Reflections on dipolar quantum fluids

TL;DR

This paper develops a comprehensive thermodynamic framework for ultracold dipolar gases, accounting for their long-range interactions and anisotropy, and explores implications for phase transitions and droplet formation.

Contribution

It introduces a novel thermodynamic description including an additional field for dipolar gases, deriving new relations and criteria for phase transitions and droplet stability.

Findings

Uniaxial pressure deviates from Gibbs-Duhem relation in trapped gases.

Condition for self-bound droplets to have zero uniaxial pressure.

A criterion for the transition to a superfluid mass density wave.

Abstract

We present a thermodynamic description of ultracold gases with dipolar interactions which properly accounts for the long-range nature and broken rotation invariance of the interactions. It involves an additional thermodynamic field conjugate to the linear extension of the gas along the direction of the dipoles. The associated uniaxial pressure shows up as a deviation from the Gibbs-Duhem relation in the density profile of a trapped gas. It has to vanish in self-bound droplets, a condition which determines the observed dependence of the aspect ratio on particle number. A tensorial generalization of the virial theorem and a number of further exact thermodynamic relations are derived. Finally, extending a model due to Nozi\`eres, a simple criterion for the freezing transition to a superfluid mass density wave is given.