1,-1)', 'T(0,0)T(1,1)', 'T(1,0)T(1,1)', 'T(1,1)T(0,0)', 'T(1,1)T(1,0)', 'T(1,1)T(1,1)']

[11]:

B_ST['T(1,-1)T(1,-1)'].matrix

[11]:
$\displaystyle \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\1.0 & 0 & 0 & 0\end{matrix}\right]$