Isotropy and optimal Leggett-bound directions at arbitrary interactions and temperatures

Establish whether, for two-dimensional Bose–Einstein condensates subjected to composite optical potentials whose Fourier spectra consist of one or more regular polygons (including square, triangular, Kagomé, and certain quasicrystal lattices and superlattices), the superfluid fraction tensor remains fully isotropic and the optimal measurement directions for Leggett’s bounds persist for all parameter regimes—specifically, that the upper bound is maximized when the dominant Fourier components are aligned with the current direction and the lower bound is maximized when they are perpendicular—holding for any value of the interaction strength and at finite temperatures.

Background

The paper analyzes the superfluid response of dilute bosonic fluids in a broad class of two-dimensional composite optical potentials formed by superposing plane waves whose Fourier components lie on the vertices of regular polygons. Within a zero-temperature, mean-field framework and using perturbative analysis (supplemented by numerical Gross–Pitaevskii simulations), the authors demonstrate that these multishell potentials yield an isotropic superfluid fraction and derive analytical expressions for the angular dependence of Leggett’s upper and lower bounds, identifying optimal measurement directions tied to the potential’s Fourier geometry.

In the conclusion, the authors conjecture that these geometry-driven properties are universal, i.e., independent of interaction strength and temperature. They explicitly call for verification of this conjecture in the strongly interacting and finite-temperature regimes, which would extend their zero-temperature, weak-potential results to general conditions.