Brillouin propagation modes of cold atoms undergoing Sisyphus cooling

An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. The calculations are for a Jg = 1/2 -> Je = 3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.

Automated summary

The article derives an exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice using semiclassical equations. The expression is based on the amplitudes of atomic density waves. The calculations are specifically for a Jg = 1/2 -> Je = 3/2 transition, commonly used in theoretical studies of Sisyphus cooling. The new expression allows the quantification of the contribution of specific atomic waves to the atomic motion, revealing unexpected counterpropagating contributions from many modes. Additionally, the method provides a generic threshold for the transition into the regime of infinite density.