Semiclassical Corrections to a Static Bose-Einstein Condensate at Zero Temperature

TL;DR

This paper calculates semiclassical quantum corrections to the mean-field description of a static Bose-Einstein condensate at zero temperature, including vortex states, by extending the Gross-Pitaevskii and hydrodynamic equations.

Contribution

It extends previous semiclassical correction calculations to include vortex states and provides local correction terms in the Thomas-Fermi limit.

Findings

Semiclassical corrections can be incorporated as local terms in the Gross-Pitaevskii equation.

Second-order corrections modify the hydrodynamic equations for the condensate.

The approach applies to general time-independent condensate states, including vortices.

Abstract

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations.