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Quantum jump calculations of sub-recoil cooling in one and two dimensions

Haibin Wu, Murray Holland, Christopher J. Foot

Published Aug 24, 2005• 0 citations
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Abstract

Summary form only given. Fully quantum calculations are needed for laser cooling techniques in which the momentum of the atoms is reduced close to, or below, the recoil limit. We have proposed an efficient quantum jump method that is suitable for the study of subrecoil cooling. It can also be applied to the calculation of three-dimensional velocity selective coherent population trapping proposed by Mauri and Arimondo in F=3/2 to F=3/2 transition.

DOI
10.1109/cleopr.1995.527173

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Summary form only given. Fully quantum calculations are needed for laser cooling techniques in which the momentum of the atoms is reduced close to, or below, the recoil limit. We have proposed an efficient quantum jump method that is suitable for the study of subrecoil cooling. It can also be applied to the calculation of three-dimensional velocity selective coherent population trapping proposed by Mauri and Arimondo in F=3/2 to F=3/2 transition.
Velocity-selective coherent population trapping is a technique for laser-cooling atoms to below the recoil limit where the momenta of the atoms and photons in the light field are equal. We have studied this mechanism using an efficient simulation model, which both simplifies the calculations and gives a physical insight into the dynamics of the anomalous diffusion process. Our calculations have been carried out for transitions in which the total atomic angular momentum is F=1 to 1 in both one and two dimensions and F=2 to 2 in one dimension. In the latter case, no exact dark state exists, and the momentum distribution tends towards a Lorentzian in the steady 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.
We present a fully quantum-mechanical analysis of laser cooling of an angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ``precooling'' of the initial momentum distribution and (ii) in the long-time limit ``confinement of velocities.'' This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.
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.
Two-dimensional laser cooling based on velocity-selective coherent population trapping is investigated theoretically for the J = 1 ↔ J = 1 atomic transition. Wave vectors and polarizations of three laser beams are chosen to realize a coherent superposition of three degenerate ground states. For the first time forces related to Doppler and interference effects are combined with coherent population trapping to realize a very efficient cooling. Numerical solutions are presented for laser cooling of helium atoms.