Floquet states of driven quantum system using Qutip.floquet.

[usma...@phys.qau.edu.pk]

I was trying to execute driven system written in terms of harmonic oscillator creation and annihilation operators using Floquet Formulism. But it was giving bugs on incompatible shapes and sometimes for incompatible Hamiltonians. Kindly guide me how could one extract evolved floquet states and quasi-energies of such a driven system?

The code Follows:

from qutip import *

from numpy import *

import matplotlib.pyplot as plt

from matplotlib import figure

## Return the cosine of an operator ##

def cosine(Op):

    return 0.5*( (i*Op).expm() + (-i*Op).expm() )

# parameter values

i = 1.0j 

wc = 1.0 * 2 * pi

wp = 1.5 * 2 * pi

T = (2 * pi) / wp

N = 16

tlist  = linspace(0.0, 10 * T, 101)

psi0   = coherent(2,2)

epsilon = 0.165

etta = 0.707

# generate operators

a = destroy(N)

# define time-independent Hamiltonian term

H0 = wc * (a.dag() * a + 0.5) 

                                                                                         

# amplitude-dependent Hamiltonian term

H1 = epsilon*(cosine(etta*(a + a.dag())))

args = {'wp': wp}

# H = H0 + H1 * cos(w * t) in 'list-string' format

H = [H0, [H1, 'cos(wp * t)']]

# find the Floquet modes

f_modes_0, f_energies = floquet_modes(H, T, args)

# decompose the inital state in the floquet modes

f_coeff = floquet_state_decomposition(f_modes_0, f_energies, psi0)

# calculate the wavefunctions using the from the floquet modes

p_ex = zeros(len(tlist))

for n, t in enumerate(tlist):

    psi_t = floquet_wavefunction_t(f_modes_0, f_energies, f_coeff, t, H, T, args)

print psi_t

Output: TypeError: Incompatible Qobj shapes

Sincerely,

Usman-Ali