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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Reaction coordinate solver for 2-level bosonic system
Author
Step1:  Defining the 2-level system
Step2:  Defining the coupling Q such that
Step3:  Plotting the TLS state occupation
Step4:  Plotting the photon distributions at arbitrary times
Step5:  Plotting the wigner function at arbitrary times
Step6:  Software versions
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Python Code:
%pylab inline
from qutip import *
from qutip import rcsolve
Explanation: Reaction coordinate solver for 2-level bosonic system
Author: Neill Lambert (nwlambert@gmail.com)
        Anubhav Vardhan (anubhavvardhan@gmail.com)
For more information about QuTiP see http://qutip.org
Introduction
Reference: link.aps.org/doi/10.1103/PhysRevA.90.032114 
In this model, we take a quantum system coupled to a bosonic environment and map to a model
in which a collective mode of the environment, known as the reaction coordinate 
(RC), is incorporated within an effective system Hamiltonian. We then treat the 
residual environment within a full second-order Born-Markov master equation
formalism. Thus, all important system-bath, and indeed intrabath, correlations 
are incorporated into the system-RC Hamiltonian in the regimes we study.
End of explanation
Del = 1.0    # The number of qubits in the system.
wq = 0.5     # Energy of the 2-level system.
Hsys = 0.5 * wq * sigmaz() + 0.5 * Del * sigmax()
Q = sigmaz()
Explanation: Defining the 2-level system
End of explanation
wc = 0.05                # Cutoff frequency.
alpha = 2.5/pi           # Coupling strength.
N = 10                   # Number of cavity fock states.
Temperature = 1/0.95     # Tempertaure.
tlist = np.linspace(0, 40, 600)
initial_state = basis(2,1) * basis(2,1).dag()                # Initial state of the system.
return_vals = [Q]            # List for which to calculate expectation value                                          
options = Options(nsteps=15000, store_states=True)        # Options for the solver.
output = rcsolve(Hsys, initial_state, tlist, return_vals, Q, wc, alpha, N, 
                Temperature, options=options)
Explanation: Defining the coupling Q such that:
Decoupled Hamiltonian-
$H_0 = \omega a^\dagger a + \frac{1}{2}\omega_q\sigma_z + \frac{1}{2}\delta\sigma_x$
Interaction-
$H_1 = g(a^\dagger + a)\sigma_z$
Total Hamiltonian-
$H = H_0 + H_1$
Solving the RC master equation
End of explanation
fig, axes = subplots(1, 1, sharex=True, figsize=(8,4))
axes.plot(tlist, real(output.expect[0]), 'b', linewidth=2, label="P12")
axes.legend(loc=0)
Explanation: Plotting the TLS state occupation
End of explanation
output.states[0]
t_idx_vec = range(0,len(tlist),200) 
fig, axes = subplots(len(t_idx_vec), 1, sharey=True, figsize=(8,2*len(t_idx_vec)))
for idx, t_idx in enumerate(t_idx_vec):
    psi_a = ptrace(output.states[t_idx], 0)
    
    cont1 = axes[idx].bar(range(0, N), real(psi_a.diag()))
    
fig.tight_layout()
Explanation: Plotting the photon distributions at arbitrary times
End of explanation
xvec = linspace(-5,5,200)
t_idx_vec = range(0,len(tlist),200) 
fig, axes = subplots(len(t_idx_vec), 1, sharex=True, sharey=True, figsize=(8,4*len(t_idx_vec)))
for idx, t_idx in enumerate(t_idx_vec):
    psi_a = ptrace(output.states[t_idx], 0)
    
    W_a = wigner(psi_a, xvec, xvec)
    
    
    cont1 = axes[idx].contourf(xvec, xvec, W_a, 100)
   
Explanation: Plotting the wigner function at arbitrary times
End of explanation
from qutip.ipynbtools import version_table
version_table()
Explanation: Software versions
End of explanation
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