Time evolution of quantum interference in fluorescence spectra
In this tutorial, the photon scattering rate of 7Li is calculated using different coherent and perturbative
solvers included in qspec.simulate.
The resulting scattering rates reproduce the simulated fluorescence spectra shown in Fig. 2
by Brown et al. [1].
This tutorial is also part of qspec's publication.
import numpy as np import qspec.simulate as sim f_sp = 446810183.163 # Transition frequency (MHz) a_sp = 36.891 # Einstein coefficient (rad MHz) s_hyper = [401.75825] # HFS constants (MHz) p_hyper = [-3.055038, -0.29670] s = sim.construct_electronic_state( 0., s=0.5, l=0, j=0.5, i=1.5, hyper_const=s_hyper, label='s') p = sim.construct_electronic_state( f_sp, s=0.5, l=1, j=1.5, i=1.5, hyper_const=p_hyper, label='p') decay = sim.DecayMap(labels=[('s', 'p')], a=[a_sp]) li7 = sim.Atom(s + p, decay) intensity = 1. # uW /mm**2 polarization = sim.Polarization([0, 1, 0]) # Linear polarization laser = sim.Laser(f_sp, intensity, polarization) inter = sim.Interaction(li7, [laser]) inter.controlled = True # Error controlled integrator t = 0.2 # Integration time (us) delta = np.linspace(-325, -275, 201) # Frequency detunings (MHz) theta, phi = 0., 0. # Angles from z-axis in x- and y-direction (rad) n = inter.rates(t, delta) # Rate equations, 0.2 us y_rates = li7.scattering_rate(n, theta, phi, as_density_matrix=False) rho = inter.master(t, delta) # Master equation, 0.2 us y_master = li7.scattering_rate(rho, theta, phi) rho = inter.master(0.4, delta) # Master equation, 0.4 us y4_master = li7.scattering_rate(rho, theta, phi) sr = sim.ScatteringRate(li7, laser=laser) y_brown = sr.generate_y(delta, theta, phi)[:, 0, 0] # Brown et al.
Using matplotlib, we can generate the plot from the publication.
import matplotlib.pyplot as plt scale = 1e3 x_lim = delta[0], delta[-1] fig, (m, r) = plt.subplots( 2, 1, sharex='all', height_ratios=[3, 1], figsize=(6, 5)) m.plot(delta, y_brown * scale, '-k', label=r'Brown $et\,al.$', zorder=20) m.plot(delta, y_rates[:, -1] * scale, '-C0', label=r'rates, $t = 0.2\,\mu$s', zorder=0) m.plot(delta, y_master[:, -1] * scale, '-C1', label=r'master, $t = 0.2\,\mu$s', zorder=60) m.plot(delta, y4_master[:, -1] * scale, '--C3', label=r'master, $t = 0.4\,\mu$s', linewidth=1.5, zorder=30) r.plot(delta, (y_brown - y_rates[:, -1]) * scale, '-k', zorder=20) r.plot(delta, (y_master[:, -1] - y_rates[:, -1]) * scale, '-C1', zorder=60) r.plot(delta, (y4_master[:, -1] - y_rates[:, -1]) * scale, '--C3', linewidth=1.5, zorder=10) r.hlines(0, *x_lim, 'C0', '-', zorder=0) m.legend() m.set_ylabel(r'$\mathrm{d}\Gamma / \mathrm{d}\Omega$ (kHz)') m.set_xlim(*x_lim) r.set_xlabel('Relative frequency (MHz)') r.set_ylabel('Residuals (kHz)') y_lim = m.get_ylim() r.set_ylim(-(y_lim[1] - y_lim[0]) / 6, (y_lim[1] - y_lim[0]) / 6) plt.subplots_adjust(left=0.09, bottom=0.1, right=0.99, top=0.99, hspace=0.05) plt.show()
