<jupyter_start><jupyter_text>Constants<jupyter_code>N = 3
r = 20 # k1/k2
k1 = 1<jupyter_output><empty_output><jupyter_text>Coherent States<jupyter_code>alphas = [1, 0.5+0.5j, 1j, 1+1j]
x = np.linspace(-4, 4, 1_000)
y = np.linspace(-4, 4, 1_000)

fig, axs = plt.subplots(1, len(alphas), figsize=[7*len(alphas), 5])
for alpha, ax in zip(alphas, axs):
    plot_wigner(coherent(N, alpha), x, y, ax=ax, fig=fig, cmap='inferno')<jupyter_output><empty_output><jupyter_text>QHO Operators<jupyter_code>a = create(N)
adag = destroy(N)<jupyter_output><empty_output><jupyter_text>Operators for DynamicsNatural units so set $\hbar = 1$<jupyter_code>gain = k1 * lindblad_dissipator(adag)
loss = r/k1 * lindblad_dissipator(a**2)<jupyter_output><empty_output><jupyter_text>Steady StateFor time-independent open quantum systems with decay rates larger than the corresponding excitation rates, the system will tend toward a steady state  Interaction picture $\hat H=0$ with no signal<jupyter_code>H0 = Qobj(np.zeros([N, N]))
sstate = steadystate(H0, [gain, loss])
sstate
x = np.linspace(-3,3,100)
y = np.linspace(-3,3,100)
plot_wigner(sstate, x, y, cmap='inferno')
detuning = 0
drive_strength = k1
H_drive = detuning * adag*a + 0.5*drive_strength * (a + adag)

drive_sstate = steadystate(H_drive, [gain, loss])
drive_sstate
x = np.linspace(-4,4,100)
y = np.linspace(-4,4,100)
plot_wigner(drive_sstate, x, y, cmap='inferno')<jupyter_output><empty_output>
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