Issues with Hamiltonian in qutip

[latifeh iri]

Hi all,

Still new to QuTip and trying to use for three level systems but the problem is changing the value of H0, when I am trying to change the value and plot the expectation value based on time, there is nothing changed! and getting the same result for different H0 (this part is including cavity frequency and atomic frequency), in contrast, by changing the interaction part of Hamiltonian (including 'g' , 'adagger' and 'a'), here the figure can be changed. Could anyone please help me with this issue?

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

wf = 2.7/ 27.211

delta = 0

wa = wf

g = 1

H0 = (wf*adagger*a) + (0.5*wa*smz)

H_int = g*(smplus*a+smminus*adagger)

H = ((wf*adagger*a) + (0.5*wa*smz) + g*(smplus*a+smminus*adagger))

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

Thank you so much in advance,

Latifeh

[Anna Naden]

What are you using for your initial state?

[Anna Naden]

I am not sure about the way you have constructed your Hamiltonian.

Here is my Hamiltonian for a three-level atom in a cavity:

from qutip import tensor, Qobj, qeye, destroy

import numpy as np

def fluorescence_hamiltonian(N, g21, g10, wa0, wa1, wa2):

a10 = tensor(destroy(N), qeye(N),qeye(3))

a21 = tensor(qeye(N), destroy(N), qeye(3))

sm21 = tensor(qeye(N), qeye(N),Qobj([[0,0,0],[0,0,1],[0,0,0]])) #Transition from second to first excited state

sm10 = tensor(qeye(N), qeye(N),Qobj([[0,1,0],[0,0,0],[0,0,0]])) #Transition from first excited state to ground state

# Hamiltonian without light-matter interaction

H = (wa1-wa0) * a10.dag() * a10 + + (wa2-wa1)*a21.dag()*a21+tensor(qeye(N), qeye(N),Qobj([[0,0,0],[0,wa1,0],[0,0,wa2]]))

# Light-atom interaction

Hi = g21*(a21.dag()*sm21+sm21.dag()*a21) #Emission from second exited state, absorbsion from second exited state

Hi += g10*(a10.dag()*sm10+sm10.dag()*a10)

# Transform to interaction picture

h=[[1,0,0],[0,np.exp(1j*wa1),0],[0,0,np.exp(1j*wa2)]]

EH=tensor(qeye(N),qeye(N),Qobj(h))

H=EH*Hi*EH.dag()

# It has to be Hermitian

assert H.isherm

return H

[Anna Naden]

Here is a simpler Hamiltonian, without the transformation to interaction picture. It is for a two-level system and treats the cavity semiclassically.

def hamiltonian(omega0,omega1):

def h12(t, args):

phaseME = args['phaseME']

omega_rf = args['omega_rf']

rabi=args['rabi']

phase_rf = args['phase_rf']

phase=np.exp(1j*phaseME)

return phase*rabi*np.cos(omega_rf*t+phase_rf)

def h21(t,args):

return np.conj(h12(t,args))

H0=Qobj([[omega0,0],[0,omega1]])

Hi = np.array([[0,1],[0,0]])

Hi1=Qobj(Hi)

Hi2=Qobj(np.transpose(Hi))

H = QobjEvo([H0,[Hi1,h12],[Hi2,h21]])

return H