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Physical Review A

Transient coherent population trapping in a closed loop interaction scheme

Wolfgang Maichen, Ferruccio Renzoni, I. E. Mazets, Eugeny Korsunsky, Laurentius Windholz

Published May 1, 1996• 54 citations
Publisher

Abstract

We investigated the existence of coherent population trapping (CPT) as a transient effect dependent on the rate of change of interaction parameters between an atom and light waves. For that purpose we exploited the phase dependence of CPT in a closed double-\ensuremath{\Lambda} interaction scheme, varying the total phase of the atomic transition loop linearly in time by detuning the light waves from exact four-photon resonance. For a slowly changing phase (that is, for small detunings) we observed the subsequent creation and destruction of CPT depending on the varying phase, while for higher speed of phase change CPT disappears. An analytical solution for a special case for a double-\ensuremath{\Lambda} interaction scheme that can be used to understand the principles of this phenomenon is presented. A qualitative comparison with our experiment shows good agreement within the limits of our theoretical considerations, confirming the validity of the basic idea. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.3444

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We investigated the existence of coherent population trapping (CPT) as a transient effect dependent on the rate of change of interaction parameters between an atom and light waves. For that purpose we exploited the phase dependence of CPT in a closed double-\ensuremath{\Lambda} interaction scheme, varying the total phase of the atomic transition loop linearly in time by detuning the light waves from exact four-photon resonance. For a slowly changing phase (that is, for small detunings) we observed the subsequent creation and destruction of CPT depending on the varying phase, while for higher speed of phase change CPT disappears. An analytical solution for a special case for a double-\ensuremath{\Lambda} interaction scheme that can be used to understand the principles of this phenomenon is presented. A qualitative comparison with our experiment shows good agreement within the limits of our theoretical considerations, confirming the validity of the basic idea. \textcopyright{} 1996 The American Physical Society.
Phase-dependent coherent population trapping (CPT) was observed using a thermal Na atomic beam irradiated by four laser fields derived from two dye lasers. Investigations were made on Λ- and double Λ-systems created in the D 1 line, both with and without magnetic field that lifts degeneracy of the Zeeman sublevels. In all cases a sharp decrease of fluorescence intensity was observed for certain values of the relative phase of the light waves, indicating that the occurrence of CPT depends on this phase. The shape of the phase dependence as well as its behaviour with respect to laser intensity fits well theoretical predictions.
There presented basic information on coherent population trapping (CPT) and related phenomenon of electromagnetically induced transparence, ‘dark’ and ‘bright’ (anomalous absorption) states is presented. Spectrum transformation is considered in probe field spectroscopy for Λ-scheme in various settings. The close relation is revealed between the effect of CPT in the manifold of magnetic sublevels and the phenomenon of optical pumping (optical orientation and optical alignment). CPT is shown to be generalized to the case of several transitions with a common upper level and with the corresponding number of light fields each being in quasiresonance with its ‘own’ transition.
This work is concerned with the temporal evolution of the coherent population trapping (CPT) process in the case of additional optical pumping to states not contributing to the CPT superposition states. Special attention is paid to the influence of weak external magnetic fields that can change the laser-atom interaction considerably. The theoretical analysis is completed by experimental observations on a sodium atomic beam, which show good agreement with our theory. The results obtained are of importance for a realistic picture of CPT schemes in practical applications.
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.
The temporal evolution of coherent population trapping (CPT) was observed in rubidium atomic vapor when sudden changes were made to the detuning of a weak Raman field. The subsequent creation and destruction of CPT are caused by the temporal oscillations of optically induced Raman coherence, with their period depending on the Raman detuning. The oscillating signal was observed over a time of order of tens of milliseconds, and the dependence of the relaxation time on the cell temperature and laser power were investigated. The main features of the experimental observations were well explained by the time-dependent density-matrix equations.