Rotating Multidimensional Quantum Droplets

Liangwei Dong and Yaroslav V. Kartashov

Phys. Rev. Lett. 126, 244101 – Published 17 June 2021

Abstract

We predict a new type of two- and three-dimensional stable quantum droplets persistently rotating in broad external two-dimensional and weakly anharmonic potential. Their evolution is described by the system of the Gross-Pitaevskii equations with Lee-Huang-Yang quantum corrections. Such droplets resemble whispering-gallery modes localized in the polar direction due to nonlinear interactions and, depending on their chemical potential and rotation frequency, they appear in rich variety of shapes, ranging from nearly flat-top or strongly localized rotating wave packets, to crescentlike objects extending nearly over the entire range of polar angles. Above critical rotation frequency quantum droplets transform into vortex droplets (in two dimensions) or vortex tori (in three dimensions), whose topological charge gradually increase with the increase of the modulus of chemical potential, and therefore they belong to the family of nonlinear modes connecting fundamental and vortex quantum droplets. Rotating quantum droplets are exceptionally robust objects, stable practically in the entire range of their existence.

Received 26 January 2021
Revised 5 April 2021
Accepted 10 May 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.244101

Physics Subject Headings (PhySH)

Mixtures of atomic and/or molecular quantum gases

Solitons Superfluids

Nonlinear Dynamics

Authors & Affiliations

Liangwei Dong ^1,* and Yaroslav V. Kartashov ²

¹Department of Physics, Shaanxi University of Science & Technology, Xi’an 710021, China
²Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia

^*dongliangwei@sust.edu.cn

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Issue

Vol. 126, Iss. 24 — 18 June 2021

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Images

Figure 1
Rotating quantum droplets for various $ω$ at $μ = - 0.09$ (a), $μ = - 0.18$ (b), and $μ = - 0.35$ (c). Modulus of two identical components $| ψ_{1} | = | ψ_{2} | = | ψ |$ and phase distributions (insets) are shown within $x, y \in [- 18, + 18]$ windows. White circles indicate the potential minimum. (d) Stable rotation of quantum droplet with $ω = 0.04$ , $μ = - 0.18$ .
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Figure 2
(a) $N$ versus $μ$ for 2D rotating droplets and radially symmetric state with $m = 0$ at $ω = 0.01$ . Labels $a$ and solid lines correspond to asymmetric rotating states, while labels $s$ and dashed lines correspond to radially symmetric states. (b) $N$ versus $μ$ for rotating droplet and radially symmetric state with $m = 3$ at $ω = 0.06$ . (c) $N$ versus rotation frequency $ω$ at different $μ$ values. Radial modes from which bifurcation occurs carry charges $m = 2$ $(μ = - 0.09)$ and $m = 5$ ( $μ = - 0.18$ ). (d) $N$ versus $ω$ for nearly flat-top 2D droplets ( $μ$ decreases along the arrow from $- 0.35$ to $- 0.36$ in steps of $δ μ = 0.002$ ).
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Figure 3
Existence domains of the rotating 2D (a) and 3D (b) droplets on the ( $μ$ , $ω$ ) plane. Domains on the upper edge, where topological charge increases by 1 with an increase of $| μ |$ are marked by the dots of a different color (for 2D states the charge at $ω = ω_{m}$ increases from $m = 0$ at $μ \sim - 0.0648$ up to $m = 9$ at $μ \sim - 0.355$ , while for 3D states it increases up to $m = 4$ at $μ \sim - 0.238$ ). Droplets are unstable below red solid curves and are stable above them.
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Figure 4
(a) Norm $N$ versus $μ$ for 3D rotating droplets ( $ω = 0$ —solid black curve, $ω = 0.02$ —solid red curve) and radially symmetric state with $m = 0$ (dashed curve). (b) $N$ versus $ω$ for rotating droplets (solid curves) and radially symmetric states (dashed curves) for various $μ$ . Radially symmetric states, from which bifurcation occurs, carry topological charges $m = 3$ ( $μ = - 0.14$ ) and $m = 4$ ( $μ = - 0.23$ ). Here and below $g_{LHY} = 0.5$ , $g = 1.75$ .
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Figure 5
Isosurface $| ψ |$ plots illustrating profiles of the 3D rotating droplets at (a) $μ = - 0.238$ , (b) $μ = - 0.140$ , and (c) $μ = - 0.088$ for different $ω$ . Isosurface levels in (a),(c) are $0.10 ψ_{\max}$ , $0.55 ψ_{\max}$ , $0.95 ψ_{\max}$ , while in (b) they are $0.23 ψ_{\max}$ , $0.55 ψ_{\max}$ , $0.95 ψ_{\max}$ , where $ψ_{\max} = \max | ψ |$ for a given set of $μ$ , $ω$ parameters.
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Figure 6
Isosurface $| ψ |$ plots at different $t$ illustrating unstable (a) and stable (b),(c) evolution of the perturbed 3D droplets. In (a) $μ = - 0.238$ , $ω = 0$ ; in (b) $μ = - 0.238$ , $ω = 0.014$ ; in (c) $μ = - 0.076$ , $ω = 0.014$ . Isosurface levels in (a),(b) are $0.2 ψ_{\max}$ , $0.8 ψ_{\max}$ , $0.985 ψ_{\max}$ , while in (c) they are $0.2 ψ_{\max}$ , $0.55 ψ_{\max}$ , $0.95 ψ_{\max}$ .
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