Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Experimental Investigation of Nonergodic Effects in Subrecoil Laser Cooling

Bruno Saubaméa, Michèle Leduc, Claude N. Cohen-Tannoudji

Published Nov 8, 1999• 30 citations
Publisher

Abstract

We present the first detailed investigation of the line shape of the momentum distribution of atoms cooled far below the recoil limit. This distribution is deduced from a direct measurement of the atomic spatial correlation function of metastable helium atoms cooled by velocity-selective coherent population trapping. The measured line shape is then compared to the prediction of an analytical model of this cooling based on L\'evy statistics. A very good agreement is found between experiment and theory and fundamental features such as self-similarity and nonergodicity are identified.

DOI
10.1103/physrevlett.83.3796

Related papers

Two-Dimensional Subrecoil Laser Cooling

John Lawall, F. Bardou, Bruno Saubaméa +4 more

We report the first observation of subrecoil laser cooling in two dimensions by velocity selective coherent population trapping. We have compressed the momentum distribution of a cloud of trapped metastable helium atoms along two orthogonal axes to $\ensuremath{\delta}p=\frac{\ensuremath{\hbar}k}{4}$, where $\ensuremath{\hbar}k$ is the photon momentum. The corresponding temperature, 16 times below the single-photon recoil temperature, is 250 nK. Atoms are pumped into a nonabsorbing state exhibiting four well-resolved momentum peaks with subrecoil widths. The momentum space density in the peaks is significantly greater than that in the uncooled distribution.

Physical Review Letters•Oct 3, 1994•113 citations

Recent Advances in Subrecoil Laser Cooling

John Lawall, François Bardou, Jean‐Philippe Bouchaud +8 more

This paper presents new experimental realizations of sub‐recoil laser cooling by velocity selective coherent population trapping (VSCPT). Starting from a cloud of trapped and precooled metastable helium atoms, it has been possible to achieve a VSCPT interaction time of 500 μs. This has enabled the momentum distribution to be compressed along one or two orthogonal axes to better than δp = ħk/4 where ħk is the photon momentum. The corresponding temperature is at least 16 times smaller than the single photon recoil limit, and the de Broglie wavelength of the atoms is at least 4 times larger than the wavelength of the laser used to cool the atoms. Recent theoretical developments are also described, establishing a connection between subrecoil cooling and Lévy flights and allowing one to get analytical expressions for the proportion of cooled atoms in the long time limit. Finally, the possibility of increasing the efficiency of VSCPT by Sisyphus precooling is briefly mentioned.

AIP conference proceedings•Jan 1, 1994•1 citation

Three-Dimensional Laser Cooling of Helium Beyond the Single-Photon Recoil Limit

John Lawall, S. A. Kulin, Bruno Saubaméa +3 more

We report the first observation of subrecoil laser cooling in three dimensions, where we use the method of velocity-selective coherent population trapping. We have cooled a cloud of trapped metastable helium atoms to 180 nK, 22 times below the single-photon recoil temperature, with an enhancement in the momentum-space density of 16. We find that the efficiency with which the velocity-selective trap is populated can be augmented by Sisyphus-type frictional forces, while the cooling process is accompanied by the diffusion of atoms to states of very high velocity.

Physical Review Letters•Dec 4, 1995•120 citations

Direct Measurement of The Spatial Correlation Function of Ultracold Atoms

Bruno Saubaméa, Tom W. Hijmans, S. A. Kulin +4 more

We demonstrate a new method to directly measure, from the overlap of two atomic wave packets, the spatial correlation function of metastable helium atoms cooled by velocity selective coherent population trapping. This approach allows us to determine precisely the effective temperature of the atoms and to make quantitative comparison with theory. Temperatures as low as $1/800$ of the recoil temperature are found. Moreover, we extend this method to realize a temporal interferometer with de Broglie matter waves in the subrecoil regime.

Physical Review Letters•Oct 27, 1997•52 citations

Non–ergodic laser cooling

Claude N. Cohen-Tannoudji

Atoms can now be laser cooled, in one, two and three dimensions, below the limit corresponding to the recoil energy of an atom absorbing or emitting a single photon. Recent works have shown that all subrecoil cooling schemes are based on an anomalous random walk of the atom in momentum space which does not obey the central limit theorem and which introduces a fundamental non–ergodicity in the cooling process. Lévy statistics turn out to be very useful for analysing such a situation since they provide quantitative results for the long time limit of the momentum distribution. In this paper, we briefly review these theoretical works and we give a few references where more details can be found. We also mention a few recent experiments which have been stimulated by these theoretical developments.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 15, 1997•0 citations

Several asymptotic subrecoil laser-cooling behaviors in arbitrary degenerate Λ systems

Hong Yuan Ling

Subrecoil cooling can be achieved in three-level \ensuremath{\Lambda}-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate \ensuremath{\Lambda} systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.

Physical Review A•May 1, 1999•5 citations
We present the first detailed investigation of the line shape of the momentum distribution of atoms cooled far below the recoil limit. This distribution is deduced from a direct measurement of the atomic spatial correlation function of metastable helium atoms cooled by velocity-selective coherent population trapping. The measured line shape is then compared to the prediction of an analytical model of this cooling based on L'evy statistics. A very good agreement is found between experiment and theory and fundamental features such as self-similarity and nonergodicity are identified.
We report the first observation of subrecoil laser cooling in two dimensions by velocity selective coherent population trapping. We have compressed the momentum distribution of a cloud of trapped metastable helium atoms along two orthogonal axes to $\ensuremath{\delta}p=\frac{\ensuremath{\hbar}k}{4}$, where $\ensuremath{\hbar}k$ is the photon momentum. The corresponding temperature, 16 times below the single-photon recoil temperature, is 250 nK. Atoms are pumped into a nonabsorbing state exhibiting four well-resolved momentum peaks with subrecoil widths. The momentum space density in the peaks is significantly greater than that in the uncooled distribution.
This paper presents new experimental realizations of sub‐recoil laser cooling by velocity selective coherent population trapping (VSCPT). Starting from a cloud of trapped and precooled metastable helium atoms, it has been possible to achieve a VSCPT interaction time of 500 μs. This has enabled the momentum distribution to be compressed along one or two orthogonal axes to better than δp = ħk/4 where ħk is the photon momentum. The corresponding temperature is at least 16 times smaller than the single photon recoil limit, and the de Broglie wavelength of the atoms is at least 4 times larger than the wavelength of the laser used to cool the atoms. Recent theoretical developments are also described, establishing a connection between subrecoil cooling and Lévy flights and allowing one to get analytical expressions for the proportion of cooled atoms in the long time limit. Finally, the possibility of increasing the efficiency of VSCPT by Sisyphus precooling is briefly mentioned.
We report the first observation of subrecoil laser cooling in three dimensions, where we use the method of velocity-selective coherent population trapping. We have cooled a cloud of trapped metastable helium atoms to 180 nK, 22 times below the single-photon recoil temperature, with an enhancement in the momentum-space density of 16. We find that the efficiency with which the velocity-selective trap is populated can be augmented by Sisyphus-type frictional forces, while the cooling process is accompanied by the diffusion of atoms to states of very high velocity.
We demonstrate a new method to directly measure, from the overlap of two atomic wave packets, the spatial correlation function of metastable helium atoms cooled by velocity selective coherent population trapping. This approach allows us to determine precisely the effective temperature of the atoms and to make quantitative comparison with theory. Temperatures as low as 1/8001/8001/800 of the recoil temperature are found. Moreover, we extend this method to realize a temporal interferometer with de Broglie matter waves in the subrecoil regime.
Atoms can now be laser cooled, in one, two and three dimensions, below the limit corresponding to the recoil energy of an atom absorbing or emitting a single photon. Recent works have shown that all subrecoil cooling schemes are based on an anomalous random walk of the atom in momentum space which does not obey the central limit theorem and which introduces a fundamental non–ergodicity in the cooling process. Lévy statistics turn out to be very useful for analysing such a situation since they provide quantitative results for the long time limit of the momentum distribution. In this paper, we briefly review these theoretical works and we give a few references where more details can be found. We also mention a few recent experiments which have been stimulated by these theoretical developments.
Subrecoil cooling can be achieved in three-level \ensuremath{\Lambda}-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate \ensuremath{\Lambda} systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.