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Onedimensional purely LeeHuangYang fluids dominated by quantum fluctuations in twocomponent BoseEinstein condensates
by Xiuye Liu，Jianhua Zeng*
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Submission summary
As Contributors:  Jianhua Zeng 
Preprint link:  scipost_202107_00032v1 
Date submitted:  20210720 10:37 
Submitted by:  Zeng, Jianhua 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
LeeHuangYang (LHY) fluids are an exotic quantum matter emerged in a BoseBose mixture where the meanfield 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 meanfield (quantum manybody) effect—quantum fluctuations. Threedimensional 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 lowdimensional counterparts remain mysterious even in theory. Herein, we derive the GrossPitaevskii equation of onedimensional LHY quantum fluids in twocomponent BoseEinstein condensates, and reveal the formation, properties, and dynamics of matterwave 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 higherorder 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 linearstability 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 quantumgas experiments, providing a new insight into LHY physics in lowdimensional settings.
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Anonymous Report 2 on 2021812 (Invited Report)
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The paper considers the onedimensional BoseBose mixture tuned to the point where the interspecies attraction exactly compensates the intraspecies repulsions and where the meanfield interaction vanishes. In this case the system is governed by the GrossPitaevskii equation with attractive quadratic nonlinearity arising from the beyondmeanfield term. The authors discuss various properties of localized solutions of this equation: fundamental and higherorder 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 (higherorder 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 groundstate 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 centerofmass 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 higherorder 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?
Anonymous Report 1 on 2021730 (Invited Report)
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 quadraticonly nonlinearity in the quantum fluid, with fully balanced meanfield 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 matterwave 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 quasielastic collisions and the merger.