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arXiv:2302.07481 · Physica Scripta

Dynamics of rapidly rotating Bose–Einstein quantum droplets

Szu-Cheng Cheng, Yuwen Wang, Wen-Hsuan Kuan

Published May 13, 2024• 7 citations
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Abstract

Abstract This study presents a detailed analysis of the stationary properties and dynamics of an anharmonically trapped, rapidly rotating Bose–Einstein liquid droplet. We investigate the effects of the particle number, confining potential, and rotation speed on the formation of the energetically favored bead, multiple quantized vortex, off-center vortex, and center-of-mass states. The multi-periodic trajectories and breathing provide evidence of the collective excitations of the surface mode in the vortex states. Observation of the self-trapping phenomenon and tendency toward the lowest Landau level in rapid rotation regimes coincides well with the quantum-Hall limit. Modifying the topological charges and destroying the potential flow of the vortex state can occur if an external disturbance is imposed upon the quantum droplet.

DOI
10.1088/1402-4896/ad4ad3

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Abstract This study presents a detailed analysis of the stationary properties and dynamics of an anharmonically trapped, rapidly rotating Bose–Einstein liquid droplet. We investigate the effects of the particle number, confining potential, and rotation speed on the formation of the energetically favored bead, multiple quantized vortex, off-center vortex, and center-of-mass states. The multi-periodic trajectories and breathing provide evidence of the collective excitations of the surface mode in the vortex states. Observation of the self-trapping phenomenon and tendency toward the lowest Landau level in rapid rotation regimes coincides well with the quantum-Hall limit. Modifying the topological charges and destroying the potential flow of the vortex state can occur if an external disturbance is imposed upon the quantum droplet.
A rapidly rotating Bose gas in the quantum Hall limit is usually associated with a melted vortex lattice. In this work, we report a self-bound and visible triangular vortex lattice without melting for a two-dimensional Bose-Bose droplet rotating in the quantum Hall limit, i.e., with rotation frequency $\mathrm{\ensuremath{\Omega}}$ approaching the trapping frequency $\ensuremath{\omega}$. Increasing $\mathrm{\ensuremath{\Omega}}$ with respect to interaction strength UUU, we find a smooth crossover of the vortex lattice droplet from a needling regime, as featured by small vortex cores and an equilibrium flat-top surface, to the lowest-Landau-level regime with Gaussian-extended cores spreading over the whole surface. The surface density of such a rotating droplet is higher than that of a static one, and their ratio is found to be a universal function of $\mathrm{\ensuremath{\Omega}}/U$. We have demonstrated these results by both numerical and variational methods. The results pave the way for future experimental exploration of rapidly rotating ultracold droplets into the quantum Hall limit.
Bose mixture quantum droplets display a fascinating stability that relies on quantum fluctuations to prevent collapse driven by mean-field effects. Most droplet research focuses on untrapped or weakly trapped scenarios, where the droplets exhibit a liquidlike flat density profile. When weakly trapped droplets rotate, they usually respond through center-of-mass motion or splitting instability. Here, we study rapidly rotating droplets in the strong external confinement limit where the external potential prevents splitting and the center-of-mass excitation. We find that quantum droplets form a triangular vortex lattice as in single-component repulsive Bose-Einstein condensates (BECs), but the overall density follows the analytical Thomas-Fermi profile obtained from a cubic equation. We observe three significant differences between rapidly rotating droplets and repulsive BECs. First, the vortex core size changes markedly at finite density, visible in numerically obtained density profiles. We analytically estimate the vortex core sizes from the droplets' coherence length and find good agreement with the numerical results. Second, the change in the density profile gives a slight but observable distortion to the lattice, which agrees with the distortion expected due to nonuniform superfluid density. Lastly, unlike a repulsive BEC, which expands substantially as the rotation frequency approaches the trapping frequency, rapidly rotating droplets show only a fractional change in their size. We argue that this last point can be used to create clouds with lower filling factors, which may facilitate reaching the elusive strongly correlated regime.
We investigate the rotational properties of quantum droplets, which form in a mixture of two Bose-Einstein condensates, in the presence of an anharmonic trapping potential. We identify various phases as the atom number and the angular momentum or angular velocity of the trap vary. These phases include center-of-mass–like excitation (without or with vortices), vortices of single and multiple quantization, etc. Finally, we compare our results with those of the single-component problem. Published by the American Physical Society 2024
Abstract We consider a two-dimensional self-bound quantum droplet, which consists of a mixture of two Bose–Einstein condensates. We start with the ground state and then turn to the rotational response of this system, in the presence of an external (harmonic) potential. We identify various phases, depending on the atom number, the strength of the external confinement and the angular momentum. These include center of mass excitation, ghost vortices, as well as vortices of single and multiple quantization. According to our results, this is an excellent system for the study of superfluid states.
Recent experiments demonstrate that rapidly rotating Bose-Einstein condensates (BECs) near the lowest Landau level can self-organize into interaction-driven persistent quantum Hall droplet arrays. Inspired by this discovery, we investigate the formation and dynamics of single quantum Hall droplet and droplet arrays in rapidly rotating BECs. Guided by a rigorous theorem on localized many-body states for two-dimensional interacting systems in a magnetic field, we construct single quantum Hall droplet and droplet array states which are shown to be stationary solutions to the Gross-Pitaevskii equation in the rotating frame. The single quantum Hall droplet is shown to be dynamically stable, which underpins its role as the basic unit in a droplet array. The stability of the quantum Hall droplet arrays is demonstrated by their dynamic formation from a phase engineered initial condensate. Our study sheds light onto the nature of the quantum Hall droplet state in a rapidly rotating BEC and offers a new approach for generating and manipulating quantum Hall droplet arrays through designing the initial condensate phase.
Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar 164^{164}164Dy Quantum Droplets
We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity SSS) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) n=2Sn=2Sn=2S, up to S=6S=6S=6. The stability area of the multipoles shrinks with the increase of SSS. For higher values of SSS the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and SSS is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.