Density functional theory of a trapped Bose gas with tunable scattering length: from weak-coupling to unitarity

TL;DR

This paper develops a density functional theory approach to study a trapped Bose gas with tunable scattering length, analyzing density profiles, collective oscillation frequencies, and damping effects across weak to unitarity regimes.

Contribution

It introduces an energy density functional fitted to Monte Carlo data that spans from weak coupling to unitarity, enabling comprehensive analysis of trapped Bose gases.

Findings

Density profiles agree with Monte Carlo calculations.

Monopole mode frequency exhibits non-monotonous behavior with scattering length.

Three-body losses significantly damp collective modes.

Abstract

We study an interacting Bose gas at T=0 under isotropic harmonic confinement within Density Functional Theory in the Local Density approximation. The energy density functional, which spans the whole range of positive scattering lengths up to the unitary regime (infinite scattering length), is obtained by fitting the recently calculated Monte Carlo bulk equation of state [Phys. Rev. A 89, 041602(R) (2014)]. We compare the density profiles of the trapped gas with those obtained by MC calculations. We solve the time-dependent Density Functional equation to study the effect of increasing values of the interaction strength on the frequencies of monopole and quadrupole oscillations of the trapped gas. We find that the monopole breathing mode shows a non-monotonous behavior as a function of the scattering length. We also consider the damping effect of three-body losses on such modes.