Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice

TL;DR

This paper develops an analytical framework to describe the damping of collective excitations in 1D Bose-Einstein condensates within optical lattices, accounting for temperature, trapping potential, and nonlinear interactions, with predictions matching experimental data.

Contribution

It introduces a comprehensive analytical model for damping rates of confined phonon-like excitations, incorporating Landau and Beliaev processes at any temperature, and explores the effects of laser tuning and nonlinear interactions.

Findings

Damping rate depends linearly on temperature at high T or weak confinement.

Landau damping is exponentially suppressed at low T in the quantum limit.

Laser intensity can resonantly tune the condensate lifetime.

Abstract

We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is non-homogeneous and the collective excitations are characterized by a set of discrete confined phonon-like excitations. We derive a general convenient analytical description for the damping rate, which takes into account, the trapping potential and the optical lattice, for the Landau and Beliaev processes at any temperature, $T$. At high temperature or weak spatial confinement, we show that both mechanisms display linear dependence on $T$. In the quantum limit, we found that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of $T$. Our theoretical predictions for the damping rate under thermal regime is in completely correspondence with the experimental values reported for 1D condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a \textit{resonant effect} for the condensate lifetime. Also, we study the influence of the attractive or repulsive non-linear terms on the decay rate of the collective excitations. A general expression of the renormalized Goldstone frequency has been obtained as a function of the 1D non-linear self-interaction parameter, laser intensity and temperature.