Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light

Abstract

Abstract:We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.

Adiabatic spin-dependent momentum transfer in an SU(N) degenerate Fermi gas

“…Each of these can thus be used to selectively measure the atom number and momentum distribution in two spin states. According to numerical simulations for our parameters, the efficiency is approximately the same on all lines (∼ 80% diffracted, and 10 to 20 % undergoing spontaneous emission -typically five times less than if the evolution were incoherent [32]), but for the two extreme lines that should be less efficient (∼ 50% diffracted) due to pathologically small CG coefficients. This is in good agreement with the fact that roughly 80% of the total atom number is accounted for by the various diffraction resonances.…”

Fluorescence of rubidium vapor in a transient interaction regime

“…where Ωi,j = E0d i,j h are the matrix elements of the Rabi frequency with d i,j the matrix elements of the dipole moment for the respective transitions [9,10], E0 is the amplitude of classical electric field interacting with atomic medium of 87 Rb and 85 Rb, and ∆i,j(t) are one-photon detunings of the scanning laser field from atomic resonances. For periodic triangular temporal modulation of the laser radiation frequency, we can write ∆i,j(t) = ∆ 0 i,j + ∆ π arcsin (cos 2πfst), (6) where ∆ the spectral range of scanning, fs is the triangular modulation frequency, i = 1, 2, and j = 3, 4, 5, 6, see Fig.1b. Employing this modulation, the radiation frequency will linearly increase / decrease in time, so that the laser field will be consecutively in resonance with all the groups of transitions: 87 Rb Fg = 2 → Fe = 1, 2, 3, 85 Rb Fg = 3 → Fe = 2, 3, 4, 85 Rb Fg = 2 → Fe = 1, 2, 3, and 87 Rb Fg = 1 → Fe = 0, 1, 2, in direct (rising frequency) and reverse (falling frequency) order.…”

“…where Ωi,j = E0d i,j h are the matrix elements of the Rabi frequency with d i,j the matrix elements of the dipole moment for the respective transitions [9,10], E0 is the amplitude of classical electric field interacting with atomic medium of 87 Rb and 85 Rb, and ∆i,j(t) are one-photon detunings of the scanning laser field from atomic resonances. For periodic triangular temporal modulation of the laser radiation frequency, we can write ∆i,j(t) = ∆ 0 i,j + ∆ π arcsin (cos 2πfst), (6) where ∆ the spectral range of scanning, fs is the triangular modulation frequency, i = 1, 2, and j = 3, 4, 5, 6, see Fig. 1b.…”

“…Particularly, theoretical and experimental investigations of processes under dynamic excitation of atomic media with modulated cw laser radiation were done for nonlinear magneto-optical processes [1], saturation spectroscopy [2], four-wave mixing [3], coherent population trapping [4,5]. Analytical solutions of temporal evolution of populations in optically-pumped atoms were obtained in [6]. Besides transient processes imposed by temporally-modulated laser radiation, dynamic effects were studied also for spatial Ramsey schemes, such as dark Raman resonances caused by interference [7].…”

Collapse of Xe polarized atomic states in magnetic fields

“…Our experimental scheme has a number of important advantages compared with the detection of 1 e-mail:mdimitrijevic@aob.rs photons due to the almost 100% efficiency of extracting photoelectrons from the interaction zone. Probing excited gas media by photoionization methods allows, as well, to examine important details of nonlinear optical pump processes resulting in polarization of atomic states [7,8]. We investigated cases of weak (linear Zeeman effect) and intermediate magnetic field values and revealed collapse and revival behaviour of oscillations in photocurrent signals as a result of the Paschen-Back effect [9,10].…”