Manifestation of a gap due to the exchange energy in a spinor condensate

TL;DR

This paper explores the dynamic response of a spinor Bose condensate, revealing a gap in the inter-component current response due to exchange energy, and compares two theoretical approaches with experimental validation prospects.

Contribution

It demonstrates that the generalized random phase approximation better preserves symmetries and sum rules, predicting a gap in the inter-component current response not captured by the Bogoliubov-Popov approximation.

Findings

GRPA predicts a gapped spectrum in the inter-component current response.

BPA results show a gapless response, lacking exchange energy effects.

Proposes an experimental setup to observe the predicted gap.

Abstract

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between results obtained in the Bogoliubov-Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We argue that the GRPA is superior since, contrary to the BPA, it preserves the SU(2) symmetry and the f-sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.