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Physical Review A

Coherence-population-trapping transients induced by an ac magnetic field

L. Margalit, M. Rosenbluh, A. D. Wilson‐Gordon

Published Jun 8, 2012• 12 citations
Publisher

Abstract

Coherent-population-trapping transients induced by an ac magnetic field are investigated theoretically for a realistic three-level $\ensuremath{\Lambda}$ system in the ${D}_{1}$ line of ${}^{87}$Rb. The contributions to the transient probe absorption from the various subsystems that compose the realistic atomic system are examined and the absorption of each $\ensuremath{\Lambda}$ subsystem is compared to that of a simple $\ensuremath{\Lambda}$ system. The population redistribution due to optical pumping is shown to be the dominant cause of the difference between the contributions of the various subsystems to the oscillatory character of the probe absorption. We also discuss the series of transients that reappear every half-cycle time of a modulated magnetic field when the system is in two-photon resonance, and we study the transient behavior as a function of the probe detuning. The effect of a buffer gas on the amplitude and shape of the transients is considered.

DOI
10.1103/physreva.85.063809

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arXiv:quant-ph/0209011•Physical Review A•Jan 23, 2003•22 citations
Coherent-population-trapping transients induced by an ac magnetic field are investigated theoretically for a realistic three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system in the D1{D}_{1}D1​ line of 87{}^{87}87Rb. The contributions to the transient probe absorption from the various subsystems that compose the realistic atomic system are examined and the absorption of each \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ subsystem is compared to that of a simple \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system. The population redistribution due to optical pumping is shown to be the dominant cause of the difference between the contributions of the various subsystems to the oscillatory character of the probe absorption. We also discuss the series of transients that reappear every half-cycle time of a modulated magnetic field when the system is in two-photon resonance, and we study the transient behavior as a function of the probe detuning. The effect of a buffer gas on the amplitude and shape of the transients is considered.
We present theoretical results of coherent-population-trapping transients induced by a modulated transverse magnetic field (TMF). The application of a transverse magnetic field causes the appearance of new $\ensuremath{\Lambda}$ subsystems, creation of new dark states, and rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between steady-state situations, and we identify the various level system components of the total probe absorption. We discuss the time-dependent evolution of the probe absorption caused by the modulated TMF in the presence and absence of a constant longitudinal magnetic field (LMF). The differences between TMF modulation and LMF modulation are discussed.
We discuss the effect of static and time-dependent longitudinal and transverse magnetic fields on degenerate two-level and three-level systems in Rb atomic vapor. The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2 line of 87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a σ polarized pump in the Hanle configuration with that of a σ− probe in the presence of a σ+ pump in the pump-probe configuration, and show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to the magnitude of the TMF. Coherent population trapping (CPT) transients induced by a modulated longitudinal magnetic field (LMF) are investigated theoretically for a realistic three-level Λ system in the D1 line of 87Rb. The contributions to the transient probe absorption from the various subsystems that comprise the realistic atomic system are examined and the absorption of each Λ subsystem is compared to that of a simple Λ system. We also present theoretical results for CPT transients induced by a modulated TMF. The application of a TMF leads to the appearance of new Λ subsystems, the creation of new dark states and the rearrangement of the population among the Zeeman sublevels. We show that transients appear as the system is switched between various steady-state situations and we identify the various components of the total probe absorption.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
The quantum dynamics of a system of Rb atoms, modeled by a V-type three-level system interacting with intense probe and pump pulses, are studied. The time-delay-dependent transient-absorption spectrum of an intense probe pulse is thus predicted, when this is preceded or followed by a strong pump pulse. Numerical results are interpreted in terms of an analytical model, which allows us to quantify the oscillating features of the resulting transient-absorption spectra in terms of the atomic populations and phases generated by the intense pulses. Strong-field-induced phases and their influence on the resulting transient-absorption spectra are thereby investigated for different values of pump and probe intensities and frequencies, focusing on the atomic properties which are encoded in the absorption line shapes for positive and negative time delays.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave mixing, population modulation, and Zeeman optical pumping are derived. On all these observables, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the D2{D}_{2}D2​ line of Rb vapor are presented in good agreement with the calculations.
The temporal evolution of electromagnetically induced transparency (EIT) and absorption (EIA) coherence resonances in pump-probe spectroscopy of degenerate two-level atomic transition is studied for light intensities below saturation. Analytical expressions for the transient absorption spectra are given for simple model systems and a model for the calculation of the time-dependent response of realistic atomic transitions, where the Zeeman degeneracy is fully accounted for, is presented. EIT and EIA resonances have a similar (opposite sign) time-dependent line shape, however, the EIA evolution is slower and thus narrower lines are observed for long interaction time. Qualitative agreement with the theoretical predictions is obtained for the transient probe absorption on the 85Rb{}^{85}\mathrm{Rb}85Rb D2{D}_{2}D2​ line in an atomic beam experiment.