# Cooling phonon modes of a Bose condensate with uniform few body losses

### Submission summary

 As Contributors: Isabelle Bouchoule Arxiv Link: https://arxiv.org/abs/1806.08759v3 (pdf) Date submitted: 2018-09-18 02:00 Submitted by: Bouchoule, Isabelle Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the $j$th power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale $mc^2$, where $m$ is the mass of the particles and $c$ the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap.

### Ontology / Topics

See full Ontology or Topics database.

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

Dear editor,

Please find here a new version of our paper, with minor modifications.

Best regards,

The authors.

### List of changes

p3: the footnote on Ito vs. Stratonovich has been suppressed.

Eq.(17), first line: for consistency with the second line, we have added
the argument r to the fields \delta n and g_\nu. Same cosmetic change in
Eqs.(24,25), Eq.(37), and Eq.(58).

p12: we have added a paragraph on the thermodynamic phases that one may expect
for the Bose gas at long times.

p13: a reference to a paper by Cockburn & al,
"Comparison between microscopic methods for finite-temperature Bose gases",
Phys. Rev. A 83, 043619 (2011)
has been suppressed as it was not relevant for the 'two-temperature' case
in question. We kept the reference [5] to Johnson & al,
"Long-lived non-thermal states realized by atom losses in one-dimensional quasi-condensates",
Phys. Rev. A 96, 013623 (2017).

### Submission & Refereeing History

#### Published as SciPost Phys. 5, 043 (2018)

Resubmission 1806.08759v4 on 25 October 2018

Resubmission 1806.08759v3 on 18 September 2018
Submission 1806.08759v2 on 4 July 2018

## Reports on this Submission

### Anonymous Report 2 on 2018-10-22 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1806.08759v3, delivered 2018-10-22, doi: 10.21468/SciPost.Report.621

### Strengths

1. Timely recent topic of significant practical and theoretical interest to the community.

2. Significantly extends the regimes in which the cooling-by-losses phenomenon has been described to include largely arbitrary potentials and several different loss mechanisms.

3. The main equations derived appear to be readily usable for a wide range of future problems.

4. Very clearly written, easily understandable paper.

5. Good segregation of what went into the main body of the text and the appendices.

### Weaknesses

1. Based on three quite strong approximations: local density, close-to-adiabatic, and phonon modes only. This will makes the results inapplicable to a significant proportion of the interesting cases.

2. Although the equations are developed for arbitrary dimension, only 1d examples are provided.

3. No explicit mention of the use of these equations already in Ref. [9].

### Report

The paper concerns a topic that has drawn significant interest in the last two years - a cooling that appears due to particle losses in ultra-cold gases. It was noticed somewhat unexpectedly in some experiments in 2016, and has been discussed in the community since then. A cute thing about this mechanism is that provides a route to cooling below the level of the chemical potential that occurs naturally without complicated manipulations of the gas and seems that it could be made almost automatic. Also, it is appealing that such a process was not really suspected in the community beforehand and has now been spotted. There have been both some experimental and theoretical studies of it since the initial report, including an experiment by the present authors, Ref. [9].

This paper significantly extends the regimes in which the process has been described to include considerations of very arbitrary potentials, and several-particle loss. This will be helpful in enabling future researchers in making straightforward initial calculations of the phenomenon in a wide variety of systems.

The study bases itself very strongly on the local density and close-to-adiabatic approximations, which leads fairly directly to both the main strengths and main weaknesses of the results. The strength being that the resulting equations (23-26) can be applied to practically any potential and a variety of loss processes. Furthermore, these equations are not numerically problematic or onerous. The weakness is that the results thus obtained are restricted to slowly evolving phonon modes, with small amplitudes, in slowly varying potentials. In terms of space-dependence, anything with length-scales approaching healing length will not be treated well. Some of the earlier theoretical works on the subject go beyond these restrictions, but with more idealised potentials, losses. Overall the results of this work complement previous studies well, and significantly move the knowledge about the topic forward.

The equations that constitute the main result of the paper are derived as applicable to 1,2,3 dimensions, so it is a little disappointing (though not atypical) that only 1d examples have been provided. Still, it is nice to see that the authors note earnestly in the conclusions that the validity of the equations in 2d and 3d is likely to be more restricted.

Knowing that the present authors are also authors of the experimental work with cooling by three-body losses [9], for which the methods developed here are ideal, I was surprised to find no explicit calculations comparing to that experiment here. However, it turns out that Ref. [9] does cite the present manuscript extensively, referring to it actually as the source of the calculations made there. There is no explicit statement of the same fact here in the present manuscript though, leaving readers a bit in the dark. It would be very helpful for clarity to also explicitly explain also *here* that these methods have already been applied in [9].

Apart from this one little thing, the paper is very clearly written, with the right balance of explanation where necessary and abstention from writing out gruelling details where they can readily be filled in by those interested. The choice of which details are relegated into appendices worked well. Other than more explicitly explaining the relationship to Ref. [9], I don't really have any other changes to recommend. The paper is a very worthwhile standalone addition to the current knowledge on the topic as is.

### Requested changes

1. Please clarify that the methods presented here have already been applied in the experimental paper Ref. [9], and make a brief comment on how good the match was.

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