Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice

TL;DR

This paper investigates the stability of a three-dimensional Bose-Einstein condensate in a driven one-dimensional optical lattice, focusing on collisional instabilities and how they affect the condensate's lifetime.

Contribution

It provides a detailed analysis of collisional instabilities in Floquet-engineered BECs and shows how decay rates depend on scattering length and density, with control via transverse potentials.

Findings

Decay rates scale inversely with the square of the scattering length.

Decay rates are inversely proportional to the peak three-dimensional density.

Adding transverse potentials can control the instability rates.

Abstract

Motivated by recent experiments, we analyse the stability of a three-dimensional Bose-Einstein condensate (BEC) loaded in a periodically driven one-dimensional optical lattice. Such periodically driven systems do not have a thermodynamic ground state, but may have a long-lived steady state which is an eigenstate of a "Floquet Hamiltonian". We explore collisional instabilities of the Floquet ground state which transfer energy into the transverse modes. We calculate decay rates, finding that the lifetime scales as the inverse square of the scattering length and inverse of the peak three- dimensional density. These rates can be controlled by adding additional transverse potentials.