# import the required python packages

%pylab inline

from qutip import *

wc = 1.0  * 2 * pi  # cavity frequency
wa = 1.0  * 2 * pi  # atom frequency
g  = 0.05 * 2 * pi  # coupling strength
kappa = 0.005       # cavity dissipation rate
gamma = 0.05        # atom dissipation rate
N = 15              # number of cavity fock states
n_th_a = 0.0        # temperature in frequency units
use_rwa = True

tlist = linspace(0,25,100)

# intial state
psi0 = tensor(basis(N,0), basis(2,1))    # start with an excited atom

# operators
a  = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))

# Hamiltonian
if use_rwa:
    H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())
else:
    H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())

c_op_list = []

rate = kappa * (1 + n_th_a)
if rate > 0.0:
    c_op_list.append(sqrt(rate) * a)

rate = kappa * n_th_a
if rate > 0.0:
    c_op_list.append(sqrt(rate) * a.dag())

rate = gamma
if rate > 0.0:
    c_op_list.append(sqrt(rate) * sm)

output = mesolve(H, psi0, tlist, c_op_list, [a.dag() * a, sm.dag() * sm])

figure(figsize=(8,5))
plot(tlist, output.expect[0], label="Cavity")
plot(tlist, output.expect[1], label="Atom excited state")
legend()
xlabel('Time')
ylabel('Occupation probability')
title('Vacuum Rabi oscillations')
show()