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arXiv:2306.14958 · Physical Review A

Self-bound vortex lattice in a rapidly rotating quantum droplet

Qi Gu, Xiaoling Cui

Published Dec 4, 2023• 15 citations
arXivHTMLPDF

Abstract

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 $U$, 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.

DOI
10.1103/physreva.108.063302

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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 \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ approaching the trapping frequency \ensuremathω\ensuremath{\omega}\ensuremathω. Increasing \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ 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 \ensuremathΩ/U\mathrm{\ensuremath{\Omega}}/U\ensuremathΩ/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.
We consider a “symmetric” quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of “rapid” rotation. We examine this problem using a purely numerical approach, as well as a semianalytic Wigner-Seitz approximation (first developed by Baym, Pethick, and their co-workers) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a “large” droplet, working with a fixed rotational frequency of the trap Ω , as Ω approaches the trap frequency ω , a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the “size” of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly correlated many-body states, here no melting of the vortex lattice is present, even when Ω = ω . This difference is due to the fact that the droplet is self-bound. For Ω = ω , the “smoothed” density distribution becomes a flat top, very much like the static unconfined droplet. When Ω exceeds ω , the droplet maintains its shape and escapes to infinity, via center-of-mass motion. Published by the American Physical Society 2024
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.
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.
Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.
Rapidly rotating atomic gases provide a platform for studying phenomena akin to type-II superconductors and quantum Hall systems. Recently, these systems have attracted renewed interest due to technological advances in the trap anisotropy control, in-situ observation capabilities, and cooling and rotating complex atomic species such as dipolar gases. Understanding the vortex lattice formation and quantum melting is crucial for exploring quantum Hall physics in these systems. In this paper, we theoretically investigate the vortex lattices in anisotropic quantum gases. We formulate the rotating gas Hamiltonian in the Landau gauge, and consider the effects of additional perturbations such as the trap potential in the lowest Landau level (LLL). Focusing on the gases with short-range interactions, we obtain the many-body Hamiltonian projected to lowest Landau level. We consider the limit of full Bose-Einstein condensation and obtain the governing Gross-Pitaevskii equation to identify the possible vortex phases. We numerically solve the Gross-Pitaevskii equation using the imaginary time evolution, and demonstrate the possible vortex lattices as a function of anisotropy, rotation speed and interaction strength. We show that the number of states with a support in the LLL, which determines the number of vortices, follows a Thomas-Fermi type scaling albeit with slightly different coefficients from the usual condensates.
We discuss the feasibility of quantum Hall states of vortices in trapped low-density two-dimensional Bose gases with large particle interactions. For interaction strengths larger than a critical dimensionless 2D coupling constant g c ≈ 0.6, upon increasing the rotation frequency, the system is shown to spatially separate into vortex lattice and melted vortex lattice (vortex liquid) phases. At a first critical frequency, the lattice melts completely, and strongly correlated vortex and particle quantum Hall liquids coexist in inner and outer regions of the gas cloud, respectively. Finally, at a second critical frequency, the vortex liquid disappears and the strongly correlated particle quantum Hall state fills the whole sample.