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Physical Review Letters

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

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

Published Nov 23, 1992• 23 citations
Publisher

Abstract

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}${\mathit{k}}^{2}$ 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.

DOI
10.1103/physrevlett.69.3029

Related papers

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

Philippe Verkerk, Brahim Lounis, J.-Y. Courtois +2 more

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.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

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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 ${\mathit{J}}_{\mathit{g}}$=1\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=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.

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Magnetic inhibition of polarization-gradient laser cooling in σ+ - σ− optical molasses

M. Walhout, Uwe Sterr, S. L. Rolston

Xenon atoms are released from a magneto-optical trap and equilibrate in a one-dimensional, ${\mathrm{\ensuremath{\sigma}}}_{+}$-${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}$ optical molasses, along which a uniform magnetic field is applied. In the rest frame of the ``corkscrew'' pattern of laser polarization, the magnetic field induces a nonzero average atomic velocity. Introducing a moving molasses through a relative difference in the two laser-beam frequencies allows straightforward, accurate measurements of the molasses-frame velocity distribution over a large range of magnetic fields. The measurements reveal the loss of polarization-gradient cooling in fields higher than \ensuremath{\sim}0.2 mT, in quantitative agreement with theoretical predictions. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•22 citations
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.
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.
We present a detailed calculation of the four-wave-mixing signal from one-dimensional optical molasses, in which atoms are cooled by a pair of counterpropagating, cross-polarized fields. The contributions from both Raman and Rayleigh resonances between the discrete motional bound states and the recoil-induced resonances between the motional continuum states are analyzed. It is shown that the recoil-induced resonances can lead to a narrow central resonance peak in the four-wave-mixing signal with a width given by the transverse residual Doppler width. The calculated Raman sidebands also exhibit an asymmetry in the signal strength, a feature observed in recent experiments.
We present a calculation of the probe absorption spectrum of atoms in a one-dimensional optical molasses formed by a pair of counterpropagating, cross-polarized fields. When the finite angle \ensuremath{\theta} between the propagation direction of a probe field and that of one of the cooling fields is taken into account, we find that, apart from the contributions to the probe absorption signal that are related to the Raman and Rayleigh resonances between the discretized atomic motional states in the molasses direction, there is also a signal arising from the recoil-induced resonances between atomic states with different center-of-mass momenta in the directions transverse to the molasses beams. The magnitudes of these different contributions are compared.
Xenon atoms are released from a magneto-optical trap and equilibrate in a one-dimensional, ${\mathrm{\ensuremath{\sigma}}}_{+}$-${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{-}}}$ optical molasses, along which a uniform magnetic field is applied. In the rest frame of the ``corkscrew'' pattern of laser polarization, the magnetic field induces a nonzero average atomic velocity. Introducing a moving molasses through a relative difference in the two laser-beam frequencies allows straightforward, accurate measurements of the molasses-frame velocity distribution over a large range of magnetic fields. The measurements reveal the loss of polarization-gradient cooling in fields higher than \ensuremath{\sim}0.2 mT, in quantitative agreement with theoretical predictions. \textcopyright{} 1996 The American Physical Society.