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arXiv:quant-ph/0701008 · Physical Review A

Theory of Dicke narrowing in coherent population trapping

Ofer Firstenberg, M. Shuker, Amit Ben-Kish, Donald R. Fredkin, Nir Davidson, A. Ron

Published Jul 19, 2007• 39 citations
arXivHTMLPDF

Abstract

The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.

DOI
10.1103/physreva.76.013818

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The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison with well- known CPT resonances in transmission of the corresponding two-frequency pumping radiation. Thus CPT resonances, detected by the elaborated method, may be used in atomic frequency standards and sensitive magnetometers (based on the CPT phenomenon) and also in ultahigh resolution spectroscopy of atoms and molecules.
The principle of coherent Dicke narrowing in a thin vapor cell, in which sub-Doppler spectral line shapes are observed under a normal irradiation for a $\ensuremath{\lambda}∕2$ thickness, is generalized to two-photon spectroscopy. Only the sum of the two wave vectors must be normal to the cell, making the two-photon scheme highly versatile. A comparison is provided between the Dicke narrowing with copropagating fields, and the residual Doppler broadening occurring with counterpropagating geometries. The experimental feasibility is discussed on the basis of a first observation of a two-photon resonance in a 300-nm-thick Cs cell. Extension to the Raman situation is finally considered.
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison with well- known CPT resonances in transmission of the corresponding two-frequency pumping radiation. Thus CPT resonances, detected by the elaborated method, may be used in atomic frequency standards and sensitive magnetometers (based on the CPT phenomenon) and also in ultahigh resolution spectroscopy of atoms and molecules.
Abstract Doppler broadening in thermal ensembles degrades the absorption cross-section and the coherence time of collective excitations. In two photon transitions, it is common to assume that this problem becomes worse with larger wavelength mismatch. Here we identify an opposite mechanism, where such wavelength mismatch leads to cancellation of Doppler broadening via the counteracting effects of velocity-dependent light-shifts and Doppler shifts. We show that this effect is general, common to both absorption and transparency resonances, and favorably scales with wavelength mismatch. We experimentally confirm the enhancement of transitions for different low-lying orbitals in rubidium atoms and use calculations to extrapolate to high-lying Rydberg orbitals. These calculations predict a dramatic enhancement of up to 20-fold increase in absorption, even in the presence of large homogeneous broadening. More general configurations, where an auxiliary dressing field is used to counteract Doppler broadening, are also discussed and experimentally demonstrated. The mechanism we study can be applied as well for rephasing of spin waves and increasing the coherence time of quantum memories.
Coherent Population Trapping in An Inhomogeneously Broadened Λ\LambdaΛ-System with Multiple Excited States
We present a theoretical model using density matrix approach to study the phenomenon of coherent population trapping (CPT) in the Λ\LambdaΛ-type Doppler broadened system with multiple excited states. A multi-level Λ\LambdaΛ-system is formed by considering the closely spaced hyperfine levels in the D2 line of 87^{87}87Rb. The presence of closely spaced hyperfine levels affects the transparency window and cause asymmetry in absorption profiles. We observe the sharp CPT dip when the frequency difference of applied fields is equal to the frequency separation between two ground levels. This dip demonstrates that the system is trapped in the dark state. By performing a thermal averaging in the Doppler-broadened Λ\LambdaΛ-system, we have shown that the transparency window becomes narrower and its linewidth decreases at higher temperature. This study has potential applications in precision measurements due to the small linewidth of the transparency window.
We have detected and analysed interesting features of sub-Doppler resonances, which are induced in absorption of the weak monochromatic probe light beam (with the scanned frequency) by the counterpropagating two-frequency pumping radiation implementing the phenomenon of the coherent population trapping (CPT) on resonant Λ-systems of atomic levels. Our experimental investigations have been carried out on example of spectral components of the Doppler broadened D2line of cesium atoms. Obtained results may be used for optimization of laser frequencies stabilization on atomic transitions.