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Physical Review A

Population-loss-induced narrowing of dark resonances

Ferruccio Renzoni, E. Arimondo

Published Dec 1, 1998• 40 citations
Publisher

Abstract

The dependence of the width of the coherent population trapping (CPT) resonance on the atomic interaction time is studied theoretically. The optical Bloch equations are solved for the Hanle/CPT schemes corresponding to the open ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ transitions of the sodium ${D}_{1}$ line interacting with linearly polarized laser light. The mechanism producing the narrowing of the Hanle/CPT resonance is examined, the role of the population losses is pointed out, and the law describing the narrowing of the width of the resonance with the interaction time is determined. Our results are compared with the Hanle/CPT linewidth dependence on the interaction time occurring for a closed optical transition.

DOI
10.1103/physreva.58.4717

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 22, 2008•1 citation
The dependence of the width of the coherent population trapping (CPT) resonance on the atomic interaction time is studied theoretically. The optical Bloch equations are solved for the Hanle/CPT schemes corresponding to the open Fg\ensuremath→Fe{F}_{g}\ensuremath{\rightarrow}{F}_{e}Fg​\ensuremath→Fe​ transitions of the sodium D1{D}_{1}D1​ line interacting with linearly polarized laser light. The mechanism producing the narrowing of the Hanle/CPT resonance is examined, the role of the population losses is pointed out, and the law describing the narrowing of the width of the resonance with the interaction time is determined. Our results are compared with the Hanle/CPT linewidth dependence on the interaction time occurring for a closed optical transition.
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Coherent population trapping (CPT) with losses towards off-resonant levels is analyzed on the basis of the coupled/noncoupled states. We derive that at a long interaction time the noncoupled state is depopulated at a rate that is decreasing for decreasing Raman detuning. This behavior produces a narrowing of the dark resonance with the interaction time. The asymptotic evolution of the atomic system is completely characterized by the effective width ${\ensuremath{\Gamma}}_{\mathrm{NC}}$ of the noncoupled state. The analytic expression for this width evidences a quadratic dependence on the Raman detuning. This dependence implies that the width of the dark resonance decreases asymptotically with the inverse of the square root of the interaction time. This narrowing law, independent of the interaction scheme, has a general validity for CPT in open systems. Our analysis points out the differences between CPT with losses and CPT in closed systems.
We consider the coherent population trapping phenomenon in a thermal sodium atomic beam. We compare the different coherent population trapping schemes that can be established on the D1 line using the Zeeman sublevels of a given ground hyperfine state. The coherent population trapping preparation is examined by means of a Hanle effect configuration. The efficiency of the coherent population trapping phenomenon has been examined in presence of optical pumping into hyperfine levels external to those of the excited transition. We show that both the contrast and the width of the coherent population trapping resonance strongly decrease when the optical pumping rate is increased. In the experiment, the loss rate due to optical pumping has been controlled by means of a laser repump of variable intensity.
We consider the coherent-population-trapping phenomenon in a thermal sodium atomic beam. We compare the different coherent-population-trapping schemes that can be established on the D1{\mathrm{D}}_{1}D1​ line using the Zeeman sublevels of a given ground hyperfine state. The coherent-population-trapping preparation is examined by means of a Hanle-effect configuration. The efficiency of the coherent-population-trapping phenomenon has been examined in presence of optical pumping into hyperfine levels external to those of the excited transition. We show that both the contrast and the width of the coherent population trapping resonance strongly decrease when the optical pumping rate is increased. In the experiment, the loss rate due to optical pumping has been controlled by means of a laser repump of variable intensity.
We calculated line-shapes of the coherent population trapping (CPT) for the open transition in 87Rb by solving time-dependent optical Bloch equations and averaging results for the total excited state populations over atomic trajectories and velocities, while taking into account incident angles to the laser beam. Comparison with experiment produces good agreement for the laser intensity dependence of the CPT line-widths when the laser transverse beam profile is Gaussian. This theoretical model was used to calculate the probe laser CPT in the case of spatially separated pump beam. The probe beam is placed inside the cylindrically-shaped pump beam. The calculations as well as measurements show narrowing of the Hanle resonance due to Ramsey effect.