EIT in three-level atom

In [1]:

    

import numpy as np
from qutip import *
import matplotlib.pyplot as plt
%matplotlib inline
from IPython.display import Image


    

In [2]:

    

one, two, three = three_level_basis()
sig11 = one * one.dag()
sig22 = two * two.dag()
sig33 = three * three.dag()
sig13 = one * three.dag()
sig23 = two * three.dag()
sig12 = one * two.dag()

Image("fig/EIT_levels.png")


    

    
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In [80]:

    

# Loop over the detuning Delta and generate optical response

# constants based on Jenkins EIT masters thesis
# It seems like the values they quote aren't right. They don't match the code.

# Decay rates
Gamma = 0.1  # decay rate on probe transition
gamma = 5.0  # decay rate on control transition 
gamma_c = 0.05  # coherence decay rate (2->1)
phi = 0  # control field detuning

# Rabi frequencies for pump and control beam
omegaP = 0.1*gamma  # pump
omegaC = 1.0*gamma  # control

# Collapse operators
c1 = np.sqrt(Gamma)*sig13  # 1-3 coherence decay (probe transition)
c2 = np.sqrt(gamma)*sig23  # 2-3 coherence decay (control transition)
c3 = np.sqrt(gamma_c)*sig12  # ground state coherence decay
collapse = [c1,c2,c3]

deltalist = np.linspace(-20,20,301)

rho_33 = []
rho_31 = []
rho_13 = []
chi = []

for Delta in deltalist:
    # Define Hamiltonian for detuning Delta:
    H = (omegaP*(sig13+sig13.dag()) + omegaC*(sig23+sig23.dag()) + phi*(sig33 - sig22) + Delta*(sig33 - sig11))
    
    # find steady-state density operator:
    rho_ss = steadystate(H,collapse)
    
    # save values for plotting later:
    rho_33.append(rho_ss[2,2])  # save the exited state population
    rho_31.append(rho_ss[2,0])  # save the ground-excited coherence
    rho_13.append(rho_ss[0,2])
    # this approach is ugly because it relies on the internal matrix layout, better to use projection ops:
    
    chi.append(expect(sig13.dag(),rho_ss)) # use sig31 ( which is sig13.dag() )
    # This is not equality, but the susceptability is proportional to sig31


    

In [81]:

    

fsize = {'fontsize':'16'}
plt.plot(deltalist/gamma,np.real(rho_33))
plt.title("Excited state population")
plt.xlabel("$\Delta/\gamma$",**fsize)
plt.ylabel("$\hat{\\rho}_{33}$",**fsize)


    

    
Out[81]:





Text(0,0.5,'$\\hat{\\rho}_{33}$')






    

In [82]:

    

fsize = {'fontsize':'16'}
plt.plot(deltalist/gamma,np.real(rho_33))
plt.plot(deltalist/gamma,np.imag(rho_13))
plt.title("Excited state population")
plt.xlabel("$\Delta/\gamma$",**fsize)
#plt.ylabel("$\hat{\\rho}_{31}$",**fsize)


    

    
Out[82]:





Text(0.5,0,'$\\Delta/\\gamma$')






    

In [84]:

    

# This is probably the simplest official way to do it.
plt.plot(deltalist,np.real(chi),label="Refractive Index")
plt.plot(deltalist,np.imag(chi),label="Absorption")
plt.legend()
#plt.title("Nonlinear response")
plt.xlabel("$\Delta$")


    

    
Out[84]:





Text(0.5,0,'$\\Delta$')






    

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