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

Abstract

We introduce a nonlinear Schrödinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where a n1/3 1 with a the interatomic s -wave scattering length and n the bosonic density, to the unitarity limit, where a→+. We call this equation the unitarity Schrödinger 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. © 2008 The American Physical Society.