Effect of the Zero-Mode on the Response of a Trapped Bose-Condensed Gas

TL;DR

This paper investigates how the zero-energy excitation mode, or zero-mode, influences the response of a trapped Bose-Einstein condensate, highlighting its limited impact on observable excitation frequencies in current experiments.

Contribution

It provides a quantum field theoretical formulation of BEC response that explicitly includes the zero-mode, clarifying its role and significance in experimental observations.

Findings

Zero-mode contribution to response frequency is minimal in typical experimental parameters.

The Bogoliubov approximation remains valid despite neglecting the zero-mode.

Theoretical formulation aligns with quantum field theory principles.

Abstract

The dynamical response of a trapped Bose-Einstein condensate (BEC) is formulated consistently with quantum field theory and is numerically evaluated. We regard the BEC as a manifestation of the breaking of the global phase symmetry. Then, the Goldstone theorem implies the existence of a zero energy excitation mode (the zero-mode). We calculate the effect of the zero-mode on the response frequency and show that the contribution of the zero-mode to the first excitation mode is not so important in the parameter set realized in the existing experiment. This is the reason that experimental results can be described using the Bogoliubov prescription, although it breaks the consistency of the description in quantum field theory.