PyOR Quantum

Author: Vineeth Thalakottoor

Introduction to CSA Hamiltonians

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

# Add source path
import sys
sys.path.append(SourcePath)

import numpy as np
# Import PyOR package
from PyOR_QuantumSystem import QuantumSystem as QunS
from PyOR_Hamiltonian import Hamiltonian
from PyOR_QuantumLibrary import QuantumLibrary
import PyOR_SphericalTensors as ST
import PyOR_Rotation as Rot
QLib = QuantumLibrary()

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

# initialize the system
QS.Initialize()

Set parameters

# Master Equation
QS.PropagationSpace = "Hilbert"
QS.MasterEquation = "Redfield"

# B0 Field in Tesla, Static Magnetic field (B0) along Z
QS.B0 = QS.L100

# Offset Frequency in rotating frame (Hz)
QS.OFFSET["A"] = 0.0


# Define initial and final Spin Temperature
QS.I_spintemp["A"] = 300.0
QS.F_spintemp["A"] = 300.0

# Relaxation Process
QS.Rprocess = "Phenomenological"
QS.R1 = 1
QS.R2 = 2

QS.Update()

Rotating frame frequencies: {'A': -628541601.39}
Offset frequencies: {'A': 0.0}
Initial spin temperatures: {'A': 300.0}
Final spin temperatures: {'A': 300.0}
Radiation damping gain: {'A': 0}
Radiation damping phase: {'A': 0}

Rprocess = Phenomenological
RelaxParDipole_tau = 0.0
DipolePairs = []
RelaxParDipole_bIS = []

Zeeman Hamiltonians

# generate Larmor Frequencies
QS.print_Larmor = True
Ham = Hamiltonian(QS)

Larmor Frequency in MHz:  [-100.0355028]

# Lab Frame Hamiltonian
Hz_lab = Ham.Zeeman()
Hz_lab.Inverse2PI().matrix

$\displaystyle \left[\begin{matrix}-50017753.8359235 & 0\\0 & 50017753.8359235\end{matrix}\right]$

# Rotating Frame Hamiltonian
Hz = Ham.Zeeman_RotFrame()
Hz.Inverse2PI().matrix

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

CSA tensor PAF

delta_iso = 5.0 # Hz
delta_aniso = -10.0 # Hz

IT_PAF = Ham.InteractionTensor_PAF_CSA(Iso=delta_iso,Aniso=delta_aniso,Asymmetry=1.0)
IT_PAF.Inverse2PI().matrix

$\displaystyle \left[\begin{matrix}15.0 & 0 & 0\\0 & 5.0 & 0\\0 & 0 & -5.0\end{matrix}\right]$

PAF_Decom = Ham.InteractionTensor_PAF_Decomposition(IT_PAF)
PAF_Decom

{'Isotropic': 4.999999999999999,
 'Anisotropy': -10.0,
 'Asymmetry': 0.9999999999999999}

CSA tensor LAB

phi,theta = 20.0,40.0

IT_LAB = Ham.InteractionTensor_LAB(IT_PAF,phi,theta,0)
IT_LAB.Round(3).matrix

$\displaystyle \left[\begin{matrix}41.05 & 3.507 & -58.146\\3.507 & 32.692 & -21.163\\-58.146 & -21.163 & 20.505\end{matrix}\right]$

LAB_Decom = Ham.InteractionTensor_LAB_Decomposition(IT_LAB)
LAB_Decom['Isotropic'].matrix

$\displaystyle \left[\begin{matrix}31.4159265358979 & 0 & 0\\0 & 31.4159265358979 & 0\\0 & 0 & 31.4159265358979\end{matrix}\right]$

LAB_Decom["Symmetric"].Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}6.533 & 0.558 & -9.254\\0.558 & 5.203 & -3.368\\-9.254 & -3.368 & 3.264\end{matrix}\right]$

LAB_Decom["Antisymmetric"].Inverse2PI().Round(3).matrix

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

CSA Hamiltonian in Lab frame (Secular)

A = "A"
B = ""

Hcsa_LAB_Truncates = Ham.Interaction_Hamiltonian_LAB_CSA_Secular(A,IT_PAF,theta,phi)
Hcsa_LAB_Truncates.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & 0\\0 & -1.39\end{matrix}\right]$

CSA Hamiltonian in Lab frame (Cartesian, Euler rotation)

Hcsa_LAB_Euler = Ham.Interaction_Hamiltonian_Catesian_Euler(A,IT_PAF,B,0,theta,phi)
Hcsa_LAB_Euler.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & -4.636 + 1.033 i\\-4.636 - 1.033 i & -1.39\end{matrix}\right]$

CSA Hamiltonian in Lab frame (Cartesian, Wigner rotation)

Hcsa_LAB_Wig = Ham.Interaction_Hamiltonian_Catesian_Wigner(A,IT_PAF,B,0,theta,phi)
Hcsa_LAB_Wig.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & -4.636 + 1.033 i\\-4.636 - 1.033 i & -1.39\end{matrix}\right]$

CSA Hamiltonian in Lab frame (Spherical Tensors, Wigner Rotation)

Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,"spin-field","all", 0,theta,phi)
Hcsa_LAB_ST.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & -4.636 - 1.033 i\\-4.636 + 1.033 i & -1.39\end{matrix}\right]$

Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,"spin-field","secular", 0,theta,phi)
Hcsa_LAB_ST.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & 0\\0 & -1.39\end{matrix}\right]$

Hcsa_LAB_ST = Ham.Interaction_Hamiltonian_SphericalTensor(A,IT_PAF,B,"spin-field","secular + pseudosecular", 0,theta,phi)
Hcsa_LAB_ST.Inverse2PI().Round(3).matrix

$\displaystyle \left[\begin{matrix}1.39 & 0\\0 & -1.39\end{matrix}\right]$