Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice

TL;DR

This paper investigates the stability of a Floquet-engineered Bose-Einstein condensate in a one-dimensional optical lattice under periodic shaking, identifying conditions for stability and decay due to atomic collisions, and explaining experimental observations.

Contribution

It provides a theoretical analysis of Floquet BEC stability, mapping phase diagrams and explaining experimental long-lived condensates in shaken optical lattices.

Findings

Identified stable and unstable regions for Floquet BECs.

Explained the long lifetime (~1 second) of the condensate in experiments.

Estimated scattering rates in unstable regions.

Abstract

Motivated by recent experimental observations (C.V. Parker {\it et al.}, Nature Physics, {\bf 9}, 769 (2013)), we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such a system there is no thermodynamic ground state, but there may be a long-lived steady-state, described as an eigenstate of a "Floquet Hamiltonian". We calculate how scattering processes lead to a decay of the Floquet state. We map out the phase diagram of the system and find regions where the BEC is stable and regions where the BEC is unstable against atomic collisions. We show that Parker et al. perform their experiment in the stable region, which accounts for the long life-time of the condensate ($\sim$ 1 second). We also estimate the scattering rate of the bosons in the region where the BEC is unstable.