Interacting Fermionic Atoms in Optical Lattices Diffuse Symmetrically Upwards and Downwards in a Gravitational Potential

TL;DR

This paper studies fermionic atoms in optical lattices under gravity, revealing symmetric expansion driven by interactions and negative temperature gradients, with analytical and simulation results showing a t^(1/3) growth in cloud width.

Contribution

It provides an analytic hydrodynamic model explaining symmetric diffusion and negative temperature gradients in interacting fermionic clouds under gravity.

Findings

Cloud expands symmetrically in gravitational potential.

Interactions induce negative temperature gradients stabilizing heat currents.

Cloud width grows as t^(1/3) over time.

Abstract

We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves differently: It expands symmetrically such that gains of potential energy at the top are compensated by losses at the bottom. Interactions stabilize the necessary heat currents by inducing gradients of the inverse temperature 1/T, with T<0 at the bottom of the cloud. An analytic solution of hydrodynamic equations shows that the width of the cloud increases with t^(1/3) for long times consistent with results from our Boltzmann simulations.