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Physical Review A

Coherent-population-trapping transients induced by a modulated transverse magnetic field

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

Published Aug 14, 2013• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.88.023827

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 2015•0 citations

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Moscow University Physics Bulletin•Dec 1, 2010•4 citations
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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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.
The effect of a transverse magnetic field (TMF) on the absorption spectra of degenerate two-level systems in the D2{D}_{2}D2​ line of 87{}^{87}87Rb is investigated both analytically and numerically. We compare the effect of the TMF on the absorption of a $\ensuremath{\sigma}$ polarized pump in the Hanle configuration with that of a ${\ensuremath{\sigma}}^{\ensuremath{-}}$ probe in the presence of a ${\ensuremath{\sigma}}^{+}$ pump in the pump-probe configuration, and we show that the absorption spectra in both configurations is split in the presence of a TMF and that the splitting is proportional to its magnitude. The population redistribution in the ground state due to the TMF is reinforced by collisional effects, leading to increased splitting of the coherent population trapping (CPT) dip in the absorption spectrum. We explain the appearance of the splitting by setting the quantization axis along the total magnetic field. Then, in the Hanle configuration, the direction of the quantization axis changes as the longitudinal magnetic field is scanned, so that the laser polarization also changes. This leads to the creation of new two-photon detuned $\ensuremath{\Lambda}$ subsystems. The evolution of the populations and coherences of the ground-state Zeeman sublevels is illustrated using the angular momentum probability surface. In addition to being split, the CPT dip in the pump-probe configuration is also shifted by the longitudinal magnetic field, so that the effects of the longitudinal and transverse magnetic fields can be distinguished from each other.
Coherent-population-trapping transients induced by an ac magnetic field are investigated theoretically for a realistic three-level $\ensuremath{\Lambda}$ 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 $\ensuremath{\Lambda}$ 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.
We computationally compare Hanle-type resonances for a transition of the line for magnetic field scans parallel (longitudinal scan) and perpendicular (transverse scan) to the direction of propagation of the optical field in the presence of an additional transverse magnetic field (TMF). For a linearly polarized light, the coherent population trapping (CPT) resonances split at line centre and are identical for both longitudinal and transverse scans. When the probe beam ellipticity is varied, the effect of the TMF is found to be opposite for longitudinal and transverse scans. For a longitudinal scan, the splitting observed in the CPT resonance evolves into an enhanced absorption resonance with an increase in ellipticity. For a transverse scan, the splitting vanishes at higher ellipticities. This can be understood in terms of population redistribution in the ground state sublevels and near-neighbor ground state coherences created by the TMF. We also show that the enhanced absorption signal that splits the CPT resonance strongly depends on transit time, and the CPT resonance strength depends on the excited state dephasing rate.
Abstract We present an experimental and theoretical investigation of the influence of the transverse magnetic field (TMF) on the coherent population trapping resonances obtained on the Zeeman sublevels of the D 1 line of 87 Rb in a paraffin-coated vacuum cell. It is shown that a TMF changes the shape and sign of the resonance or destroys it completely. The role of the different rank polarization moments in the integral registered fluorescent signal in the presence of stray magnetic fields is clarified using numerical simulations.