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Author: William A. Stein

QuTiP lecture: Vacuum Rabi oscillations in the Jaynes-Cummings model

Author: J. R. Johansson ([email protected]), http://dml.riken.jp/~rob/

The latest version of this IPython notebook lecture is available at http://github.com/jrjohansson/qutip-lectures.

The other notebooks in this lecture series are indexed at http://jrjohansson.github.com.

In [1]:
# setup the matplotlib graphics library and configure it to show # figures inline in the notebook %matplotlib inline import matplotlib.pyplot as plt import numpy as np
In [2]:
# make qutip available in the rest of the notebook from qutip import *

Introduction

The Jaynes-Cumming model is the simplest possible model of quantum mechanical light-matter interaction, describing a single two-level atom interacting with a single electromagnetic cavity mode. The Hamiltonian for this system is (in dipole interaction form)

H=ωcaa+12ωaσz+g(a+a)(σ+σ+)H = \hbar \omega_c a^\dagger a + \frac{1}{2}\hbar\omega_a\sigma_z + \hbar g(a^\dagger + a)(\sigma_- + \sigma_+)

or with the rotating-wave approximation

HRWA=ωcaa+12ωaσz+g(aσ+aσ+)H_{\rm RWA} = \hbar \omega_c a^\dagger a + \frac{1}{2}\hbar\omega_a\sigma_z + \hbar g(a^\dagger\sigma_- + a\sigma_+)

where ωc\omega_c and ωa\omega_a are the frequencies of the cavity and atom, respectively, and gg is the interaction strength.

Problem parameters

Here we use units where =1\hbar = 1:

In [4]:
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 = np.linspace(0,25,101)

Setup the operators, the Hamiltonian and initial state

In [5]:
# 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())

Create a list of collapse operators that describe the dissipation

In [6]:
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)

Evolve the system

Here we evolve the system with the Lindblad master equation solver, and we request that the expectation values of the operators aaa^\dagger a and σ+σ\sigma_+\sigma_- are returned by the solver by passing the list [a.dag()*a, sm.dag()*sm] as the fifth argument to the solver.

In [7]:
output = mesolve(H, psi0, tlist, c_ops, [a.dag() * a, sm.dag() * sm])

Visualize the results

Here we plot the excitation probabilities of the cavity and the atom (these expectation values were calculated by the mesolve above). We can clearly see how energy is being coherently transferred back and forth between the cavity and the atom.

In [8]:
n_c = output.expect[0] n_a = output.expect[1] fig, axes = plt.subplots(1, 1, figsize=(10,6)) axes.plot(tlist, n_c, label="Cavity") axes.plot(tlist, n_a, label="Atom excited state") axes.legend(loc=0) axes.set_xlabel('Time') axes.set_ylabel('Occupation probability') axes.set_title('Vacuum Rabi oscillations')
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g/uDX6XQEBQUxbtw4evbsSVxcHEeOHKFz585cunSJ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bNDwaVoglv1lypXryY/p40b8xRKC7DBGM9OniRT6XzxbuHNjkUSWWRmpFpHIFXEwIAcjcSW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\na2vAyQk4epR2EuH99Rfp+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at 0x7f8f0b893668>"]}

Cavity wigner function

In addition to the cavity's and atom's excitation probabilities, we may also be interested in for example the wigner function as a function of time. The Wigner function can give some valuable insight in the nature of the state of the resonators.

To calculate the Wigner function in QuTiP, we first recalculte the evolution without specifying any expectation value operators, which will result in that the solver return a list of density matrices for the system for the given time coordinates.

In [9]:
output = mesolve(H, psi0, tlist, c_ops, [])

Now, output.states contains a list of density matrices for the system for the time points specified in the list tlist:

In [10]:
output
Odedata object with mesolve data. --------------------------------- states = True num_collapse = 0
In [11]:
type(output.states)
list
In [12]:
len(output.states)
101
In [13]:
output.states[-1] # indexing the list with -1 results in the last element in the list
Quantum object: dims = [[15, 2], [15, 2]], shape = [30, 30], type = oper, isherm = True

Now let's look at the Wigner functions at the point in time when atom is in its ground state: t=5,15,25t = \\{5, 15, 25\\} (see the plot above).

For each of these points in time we need to:

  1. Find the system density matrix for the points in time that we are interested in.
  2. Trace out the atom and obtain the reduced density matrix for the cavity.
  3. Calculate and visualize the Wigner function fo the reduced cavity density matrix.
In [14]:
# 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]
array([ 0., 5., 15., 25.])
In [15]:
# get a list density matrices rho_list = array(output.states)[t_idx]
In [17]:
# loop over the list of density matrices xvec = np.linspace(-3,3,200) fig, axes = plt.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=plt.get_cmap('RdBu')) axes[idx].set_title(r"$t = %.1f$" % tlist[t_idx][idx], fontsize=16)
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s2Wu4O9wz/Ssw7AJnAL5eTXV9+3K+tI64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1xDwLjIMM71c/1DzoCyBAEBaugli8OF/Wk9wI3A9/zu1PL4xv6fu3cmXP+kbwpj38Ah7vfV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\nmI1lf7n9QYEtq/y/LgAXm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at 0x7f8f0b77f320>"]}

At t=0t =0, the cavity is in it's ground state. At t=5,15,25t = 5, 15, 25 it reaches it's maxium occupation in this Rabi-vacuum oscillation process. We can note that for t=5t=5 and t=15t=15 the Wigner function has negative values, indicating a truely quantum mechanical state. At t=25t=25, however, the wigner function no longer has negative values and can therefore be considered a classical state.

Alternative view of the same thing

In [22]:
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 = plt.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 = plt.subplot2grid(fig_grid, (0, 2*idx), colspan=2) ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=plt.get_cmap('RdBu')) ax.set_title(r"$t = %.1f$" % tlist[t_idx][idx], fontsize=16) # plot the cavity occupation probability in the ground state ax = plt.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');
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Mlsw+x24LvV5bjC0TcP3v2/94zRWO2NLabg/1u7ql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pTyaYxWomaBftMs+Zo0GTmXCr3ZP9HxNaWKpWmWZfhNNhv4mkDXxPB4AvsaM7wBMBXR9+jT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NSjTB2lL+lzZlFhZQv774SEyEsDDYvx9GjRKJVM2a4llQqRLY2YmPfPkgwztqRGi1YlrT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\nJEmSpLL/A7yznGPc4KRnAAAAAElFTkSuQmCC\n","text":["<matplotlib.figure.Figure at 0x7f8f0a977160>"]}

Software versions

In [23]:
from qutip.ipynbtools import version_table version_table()
SoftwareVersion
SciPy0.13.3
OSposix [linux]
Cython0.20.1post0
QuTiP3.0.0.dev-5a88aa8
matplotlib1.3.1
IPython2.0.0
Python3.4.1 (default, Jun 9 2014, 17:34:49) [GCC 4.8.3]
Numpy1.8.1
Thu Jun 26 13:57:53 2014 JST