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import numpy as np
from matplotlib import pyplot
import qutip
delta = 0.2 * 2*np.pi
eps0 = 1.0 * 2*np.pi
A = 0.5 * 2*np.pi
omega = 1.0 * 2*np.pi
T = (2*np.pi)/omega
tlist = np.linspace(0.0, 10 * T, 101)
psi0 = qutip.basis(2, 0)
H0 = - delta/2.0 * qutip.sigmax() - eps0/2.0 * qutip.sigmaz()
H1 = A/2.0 * qutip.sigmaz()
args = {'w': omega}
H = [H0, [H1, lambda t, w: np.sin(w * t)]]
# Create the floquet system for the time-dependent hamiltonian
floquetbasis = qutip.FloquetBasis(H, T, args)
# decompose the inital state in the floquet modes
f_coeff = floquetbasis.to_floquet_basis(psi0)
# calculate the wavefunctions using the from the floquet modes coefficients
p_ex = np.zeros(len(tlist))
for n, t in enumerate(tlist):
psi_t = floquetbasis.from_floquet_basis(f_coeff, t)
p_ex[n] = qutip.expect(qutip.num(2), psi_t)
# For reference: calculate the same thing with mesolve
p_ex_ref = qutip.mesolve(H, psi0, tlist, e_ops=[qutip.num(2)], args=args).expect[0]
# plot the results
pyplot.plot(tlist, np.real(p_ex), 'ro', tlist, 1-np.real(p_ex), 'bo')
pyplot.plot(tlist, np.real(p_ex_ref), 'r', tlist, 1-np.real(p_ex_ref), 'b')
pyplot.xlabel('Time')
pyplot.ylabel('Occupation probability')
pyplot.legend(("Floquet $P_1$", "Floquet $P_0$", "Lindblad $P_1$", "Lindblad $P_0$"))
pyplot.show()
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