Collisional dynamics of symmetric two-dimensional quantum droplets

doi:10.1007/s11467-022-1192-z

Front. Phys.

2022, Vol. 17

Issue (6) : 61505 https://doi.org/10.1007/s11467-022-1192-z

RESEARCH ARTICLE

Collisional dynamics of symmetric two-dimensional quantum droplets

Yanming Hu¹, Yifan Fei², Xiao-Long Chen²(

), Yunbo Zhang²(

)

¹. Institute of Theoretical Physics and State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
². Department of Physics and Key Laboratory of Optical Field Manipulation of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou 310018, China

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Abstract

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberN_c ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.

Keywords ultracold atoms quantum droplets collisions

Corresponding Author(s): Xiao-Long Chen,Yunbo Zhang

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Issue Date: 18 August 2022

Cite this article:

Yanming Hu,Yifan Fei,Xiao-Long Chen, et al. Collisional dynamics of symmetric two-dimensional quantum droplets[J]. Front. Phys. , 2022, 17(6): 61505.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1192-z
https://academic.hep.com.cn/fop/EN/Y2022/V17/I6/61505

Fig.1 The density plots of the collisional dynamics of two droplets showing three different phases after the collision: (a) merging, (b) separation, and (c) evaporation, depending on the relative incident momentum

k = 0.2, 0.4

, and

1.8

, respectively, from top to bottom panels. Both droplets are initially normalized to a total particle number

N 1 = N 2 = 200

and all three cases correspond to the in-phase collisions with

? = 0

Fig.2 Typical quadrupole mode oscillation of the droplet in the merging phase and the damped oscillation in the separation phase. In the merging case (

k = 0.2

) the droplet widths

P x

(blue solid circle) and

P y

(open red circle) oscillate periodically with time. In the separation case (

k = 0.4

) the oscillation in

P x

(green solid circle) is quickly damped after the collision and the small fluctuation never exceeds half of the maximum value of droplet width

P x

. Here

N 1 = N 2 = 200

Fig.3 Period of quadrupole oscillation as a function of the particle number in the merging region for different incident momenta

k = 0.1, 0.15, 0.2, 0.3

. For

k = 0.3

, the colliding droplets will not merge for

N > 150

. The calculation is done in a 2D space with a sufficiently large length

L = 100 x 0

to assure the accuracy for large

N

Fig.4 Phase diagram of the in-phase collisional dynamics of two droplets with equal particle number

N 1 = N 2 = N

and

? = 0

. The boundaries between merging, separation and evaporation phases are determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode, respectively. A stability peak for the existence of droplets emerges at the critical value

N c ? 48

for the quasi-Gaussian and flat-top shapes of the droplets.

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