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One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates

by Xiuye Liu,Jianhua Zeng*

This is not the current version.

Submission summary

As Contributors: Jianhua Zeng
Preprint link: scipost_202107_00032v1
Date submitted: 2021-07-20 10:37
Submitted by: Zeng, Jianhua
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Quantum Physics
Approach: Theoretical


Lee-Huang-Yang (LHY) fluids are an exotic quantum matter emerged in a Bose-Bose mixture where the mean-field interactions, interspecies attraction (g_{12}) and intraspecies repulsive (g_{11}, g_{22}), are tuned to cancel completely when g_{12}=-\sqrt{g_{11}g_{22}} and atom number N_2=\sqrt{g_{11}/g_{22}}N_1 , and as such the fluids are purely dominated by beyond mean-field (quantum many-body) effect—quantum fluctuations. Three-dimensional LHY fluids were proposed in 2018 and demonstrated by the same group from Denmark in recent ultracold atoms experiments [T. G. Skov, et al., Phys. Rev. Lett. 126, 230404 (2021)], while their low-dimensional counterparts remain mysterious even in theory. Herein, we derive the Gross-Pitaevskii equation of one-dimensional LHY quantum fluids in two-component Bose-Einstein condensates, and reveal the formation, properties, and dynamics of matter-wave structures therein. An exact solution is found for fundamental LHY fluids. Considering a harmonic trap, approximate analytical results are obtained based on variational approximation, and higher-order nonlinear localized modes with nonzero nodes \Bbbk=1 and 2 are constructed numerically. Stability regions of all the LHY nonlinear localized modes are identified by linear-stability analysis and direct perturbed numerical simulations. Movements and oscillations of single localized mode, and collisions between two modes, under the influence of different incident momenta are also studied in dynamical evolutions. The predicted results are available to quantum-gas experiments, providing a new insight into LHY physics in low-dimensional settings.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2021-8-12 (Invited Report)


The paper considers the one-dimensional Bose-Bose mixture tuned to the point where the interspecies attraction exactly compensates the intraspecies repulsions and where the mean-field interaction vanishes. In this case the system is governed by the Gross-Pitaevskii equation with attractive quadratic nonlinearity arising from the beyond-mean-field term. The authors discuss various properties of localized solutions of this equation: fundamental and higher-order modes (with one or two nodes) in free space and under harmonic confinement, their stability analysis, collisions between two localized modes.

The paper contributes to a popular topic, but its quality can be improved. The authors should better account for existing results. The discussion of new subjects (higher-order modes, influence of the trap) is numerical and very superficial. I cannot recommend publication, at least, in the present form. The following comments came up while I was reading the manuscript.

1) The analytic droplet solution has been obtained in Ref.[28] in the general case, including the point of vanishing mean field.

2) The stability analysis (Bogoliubov modes) of the ground-state droplet solution in free space has been performed by Tylutki et al., Phys. Rev. A 101, 051601 (2020). The droplet is found stable. I thus do not understand the authors' conclusion on "very limited stability interval for fundamental modes" in this case. Accordingly, I also do not understand Fig.4d. The validity is questionable.

3) Figures 4b, 4c, 4e, and 4f seem to show trivial center-of-mass dipole oscillations in the harmonic trap. I see no monopole mode there. I thus doubt that this figure is useful.

4) There is a significant overlap between this manuscript and the work of Astrakharchik and Malomed, Phys. Rev. A 98, 013631 (2018) who studied collisions between droplets in a slightly more systematic manner.

5) There are many inconsistencies. Some examples are the absence of "yellow dashed line" in Fig.2d, no "shapes' comparison" in Figs.2a and 2b, no labels a, b, c, and d in Fig. 3, etc. The authors should have carefully read their draft before submitting.

6) The potential impact of the paper could be improved if the authors better explain physical motivation for studying higher-order modes. It would also help if they discuss stability of these modes in a more systematic manner. Are there stability thresholds for excited modes in Fig.3? If yes, what is their physical meaning?

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Anonymous Report 1 on 2021-7-30 (Invited Report)


The consideration of the topic of "quantum droplets" is currently very timely and relevant, in view of the great advancement in the theoretical prediction and experimental realization of such "droplets" in binary atomic BEC. In this context, the results reported in this manuscript may be appropriate for the publication, as they predict new dynamical effects which probably may be implemented in the experiment. These include, in particular, motion of droplets trapped in an external potential, intrinsic excitations in them, and collisions. In particular, the analysis in this paper focuses on the experimentally relevant limit of the quadratic-only nonlinearity in the quantum fluid, with fully balanced mean-field repulsion and attraction.

However, the manuscript contains some inaccuracies which should be fixed. In particular, I surmise that there are typos in Eqs. (1) and (3), as it seems strange that the second terms in those expressions do not include any density of the condensate. By the way, what is meant by the "momentum integration" of Eq. (1)? It is also recommended to be more accurate in references. Particularly, the statement that Eq. (9) is a completely new solution seems disputable, as it is a special case of a more general solution (16) for the "droplets", reported in Ref. [28]. Another inaccuracy is the reference to Fig. 5(b) as the formation of "two matter-wave breathers", while in reality one observes merger of colliding droplets into a single breather in this figure.

Lastly, it is recommended to present results for collisions between the "droplets" in a more systematic form. In particular, it is relevant to find a critical collision velocity separating quasi-elastic collisions and the merger.

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