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Annual Meeting Optical Society of America

Measurement of the friction coefficient in 1D corkscrew molasses by Rayleigh spectroscopy

Philippe Verkerk, Brahim Lounis, J.-Y. Courtois, Christopher E. Salomon, G. Grynberg

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Probe transmission spectrum in a one-dimensional cesium corkscrew molasses displays a narrow (=30-70 kHz) Rayleigh resonance, which permits to estimate the friction coefficient of the cooling force to be a 5.8 ± 0.4 hk2 at 31.
DOI
10.1364/oam.1992.pd24

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The transmission spectrum of a probe interacting with one-dimensional cesium optical molasses made from two circularly cross-polarized cooling beams (corkscrew molasses) displays a narrow (\ensuremath{\approxeq}30--70 kHz) Rayleigh resonance. From the width of this resonance we deduce the friction coefficient of the cooling force to be \ensuremath{\alpha}=(5.8\ifmmode\pm\else\textpm\fi{}0.4)\ensuremath{\Elzxh}k2{\mathit{k}}^{2}k2 for a detuning from resonance equal to 3\ensuremath{\Gamma}. This value is in quantitative agreement with theoretical predictions. We also show that the shape of the Rayleigh resonance depends dramatically on the efficiency of the sub-Doppler cooling mechanism.
We present a detailed theoretical investigation of the absorption spectrum of a probe beam after transmission through a one-dimensional optical molasses obtained with circularly cross-polarized counterpropagating pump beams (corkscrew molasses). The study is performed for a Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=2 atomic transition and the external degrees of freedom are described by means of a Fokker-Planck equation in the regime where the stationary momentum distribution lies within the range of linearity of the cooling force. We analyze the stimulated Raman transitions occurring between differently populated and light-shifted ground-state Zeeman sublevels. In the case where the probe beam has the same polarization as the copropagating cooling beam, an additional narrow Rayleigh resonance appears for a probe frequency close to the pump frequency. Its width is equal to 2\ensuremath{\alpha}/M, where \ensuremath{\alpha} is the friction coefficient of the cooling force and M is the atomic mass. In the case where the probe beam has the same polarization as the counterpropagating cooling beam, a central recoil-induced resonance is expected. Its width is related to the Doppler width of the optical molasses.
The spatial distribution and the dynamics of Cs atoms in a 1D optical molasses are probed by measuring the absorption (or amplification) spectrum of a weak laser beam. Narrow (35--50 kHz) Raman lines give access for the first time to the frequency and to the damping of the atom's oscillation in the potential wells associated with light shifts. A narrower (8 kHz) Rayleigh resonance demonstrates the existence of a large-scale spatial order of the atoms, presenting some analogy with an antiferromagnetic medium.
Early experiments on ultracold optical molasses relied on time-of-flight and other ballistic techniques to measure the temperature of atoms released from the molasses.1,2 At the extremely low temperatures observed, the size of the molasses, the effects of gravity, the probe that detected the falling atoms, and the way in which the laser beams forming the molasses were turned off produced a large systematic uncertainty in the temperature determination. Here, we report a direct measurement of the Doppler width of the fluorescence spectrum of Na atoms still viscously confined in the molasses. We determined this spectrum using an optical heterodyne technique and we believe this to be the first time an atomic fluorescence spectrum has been heterodyned. The temperature deduced from the Doppler width is in good agreement with that determined using improved time-of-flight techniques. The heterodyne technique has the added advantage of providing spatially resolved temperature measurements. In addition to the nominally 600-kHz wide Doppler peak, we see a much narrower (60-kHz wide) peak which we tentatively ascribe to Dicke narrowing due to confinement by optical forces.
We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.