A Fermion-like description of condensed Bosons in a trap

TL;DR

This paper presents a novel fermion-like mapping of a Bose-Einstein condensate in a trap, enabling analytical estimates of ground state properties and excitations, revealing new collective behaviors.

Contribution

It introduces a fermion-like model for trapped bosons that reproduces ground state properties and predicts new collective excitations.

Findings

Mapping reproduces ground state properties of the condensate

Analytical estimate of vortex excitation energy

Predicts novel collective excitations in the condensed phase

Abstract

A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock fermions'' have a state occupancy factor $(>>1)$ proportional to the ratio of the coherance length to the ``hard-core'' radius of the atom. The mapping reproduces the ground state properties of the condensate, and is used to estimate the vortex excitation energy analytically. The ``mock-fermion'' description predicts some novel collective excitation in the condensed phase.