Excitation spectrum of a bright solitary wave in a Bose-Einstein condensate and its connection with the Higgs and the Goldstone modes

TL;DR

This paper investigates the excitation spectrum of bright solitary waves in a Bose-Einstein condensate confined in a one-dimensional toroidal trap, revealing analogs of Goldstone and Higgs modes through analytical and numerical methods.

Contribution

It provides a detailed analysis of the excitation spectrum, identifying Goldstone and Higgs mode analogs in a BEC with attractive interactions, linking condensed matter phenomena with fundamental particle physics modes.

Findings

Identification of Goldstone mode in excitation spectrum

Observation of Higgs mode analog in BEC

Analytical and numerical characterization of excitations

Abstract

We consider the problem of Bose-Einstein condensed atoms, which are confined in a (quasi) one-dimensional toroidal potential. We focus on the case of an effective attractive interaction between the atoms. The formation of a localized blob (i.e., a ``bright" solitary wave) for sufficiently strong interactions provides an example of spontaneous symmetry breaking. We evaluate analytically and numerically the excitation spectrum for both cases of a homogeneous and of a localized density distribution. We identify in the excitation spectrum the emergence of the analogous to the Goldstone and the Higgs modes, evaluating various relevant observables, gaining insight into these two fundamental modes of excitation.