Superfluid response of bosonic fluids in composite optical potentials: angular dependence and Leggett's bounds

TL;DR

This paper investigates how composite optical potentials affect the superfluid response of dilute bosonic fluids, deriving conditions for isotropy, analytical bounds, and confirming results through numerical solutions.

Contribution

It provides analytical expressions for Leggett's bounds in composite potentials and identifies optimal measurement directions, supported by numerical validation.

Findings

Potential yields fully isotropic superfluid response under certain conditions.

Derived analytical bounds for superfluid fraction in perturbative regime.

Numerical solutions confirm analytical predictions and optimal directions.

Abstract

We study the superfluid response of a dilute bosonic fluid in the presence of two-dimensional composite potentials (such as triangular, Kagom\'e and quasiperiodic potentials, or superlattices), which may be obtained for example by superposing multiple laser beams. We first find a sufficient condition for the external potential to yield a fully isotropic superfluid response. Then, we derive analytical expressions for Leggett's upper and lower bounds to the superfluid fraction (valid in the perturbative regime) that allow us to find the optimal direction along which each bound should be measured. Finally, we solve the problem numerically, and we confirm our analytical findings.