Coarse-Grained Finite-Temperature Theory for the Condensate in Optical Lattices

TL;DR

This paper develops a coarse-grained finite-temperature theoretical framework for Bose condensates in one-dimensional optical lattices, capturing non-equilibrium dynamics, dissipative effects, and instabilities through a variational approach based on the 2PI effective action.

Contribution

It introduces a novel coarse-grained effective action derived from the 2PI formalism, incorporating dissipative dynamics and analyzing Landau instability in optical lattice condensates.

Findings

Dissipative equations of motion include condensate-noncondensate collisions.

Collisional damping rate changes sign at a critical velocity.

Landau instability aligns with the Landau criterion.

Abstract

In this work, we derive a coarse-grained finite-temperature theory for a Bose condensate in a one-dimensional optical lattice, in addition to a confining harmonic trap potential. We start from a two-particle irreducible (2PI) effective action on the Schwinger-Keldysh closed-time contour path. In principle, this action involves all information of equilibrium and non-equilibrium properties of the condensate and noncondensate atoms. By assuming an ansatz for the variational function, i.e., the condensate order parameter in an effective action, we derive a coarse-grained effective action, which describes the dynamics on the length scale much longer than a lattice constant. Using the variational principle, coarse-grained equations of motion for the condensate variables are obtained. These equations include a dissipative term due to collisions between condensate and noncondensate atoms, as well as noncondensate mean-field. To illustrate the usefulness of our formalism, we discuss a Landau instability of the condensate in optical lattices by using the coarse-grained generalized Gross-Pitaevskii hydrodynamics. We found that the collisional damping rate due to collisions between the condensate and noncondensate atoms changes sign when the condensate velocity exceeds a renormalized sound velocity, leading to a Landau instability consistent with the Landau criterion. Our results in this work give an insight into the microscopic origin of the Landau instability.