help

[mahmoud mohammadi]

Hello, dear members of the group

I want to get the Thermal density matrix for a cavity-atomic system whose Hamiltonian depends on space and time, and I need help. I have written the program code to get the Hamiltonian that I am sending. Thank you for your attention.

import numpy as np

from qutip import *

import matplotlib.pyplot as plt  

wc = 1.2 #avity frequency in 1000THZ

wa = 1.2 #  qubit/atom frenqency in 1000THZ

g = 0.3 # coupling strenght

etal = 1. # in range unit

etaT = 1. # in range unit

h= 1.054*10**-34 # constant plank

# poump frequency

wl = 1.2 # poump longitudinal frenqency in 1000THZ

wT = 0.001 # poump transverse frenqency in 1000THZ

# mass of atom in kg

m = 141.8765 *10**-27 

t = np.linspace(0,100,100)

x = np.linspace(0,100,100)

times = np.linspace(0,100,100)

#initial state for atom

gr=basis(2,0)

ex=basis(2,1)

psi0atom=(1/np.sqrt(2))*(gr+ex)

# definition state for cavity 

psi0cavity = (1/np.sqrt(2))*(basis(2,0)+ basis(2,1))

#definition states for atom_cavity system

psi0= tensor( psi0atom,psi0cavity)

# definition Hamiltonian H=H0+Hint

#term H0= kinetic energy atom + free term atom and cavity

ke=(1/h)*(tensor((momentum(2)**2)/(2.*m),qeye(2)))

a = destroy(2)

H0=ke+wc*(tensor(qeye(2),a.dag()*a)) +wa*tensor(sigmaz(),qeye(2))

# Hamiltoni interaction atom and field

Hint=g*(tensor(sigmap(),a)+tensor(sigmam(),a.dag()))

def f0(x,args):

    return np.cos(x)

hpl=1j*etal*(tensor(qeye(2),a.dag()))

hpll=-1j*etal*(tensor(qeye(2),a))

hpT=1j*etaT*(tensor(sigmap(),qeye(2)))

hpTT=-1j*etaT*(tensor(sigmam(),qeye(2)))

################################

def f1(t,args):

    return np.exp(-1j*wl*t)

     

def f2(t,args):

    return np.exp(1j*wl*t)

def f3(t,args):

    return np.exp(-1j*wT*t)

def f4(t,args):

    return np.exp(1j*wT*t)

##################################

# H is with random walk and HH is without random walk and print it 

h0=wc*(tensor(qeye(2),a.dag()*a))+wa*tensor(sigmaz(),qeye(2))

HH=[h0,Hint,[hpl,f1],[hpll,f2]]

H = [H0,[Hint,f0],[hpl,f1],[hpll,f2],[hpT,f3],[hpTT,f4]]

H