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Physical Review Letters

Two-Dimensional Subrecoil Laser Cooling

John Lawall, F. Bardou, Bruno Saubaméa, Kazuko Shimizu, Michèle Leduc, Alain Aspect, Claude N. Cohen-Tannoudji

Published Oct 3, 1994• 113 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.73.1915

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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 \ensuremathδp=\ensuremathℏk4\ensuremath{\delta}p=\frac{\ensuremath{\hbar}k}{4}\ensuremathδp=4\ensuremathℏk​, where \ensuremathℏk\ensuremath{\hbar}k\ensuremathℏk 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.
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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 demonstrate subrecoil cooling of rubidium atoms by velocity-selective coherent population trapping. By adiabatic transfer of the cooled atoms into a spin polarized single momentum state we show the coherence of the trapped state. Our cooling scheme takes advantage of the rubidium hyperfine structure to integrate subrecoil and sub-Doppler cooling. Starting from an initial velocity distribution of twice the recoil temperature $[{T}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{\Elzxh}k{)}^{2}{/k}_{B}M]$, we cool down to 100 nK $(\ensuremath{\approx}\frac{1}{3}{T}_{\mathrm{rec}})$ within 1 ms, while almost completely suppressing the diffusive heating of velocity-selective coherent population trapping.
We present a new laser-cooling scheme based on velocity-selective optical pumping of atoms into a nonabsorbing coherent superposition of states. This method has allowed us to achieve transverse cooling of metastable 4He^{4}\mathrm{He}4He atoms to a temperature of 2 \ensuremath{\mu}K, lower than both the usual Doppler cooling limit (23 \ensuremath{\mu}K) and the one-photon recoil energy (4 \ensuremath{\mu}K). The corresponding de Broglie wavelength (1.4 \ensuremath{\mu}m) is larger than the atomic-transition optical wavelength.
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 present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.