Inelastic collisions in ultracold gases confined by one-dimensional optical lattices

Abstract

We present a formalism for rigorous multichannel scattering calculations of cross sections for inelastic collisions of atoms and molecules confined in one-dimensional optical lattices. We obtain analytical expressions for the mean frequency of inelastic collisions in a confined gas in the temperature regime $T~\ensuremath{\hbar}\ensuremath{\omega}$ and at temperatures $T\ensuremath{\gg}\ensuremath{\hbar}\ensuremath{\omega}$, where $\ensuremath{\omega}$ is the oscillation frequency of trapped particles in the confining potential. Our numerical calculations for the gaseous mixture of Li and Rb atoms show that inelastic collisions in the temperature regime $T~\ensuremath{\hbar}\ensuremath{\omega}$ exhibit a deviation from three-dimensional scattering. This deviation is more significant for systems with stronger confinement and larger scattering lengths. We find that the ratios of rate constants for inelastic scattering and elastic collisions are suppressed in confined gases at $T~\ensuremath{\hbar}\ensuremath{\omega}$, and this suppression is significant for Li-Rb collisions at $T<40$ $\ensuremath{\mu}$K.