Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

TL;DR

This paper explores the theoretical properties of Nambu-Goldstone bosons in a single-component Bose-Einstein condensate, revealing multiple massless modes and clarifying their lifetimes and underlying structures.

Contribution

It demonstrates the existence of multiple Nambu-Goldstone bosons in a single-component BEC and clarifies their distinct properties and origins, especially the lifetime of the modes.

Findings

Multiple Nambu-Goldstone bosons can exist in a single-component BEC.

The second mode has an infinite lifetime in the long-wavelength limit.

The first mode, the Bogoliubov mode, is a fluctuating 'bubbling' mode with a substantial lifetime.

Abstract

We theoretically study the properties of Nambu-Goldstone bosons in an interacting single-component Bose-Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone, et al. [Phys. Rev. {\bf 127} (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function $\hat{G}$, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu-Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from $\hat{G}$, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a "bubbling" mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an "improper" structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.