# Phonon redshift and Hubble friction in an expanding BEC

### Submission summary

 As Contributors: Stephen Eckel Arxiv Link: https://arxiv.org/abs/2009.04512v2 (pdf) Date submitted: 2020-09-18 17:38 Submitted by: Eckel, Stephen Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Gravitation, Cosmology and Astroparticle Physics Approach: Theoretical

### Abstract

We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot{\cal V}/{\cal V}$, where $\cal{V}$ is the volume of the background condensate. This behavior is analogous to the redshifting and "Hubble friction" for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2009.04512v3 on 12 November 2020

Submission 2009.04512v2 on 18 September 2020

## Reports on this Submission

### Strengths

A perturbative analysis is introduced to analyse azimuthal phonons' dynamics in an expanding ring BEC. This analysis is first applied to the case of a static cylindrical condensate (where known results are recovered), and can also be useful to address scenarios more complicated than those considered.

### Weaknesses

The analysis is rigorous and thorough, I do not see weaknesses.

### Report

This is a technically very valuable paper. In the context of the gravitational analogy the authors first write down a 3D action for the linearised perturbations (phonons) in a BEC. Then, for both static cylindrical and expanding ring condensates, they derive dimensionally reduced 1D actions for phonon fields phi_1 constant in the transverse dimensions. In the latter case, the phonon field wave equation is similar to that of a scalar field in an expanding universe.
Their perturbative analysis allows to compute the corrections due to transverse modes, and the results show that these corrections are small. In the case of the expanding ring BEC, they improve their theoretical predictions with respect to their experiment [19], also in connection with the published results in [20].
In my opinion, after the authors have considered the two (small) points below, both for the analysis and the results the paper meets publishing criteria.

### Requested changes

A couple of points:
- In section 4.1, for the expanding ring BEC, they mention that the static approximation is surprisingly accurate even though in [19] the condition \dot R << c is violated (and they show in the appendix that the corrections to the static approximation are indeed small). Do the authors understand why ?
- in the definition of the speed of sound c_theta^2 in (4.19), isn't the factor (1+rho/R) in the numerator?

• validity: high
• significance: high
• originality: high
• clarity: top
• formatting: excellent
• grammar: perfect

### Strengths

The paper is clearly written in a rather pedagogical way that allows even not expert in the field to appreciate it.

### Report

The authors discuss in a detailed way the phonon wave equation in an expanding
ring BEC by dimensional reduction , showing characteristic effects one finds in cosmology , namely redshifting and Hubble friction experienced by quantum fields in an expanding universe.

• validity: top
• significance: top
• originality: high
• clarity: top
• formatting: excellent
• grammar: perfect