Introduction to 1D pulse acquisition (User defiend Hamiltonian)

Author: Vineeth Thalakottoor

Email: vineeth.thalakottoor@ens.psl.eu or vineethfrancis.physics@gmail.com# PyOR Quantum

[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
import numpy as np
%matplotlib ipympl

# Import PyOR package
from PyOR_QuantumSystem import QuantumSystem as QunS
from PyOR_HardPulse import HardPulse
from PyOR_Evolution import Evolutions
from PyOR_Plotting import Plotting
import PyOR_SignalProcessing as Spro

[2]:

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

# initialize the system
QS.Initialize()

Set parameters

[3]:

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

# Operator Basis
QS.Basis_SpinOperators_Hilbert = "Zeeman" # TTry "Singlet Triplet" and see what happen to the all spin operators and Hamiltoninas

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

QS.Update()

Larmor Frequency in MHz:  [-400.22801765 -400.22801765]

Spin operators

[4]:

QS.Az

[4]:

<PyOR_QuantumObject.QunObj at 0x7f2f6159e5d0>

[5]:

QS.Az.matrix

[5]:

$\displaystyle \left[\begin{matrix}0.5 & 0 & 0 & 0\\0 & 0.5 & 0 & 0\\0 & 0 & -0.5 & 0\\0 & 0 & 0 & -0.5\end{matrix}\right]$

[6]:

QS.Az.data

[6]:

array([[ 0.5+0.j,  0. +0.j,  0. +0.j,  0. +0.j],
       [ 0. +0.j,  0.5+0.j,  0. +0.j,  0. +0.j],
       [ 0. +0.j,  0. +0.j, -0.5+0.j, -0. +0.j],
       [ 0. +0.j,  0. +0.j, -0. +0.j, -0.5+0.j]])

[7]:

QS.Az_sub

[7]:

<PyOR_QuantumObject.QunObj at 0x7f2f61d3b200>

[8]:

QS.Az_sub.matrix

[8]:

$\displaystyle \left[\begin{matrix}0.5 & 0\\0 & -0.5\end{matrix}\right]$

Generate Hamiltonians

[9]:

# 1. Zeeman Hamiltonian

Hz = 2.0 * np.pi * 10 * QS.Az + 2.0 * np.pi * 50 * QS.Bz
Hz.Inverse2PI().matrix

[9]:

$\displaystyle \left[\begin{matrix}30.0 & 0 & 0 & 0\\0 & -20.0 & 0 & 0\\0 & 0 & 20.0 & 0\\0 & 0 & 0 & -30.0\end{matrix}\right]$

[10]:

# 2. J coupling Hamiltonian

Hj = 2.0 * np.pi * 5 * (QS.Ax * QS.Bx + QS.Ay * QS.By + QS.Az * QS.Bz)
Hj.Inverse2PI().matrix

[10]:

$\displaystyle \left[\begin{matrix}1.25 & 0 & 0 & 0\\0 & -1.25 & 2.5 & 0\\0 & 2.5 & -1.25 & 0\\0 & 0 & 0 & 1.25\end{matrix}\right]$

Initialize density matrix

[11]:

# Initial Density Matrix
rho_in = QS.Az + QS.Bz
rho_in.matrix

[11]:

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

[12]:

# Final Density Matrix
rhoeq = QS.Az + QS.Bz
rhoeq.matrix

[12]:

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

Hard Pulse

[13]:

HardP = HardPulse(QS)

flip_angle = 90.0   # Flip angle
rho = HardP.Rotate_Pulse(rho_in,flip_angle,QS.Ay + QS.By).Tolarence(1.0e-5)
rho.matrix

[13]:

$\displaystyle \left[\begin{matrix}0 & 0.5 & 0.5 & 0\\0.5 & 0 & 0 & 0.5\\0.5 & 0 & 0 & 0.5\\0 & 0.5 & 0.5 & 0\end{matrix}\right]$

Evolution

[14]:

QS.AcqDT = 0.0001
QS.AcqAQ = 5.0
QS.OdeMethod = 'DOP853'
QS.PropagationMethod = "ODE Solver"

EVol = Evolutions(QS)

start_time = time.time()
t, rho_t = EVol.Evolution(rho,rhoeq,Hz+Hj)
end_time = time.time()
timetaken = end_time - start_time
print("Total time = %s seconds " % (timetaken))

Larmor Frequency in MHz:  [-400.22801765 -400.22801765]
Total time = 3.014617443084717 seconds

Expectation

[15]:

det_Mt = QS.Ap + QS.Bp
det_Z = QS.Az + QS.Bz

t, Mt = EVol.Expectation(rho_t,det_Mt)
t, Mz = EVol.Expectation(rho_t,det_Z)

Plotting

[16]:

plot = Plotting(QS)

[23]:

plot.PlotFigureSize = (10,5)
plot.PlotFontSize = 20
plot.PlotXlimt= (0,5)
plot.PlotYlimt= (-2,2)
plot.Plotting_SpanSelector(t,Mt,"time (s)",r"$M_T$","red",saveplt=True,savename="Transverse Magnetization")

/opt/anaconda3/lib/python3.12/site-packages/matplotlib/cbook.py:1762: ComplexWarning: Casting complex values to real discards the imaginary part
  return math.isfinite(val)
/opt/anaconda3/lib/python3.12/site-packages/matplotlib/cbook.py:1398: ComplexWarning: Casting complex values to real discards the imaginary part
  return np.asarray(x, float)

[23]:

(<Figure size 1000x500 with 1 Axes>,
 <matplotlib.widgets.SpanSelector at 0x7f2f51ddac60>)

[21]:

plot.PlotFigureSize = (10,5)
plot.PlotFontSize = 20
plot.PlotXlimt= (0,5)
plot.PlotYlimt= (0,2)
plot.Plotting_SpanSelector(t,Mz,"time (s)",r"$M_Z$","red")

[21]:

(<Figure size 1000x500 with 1 Axes>,
 <matplotlib.widgets.SpanSelector at 0x7f2f538657c0>)

Fourier Transform

[19]:

freq, spectrum = Spro.FourierTransform(Mt,QS.AcqFS,5)

[20]:

plot.PlotFigureSize = (10,5)
plot.PlotFontSize = 20
plot.PlotXlimt= (0,60)
plot.PlotYlimt= (0,6000)
plot.Plotting_SpanSelector(freq,spectrum,"Frequency (Hz)","Spectrum","red")

[20]:

(<Figure size 1000x500 with 1 Axes>,
 <matplotlib.widgets.SpanSelector at 0x7f2f51e97020>)