Can QuTiP generate spectral line shapes?

[alexa...@gmail.com]

Can QuTiP generate spectral line shapes?

[Andrew Dawes]

You may be interested in the spectrum function: http://qutip.org/docs/latest/apidoc/functions.html?highlight=spectrum#qutip.correlation.spectrum

Here is some sample code that shows two ways to calculate a spectrum. It is based on an older example: http://qutip.org/docs/3.1.0/guide/guide-correlation.html

I’ve updated it to use the “correlation_2op_1t” function.

import numpy as np

from qutip import *

import pylab as plt

%matplotlib inline

N = 4                   # number of cavity fock states

wc = wa = 1.0 * 2 * np.pi  # cavity and atom frequency

g  = 0.1 * 2 * np.pi       # coupling strength

kappa = 0.75            # cavity dissipation rate

gamma = 0.25            # atom dissipation rate

# Jaynes-Cummings Hamiltonian

a  = tensor(destroy(N), qeye(2))

sm = tensor(qeye(N), destroy(2))

H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())

# collapse operators

n_th = 0.25

c_ops = [np.sqrt(kappa * (1 + n_th)) * a, np.sqrt(kappa * n_th) * a.dag(), np.sqrt(gamma) * sm]

# calculate the correlation function using the mesolve solver, and then fft to

# obtain the spectrum. Here we need to make sure to evaluate the correlation

# function for a sufficient long time and sufficiently high sampling rate so

# that the discrete Fourier transform (FFT) captures all the features in the

# resulting spectrum.

tlist = np.linspace(0, 100, 5000)

corr = correlation_2op_1t(H, None, tlist, c_ops, a.dag(), a)

wlist1, spec1 = spectrum_correlation_fft(tlist, corr)

# calculate the power spectrum using spectrum, which internally uses essolve

# to solve for the dynamics (by default)

wlist2 = np.linspace(0.25, 1.75, 200) * 2 * np.pi

spec2 = spectrum(H, wlist2, c_ops, a.dag(), a)

# plot the spectra

fig, ax = plt.subplots(1, 1)

ax.plot(wlist1 / (2 * np.pi), spec1, 'b', lw=2, label='eseries method')

ax.plot(wlist2 / (2 * np.pi), spec2, 'r--', lw=2, label='me+fft method')

ax.legend()

ax.set_xlabel('Frequency')

ax.set_ylabel('Power spectrum')

ax.set_title('Vacuum Rabi splitting')

ax.set_xlim(wlist2[0]/(2*np.pi), wlist2[-1]/(2*np.pi))

On Mar 21, 2018, at 4:46 AM, alexa...@gmail.com wrote:

Can QuTiP generate spectral line shapes?

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