We discuss theoretically the cooling and localization of atoms in deep potentials induced by a far-off-resonant standing-wave laser. For a two-level atom cooling occurs via a Sisyphus mechanism. For a \ensuremath{\Lambda} system we discuss a Raman cooling scheme similar to the one proposed for laser cooling in ion traps.
We present a general theoretical description of laser cooling of three-level atoms in a Λ configuration in two standing waves. Detunings, intensity, and spatial phase difference of the two waves are arbitrary. We demonstrate that, for a zero spatial phase shift, sub-Doppler cooling requires equal detunings. The basic mechanism is then coherent population trapping. For different detunings sub-Doppler cooling occurs only when the spatial phases of the two standing waves are different. This effect can be traced back to a mechanism of the Sisyphus type. These schemes of sub-Doppler cooling require neither polarization gradients nor magnetic fields.
We present theoretical descriptions of Sisyphus cooling in a two-dimensional laser configuration, based on semiclassical as well as quantum approaches. A detailed comparison of these various approaches and a discussion of their range of validity are given. Features of the cooled atomic distribution such as channeling of the atoms along specific lines in momentum space and the observability of tunneling induced resonances in the population of the ground state of the atomic motion in the optical potential wells are discussed.
Laser cooling of trapped ions in a standing- and running-wave configuration is discussed theoretically. The ions are assumed to be spatially localized on the scale provided by the wavelength of the laser (Lamb-Dicke limit). A master equation for the center-of-mass distribution of the ion is derived for a multilevel system, and explicit results are presented for two- and three-level systems and harmonic trapping potentials. For the two-level system located at the node of the standing wave, we find final temperatures that are a factor of 2 lower than the limit for a running wave and cooling rates that do not saturate with the laser intensity. At the point of maximum gradient of the standing wave, blue detuned cooling is found that is analogous to the Sisyphus cooling of free atoms. For a three-level system we compare our results with those of Wineland, Dalibard, and Cohen-Tannoudji [J. Opt. Soc. Am. B 9, 32 (1992)].
We have investigated the localization of atoms in two configurations of laser fields: monochromatic and bichromatic standing waves. A quasi resonant monochromatic laser field creates a spatially periodic potential field with period equal to half of the wavelength. If the atomic kinetic energy is less than the height of the potential wells then atoms could be trapped in the wells. The motion of atoms in a standing wave is governed by the gradient force, friction force, and momentum diffusion. We studied one dimensional localization of sodium atoms in such a standing wave, as well as the influence of friction and diffusion on the motion of these atoms. The effect of accumulation of atoms at the bottom of potential wells (nodes of a standing wave) was observed. This leads to a new scheme of laser cooling of atoms with a minimum temperature below the Doppler limit.
We propose a laser-driven Sisyphus-cooling scheme for atoms confined in a far-off resonance optical dipole trap. Utilizing the differential trap-induced ac Stark shift, two electronic levels of the atom are resonantly coupled by a cooling laser preferentially near the trap bottom. After absorption of a cooling photon, the atom loses energy by climbing the steeper potential, and then spontaneously decays preferentially away from the trap bottom. The proposed method is particularly suited to cooling alkaline-earth-metal-like atoms where two-level systems with narrow electronic transitions are present. Numerical simulations for the cases of 88Sr and 174Yb demonstrate the expected recoil and Doppler temperature limits. The method requires a relatively small number of scattered photons and can potentially lead to phase-space densities approaching quantum degeneracy in subsecond time scales.
We present a calculation of cooling of Rydberg atoms in bichromatic standing light waves. The atoms in our model are assumed to have a cascade three-level transition scheme, with the second excited level being the Rydberg state. The cooling fields, which also excite the atoms to the Rydberg state, consist of two standing waves whose frequencies are tuned near the two transition frequencies of the cascade atomic system. It is shown that the mechanisms of Sisyphus cooling and velocity-selective coherent population trapping can co-exist in such a configuration, and under certain conditions the majority of the laser-cooled atoms are in the Rydberg state.