Nonlinear Schroedinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

TL;DR

This paper develops a nonlinear Schrödinger equation, called the unitarity Schrödinger equation (USE), to model superfluid Bose gases across the entire interaction spectrum, from weak coupling to unitarity, and investigates vortex structures and collective modes.

Contribution

The paper introduces the USE, a new equation that accurately describes Bose gases from weak coupling to unitarity, extending beyond the Gross-Pitaevskii framework.

Findings

Vortex profiles and core radii are computed using the USE.

The USE predicts vortex and breathing mode properties across interaction regimes.

Results show good agreement with known limits and experimental data.

Abstract

We introduce a nonlinear Schroedinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where $a n^{1/3}\ll 1$ with $a$ the inter-atomic s-wave scattering length and $n$ the bosonic density, to the unitarity limit, where $a\to +\infty$. We call this equation the {unitarity Schroedinger equation} (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically-symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.