Decay of Persistent Currents in Annular Atomic Superfluids

Round 1

Reviewer 1 Report

In this manuscript, the authors study theoretically the stability of the persistent current of a three dimensional atomic superfluid in an annular geometry. This work is strongly correlated to their previous experimental findings where they observed such persistent current and its decay. In particular, they identity two sources for the superfluid current to decay. 1) imperfections in the phase imprinting technique to induce the superflow that create initial density fluctuations in the gas that may lead to the creation of vortices. 2) the effect of a localised impurity potential that can reduce the expected critical velocity due to the creation of pairs of vortices with opposite circulation.

To do so, they use the three dimensional Gross-Pitaevskii equation both for computing the initial state and its time evolution as close as possible to their initial experimental protocol. It is important to recall that under perfect conditions (no obstacle, perfect phase imprinting), the circulation of the fluid must be quantized and (meta)stable below the sound velocity. In the presence of a localised impurity, the critical circulation is reduced and a flow with an initial circulation above this critical value shall decay by the generation of a precise number of vortex/anti vortex pairs. Although this mechanism is well known (and very well explained in the manuscript) the critical circulation has a non trivial dependence on the obstacle parameters (strength and width) and is not very well established in the literature. In that respect, this work is important for the community of superfluids. On the other side, in the absence of an obstacle, the authors observe and explain why the superflow decays above a maximal value of the initial circulation. By comparing the results of simulations with a perfect initial condition and with a realistic experimental situation (where the initial phase imprinted in the condensate has some imperfections) their work shed light on experimental limitations to study and manipulate superflows. If at first glance this work seems to be interesting for their experiment only it is actually of much wider interest.

The paper is very well written and extremely pleasant to read. Even if the accuracy of the three dimensional Gross-Pitaevkii equation for describing their experiment is not a surprise, the authors discuss the variety of physical processes involved in the non linear dynamics of the condensate in great details and in very pedagogical way. I have not seen so many papers on the subject with such a deep physical analysis and clear experimental data. I was in particular impressed by the discussion of the different mechanisms leading to vortex formation, blurring of the winding number and the local Landau's criterion.

For those reasons I believe, with no doubt, that this paper must be published in your journal. I may have found only one mistake at line 213. The authors wrote $\Delta \phi_I > 5$ but I think they wanted to write $\Delta \phi_I /2\pi > 5$. This has to be checked.

Author Response

We sincerely thank the referee for her/his appreciation of our work and for noticing this mistake in line 213 which we have now corrected.

Reviewer 2 Report

This paper studied numerically the stability of persistent currents in a Bose-Einstein condensate in a clean ring and in the presence of a localized defect. Interesting dynamical evolution of currents was shown and the vortex emission was identified as the source of the instability in both contexts.

 

The paper is well written, the physical description is concise and reasonable, solid results obtained by numerical simulations were collected and shown up. I recommend the acceptance of it in Atoms.

 

Driven by curiosity, I encourage the authors to discuss roughly the influence of the size of the defect on mean circulation.

Author Response

We thank the referee for her/his comments and for her/his suggestion on commenting on the effect of defect's width. We have now added a phrase in line 345-347 commenting on the effect we expect the defect's width to have on the critical circulation and on the decay of the current.

Reviewer 3 Report

This manuscript follows up the experimental work published in Phys. Rev. X 12, 041037 (2022) and expands on the theoretical analysis presented therein, by investigating the role of vortices in the decay of persistent current states of annular atomic superfluids. To this end, the time-dependent Gross-Pitaevskii equation is solved numerically in the BEC limit of the inter-particle interaction at zero temperature, with special emphasis on the optical phase-imprinting technique employed to experimentally to excite finite-circulation states and on the effect of a point-like obstacle with variable potential height. These are the main questions addressed by the research.

In the manuscript, numerical and experimental observables are accurately compared in several figures. To this end, the authors utilize a rather standard methodology for which full numerical control can be guaranteed. In particular, the dynamics is studied in details of how a vortex enters the bulk density from the inner ring radius, by considering both ideal and realistic phase imprinting which makes the circulation to decay to a smaller value.  The effect of a localized defect on the ring persistent current is also studied, with the emergence of a critical circulation which is limited by the emission of quantized vortices. In this case, it is found that a stronger obstacle leads to a lower critical circulation and a faster decay. This whole analysis appears original, rather complete,  and definitely relevant in this field.

The conclusions reached by this manuscript appear to be consistent with the experimental evidence gathered previously by the same group. In addition, the arguments presented in the present manuscript are well justified and physically sound. For all the above reasons, I recommend publication of this manuscript in the present form.

There are only minor points to be revised.

Author Response

We thank the referee for the appreciation of our work and we did some minor editing of English language.

Reviewer 4 Report

To investigate the effect of phase imprinting on the persist current including winding number is an interesting topic. I think the method is solid and the result reproduce the results in Ref. 1. I recommend publication!

Author Response

We thank the referee for her/his recommendation of our work for publication.