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Physical Review Letters

Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping

Alain Aspect, E. Arimondo, Robin Kaiser, Nathalie Vansteenkiste, Claude N. Cohen-Tannoudji

Published Aug 15, 1988• 865 citations
Publisher

Abstract

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 $^{4}\mathrm{He}$ 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.

DOI
10.1103/physrevlett.61.826

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Cambridge University Press eBooks•Sep 2, 2010•0 citations
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 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.
We present a new scheme of sub-Doppler laser cooling for atoms used in atomic frequency standards, particularly for 40Ca. We perform calculations concerning optical pumping via a velocity- selective state based upon velocity-selective coherent population trapping. Optical pumping on the Raman transition 41S0- 41P1-31D2 leads to population of the metastable singlet state followed by a decay into the metastable triplet state 4P1. The momentum distribution of atoms in that state (with a half-maximum width of about one corresponding photon recoil momentum) is a direct replica of the distribution of atoms in the 3D2 state.
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 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.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).