def test_spectrum_esfft():
"""
correlation: comparing spectrum from es and fft methods
"""
# use JC model
N = 4
wc = wa = 1.0 * 2 * np.pi
g = 0.1 * 2 * np.pi
kappa = 0.75
gamma = 0.25
n_th = 0.01
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())
c_ops = [np.sqrt(kappa * (1 + n_th)) * a,
np.sqrt(kappa * n_th) * a.dag(),
np.sqrt(gamma) * sm]
with warnings.catch_warnings():
warnings.simplefilter("ignore")
tlist = np.linspace(0, 100, 2500)
corr = correlation_ss(H, tlist, c_ops, a.dag(), a)
wlist1, spec1 = spectrum_correlation_fft(tlist, corr)
spec2 = spectrum_ss(H, wlist1, c_ops, a.dag(), a)
assert_(max(abs(spec1 - spec2)) < 1e-3)
def test_spectrum_esfft():
"""
correlation: comparing spectrum from es and fft methods
"""
# use JC model
N = 4
wc = wa = 1.0 * 2 * np.pi
g = 0.1 * 2 * np.pi
kappa = 0.75
gamma = 0.25
n_th = 0.01
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())
c_ops = [
np.sqrt(kappa * (1 + n_th)) * a,
np.sqrt(kappa * n_th) * a.dag(),
np.sqrt(gamma) * sm
]
with warnings.catch_warnings():
warnings.simplefilter("ignore")
tlist = np.linspace(0, 100, 2500)
corr = correlation_ss(H, tlist, c_ops, a.dag(), a)
wlist1, spec1 = spectrum_correlation_fft(tlist, corr)
spec2 = spectrum_ss(H, wlist1, c_ops, a.dag(), a)
assert_(max(abs(spec1 - spec2)) < 1e-3)
def _spectrum_fft(H, c_ops, a, b):
times = np.linspace(0, 100, 2500)
correlation = qutip.correlation_ss(H, times, c_ops, a, b)
frequencies, spectrum = qutip.spectrum_correlation_fft(times, correlation)
return spectrum, frequencies
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_ss(H, tlist, c_ops, a.dag(), a)
wlist1, spec1 = qt.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 = qt.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))