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Journal of Physics B Atomic Molecular and Optical Physics

Polarization gradient cooling in three dimensions: comparison of theory and experiment

Juha Javanainen

Published Feb 14, 1994• 11 citations
Publisher

Abstract

Polarization gradient cooling of 87 Rb in lin perpendicular to lin optical molasses is studied. The author's semiclassical force-and-diffusion simulations yield laser cooling temperatures in agreement with recent experiments by Gerz et al. (1993). Anomalies in the spatial distribution of the cooled atoms and in the heterodyne spectra are discussed.

DOI
10.1088/0953-4075/27/3/001

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Journal of the Optical Society of America B•Nov 1, 1989•1,272 citations
Polarization gradient cooling of 87 Rb in lin perpendicular to lin optical molasses is studied. The author's semiclassical force-and-diffusion simulations yield laser cooling temperatures in agreement with recent experiments by Gerz et al. (1993). Anomalies in the spatial distribution of the cooled atoms and in the heterodyne spectra are discussed.
We describe a numerical implementation of our semiclassical laser-cooling theory [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] for an arbitrary multilevel atom and light field. There is satisfactory agreement between experiments and temperatures obtained from Langevin-equation simulations of the motion of an atom subject to light-pressure force and the accompanying diffusion in three-dimensional (3D) optical molasses in which there are three orthogonal pairs of counterpropagating waves with a common linear polarization for the two beams in a pair, but orthogonal polarizations between the pairs. However, the velocity distribution of the atoms is anisotropic and may deviate strongly from a Gaussian, heterodyne spectra may have a sideband, and the atomic density may be a maximum at the maximum of the potential of the dipole forces of the molasses beams. Subsequent velocity-linearized analysis of atomic damping and diffusion shows that the damping tensor may have a negative eigenvalue corresponding to heating in large regions of space, even though the light is red tuned for cooling. It is also found that the position-averaged damping and diffusion tensors make a poor predictor of the temperature obtained in Langevin-equation simulations and real experiments. Based on additional simulations of a simple 1D model, we formulate a hypothesis that connects our findings. The key idea is that an atom trapped in a minimum of the potential of the dipole forces is subject to a weaker-than-average damping, and therefore tends to boil out of the trap.
A theoretical analysis is given for laser cooling of a two-level atom with magnetic sublevels in the presence of polarization gradients. The optical Bloch equations for the multilevel system are solved numerically for four combinations of polarizations in one-dimensional optical molasses. The light-pressure force on the atom as given by a simple two-level theory is recovered in the absence of polarization gradients, whereas a spatial variation of the polarization is found to lead to a strong cooling force for slow atoms. The increased cooling force is responsible for the recent observations of atoms cooled in optical molasses to temperatures an order of magnitude below the Doppler limit.
Sisyphus polarization gradient laser cooling has been performed in a one-dimensional lin lin laser beam configuration on each of the three fine structure transitions of . Hence for the first time Sisyphus polarization gradient cooling on a transition with has been demonstrated. We have investigated the qualitative and quantitative differences between the cooling process for three transitions with . A major qualitative difference of the laser cooling on the and transitions has been observed as expected from simple theoretical arguments. In the case of sub-Doppler cooling is achieved when the laser detuning is blue. Even though the situation for the and case is qualitatively similar, we find quantitative differences which are in good agreement with Monte Carlo wavefunction simulations. For experiments where narrow velocity distributions are essential, such as atom lithography, these results can be applied.
We present a summary of the results of a simple two-level theory of Doppler cooling in optical molasses and contrast it with the recent theories of multilevel, polarization-gradient cooling. The effects of single-photon recoil and of trapping in microscopic optical potential wells are also considered. Experiments are described in which the temperature of sodium atoms released from optical molasses is measured and found to be well below the Doppler-cooling limit. Measurements of the temperature dependence on many experimental parameters are found to be in good qualitative agreement with the new theories of polarization-gradient cooling.
We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.