# The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

### Submission summary

 As Contributors: Alberto Biella · Leonardo Mazza · Lorenzo Rosso Arxiv Link: https://arxiv.org/abs/2106.08092v2 (pdf) Date accepted: 2022-01-06 Date submitted: 2021-10-11 15:00 Submitted by: Rosso, Lorenzo Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We study the dynamics of a one-dimensional Bose gas in presence of strong two-body losses. In this dissipative quantum Zeno regime, the gas fermionises and its dynamics can be described with a simple set of rate equations. Employing the local density approximation and a Boltzmann-like dynamical equation, the description is easily extended to take into account an external potential. We show that in the absence of confinement the population is depleted in an anomalous way and that the gas behaves as a low-temperature classical gas. The harmonic confinement accelerates the depopulation of the gas and introduces a novel decay regime, which we thoroughly characterise.

Published as SciPost Phys. 12, 044 (2022)

### List of changes

(1) We propose a new title to the article "The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement", in order to further stress the fact that our work extends the previous one (i.e. Ref.[36]) including also the effect of the trap.

(2) Two important remarks have been added in the Introduction. The former deals with highlighting the fact that GHD is only one among many theories that can be used to tackle these problems (see the sentence "...among several developments..."). The latter remark points out the two different regimes of confinement due to the presence of the trap, namely weak and strong confinement (see the part "Two regimes are identified: ...").

(3) Thanks to the observation of the reviewer 2 we have rewritten the paragraph in SubSec. 2.1 starting with "In order to prove that that the latter density matrix..."

(4) Thanks to a remark of the reviewer 1, in Sec. 3.2 we changed the name of the function g (\tilde t) with \nu (\tilde t)

(5) Thanks to a remark of the reviewer 1, in Sec. 3.2 we enlarged the discussion concerning the mean-field limit. See the paragraph starting "We find a long-time behaviour characterised by n(t)..."

(6) In Sec. 3.2 we added an equation, namely Eq. (23) in order to better clarify the mathematical steps in the derivation.

(7) We modified Fig. 3 including three vertical dashed lines marking the crossover between weak- and strong-confiniment. Moreover, the dimension of the labels has been reduced as requested.

(8) We added a new figure, namely Fig. 4, in which the spatial density profile \tilde N( \tilde x, \tilde t) is plotted.

(9) Thanks to a suggestion of the reviewer 1, the discussion in Sec. 4.4 has been enlarged. In particular, a new adimensional parameter r(t) has been introduced to mark the switch from weak- to strong-confinement. The contribution of the reviewer has been acknowledged.

(10) We modified the dimension of the labels of Fig. 5 (Fig. 4 of the previous version) as requested.

(11) Sec. 4.5 and Sec. 4.6 have been introduced in the main text. In the previous version of the paper they were in the Appendix E. We decided to move it to the main text in order to emphasize the discussion about the harmonic confinement.

(12) We added a new Appendix (now Appendix. A) titled "Homogeneous Bose gas: derivations" in order to better clarify the mathematical steps to derive Eqs. 19 and 21.

(13) We modified the dimension of the labels of Fig. 6 (Fig. 5 of the previous version) as requested.

(14) We changed the title of Appendix. E into "Analytical solution for \omega / \tilde \Gamma = 0"

### Submission & Refereeing History

Resubmission 2106.08092v2 on 11 October 2021
Submission 2106.08092v1 on 16 June 2021

## Reports on this Submission

### Report

I thank the authors for their detail answers to all the comments and questions of the first referee report. I agree with their answers and I think the paper is now ready for publication. I agree it can be publiched in Scipost Physics.

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### Anonymous Report 1 on 2021-11-25 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2106.08092v2, delivered 2021-11-25, doi: 10.21468/SciPost.Report.3900

### Report

The reviewer thanks the authors for their time taken to improve the manuscript. The current manuscript reads well and the included additions have created a thorough and well crafted explanation of their timely and useful results.

The reviewers recommendation is to publish after correcting two small typos:

1. In Figure 3 the black and cyan dashed lines should be labeled as Eq. (42) and Eq. (45), rather than the current labels of Eq. (40) and Eq. (43).

2. In Appendix C the text before Eq. (69) should read "We can also present an analytical formula for $\nu(\tilde{t})$", rather than "... also for $g(\tilde{t})$".

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -