# setup the matplotlib graphics library and configure it to show 
# figures inline in the notebook
%pylab inline

# make qutip available in the rest of the notebook
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        # avg number of thermal bath excitation
use_rwa = True

tlist = linspace(0,25,101)

# 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_ops = []

# cavity relaxation
rate = kappa * (1 + n_th_a)
if rate > 0.0:
    c_ops.append(sqrt(rate) * a)

# cavity excitation, if temperature > 0
rate = kappa * n_th_a
if rate > 0.0:
    c_ops.append(sqrt(rate) * a.dag())

# qubit relaxation
rate = gamma
if rate > 0.0:
    c_ops.append(sqrt(rate) * sm)

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

n_c = output.expect[0]
n_a = output.expect[1]

figure(figsize=(8,5))
plot(tlist, n_c, label="Cavity")
plot(tlist, n_a, label="Atom excited state")
legend()
xlabel('Time')
ylabel('Occupation probability')
title('Vacuum Rabi oscillations')
show()

output = mesolve(H, psi0, tlist, c_ops, [])

output

type(output.states)

len(output.states)

output.states[-1] # indexing the list with -1 results in the last element in the list

# find the indices of the density matrices for the times we are interested in
t_idx = where([tlist == t for t in [0.0, 5.0, 15.0, 25.0]])[1]
tlist[t_idx]

# get a list density matrices
rho_list = array(output.states)[t_idx]

# loop over the list of density matrices

xvec = linspace(-3,3,200)

fig, axes = subplots(1,len(rho_list), sharex=True, figsize=(3*len(rho_list),3))

for idx, rho in enumerate(rho_list):

    # trace out the atom from the density matrix, to obtain
    # the reduced density matrix for the cavity
    rho_cavity = ptrace(rho, 0)
    
    # calculate its wigner function
    W = wigner(rho_cavity, xvec, xvec)
    
    # plot its wigner function
    axes[idx].contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=get_cmap('RdBu'))

    axes[idx].set_title(r"$t = %.1f$" % tlist[t_idx][idx], fontsize=16)
    

t_idx = where([tlist == t for t in [0.0, 5.0, 10, 15, 20, 25]])[1]
rho_list = array(output.states)[t_idx]

fig_grid = (2, len(rho_list)*2)
fig = figure(figsize=(2.5*len(rho_list),5))

for idx, rho in enumerate(rho_list):
    rho_cavity = ptrace(rho, 0)
    W = wigner(rho_cavity, xvec, xvec)
    ax = subplot2grid(fig_grid, (0, 2*idx), colspan=2)
    ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=get_cmap('RdBu'))
    ax.set_title(r"$t = %.1f$" % tlist[t_idx][idx], fontsize=16)

# plot the cavity occupation probability in the ground stateLecture-1-Jaynes-Cumming-model
Delete

ax = subplot2grid(fig_grid, (1, 1), colspan=(fig_grid[1]-2))
ax.plot(tlist, n_c, label="Cavity")
ax.plot(tlist, n_a, label="Atom excited state")
ax.legend()
ax.set_xlabel('Time')
ax.set_ylabel('Occupation probability')