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arXiv:2406.00863 · Physical Review Letters

Collapse of a Quantum Vortex in an Attractive Two-Dimensional Bose Gas

Sambit Banerjee, Kai Zhou, Shiva Kant Tiwari, Hikaru Tamura, Rongjie Li, P. G. Kevrekidis, S. I. Mistakidis, Valentin Walther, Chen-Lung Hung

Published Jun 26, 2025• 11 citations
arXivHTMLPDF

Abstract

We experimentally and numerically study the collapse dynamics of a quantum vortex in a two-dimensional atomic superfluid following a fast interaction ramp from repulsion to attraction. We find the conditions and timescales for a superfluid vortex to radially converge into a quasistationary density profile, demonstrating the spontaneous formation of a vortex solitonlike structure in an atomic Bose gas. We record an emergent self-similar dynamics caused by an azimuthal modulational instability, which amplifies initial density perturbations and leads to the eventual splitting of a solitonic ring profile or direct fragmentation of a superfluid into disordered, but roughly circular arrays of Townes solitonlike wave packets. These dynamics are qualitatively reproduced by simulations based on the Gross-Pitaevskii equation. However, a discrepancy in the magnitude of amplified density fluctuations predicted by our mean-field analysis suggests the presence of effects beyond the mean-field approximation. Our study sets the stage for exploring out-of-equilibrium dynamics of vortex quantum matter quenched to attractive interactions and their universal characteristics.

DOI
10.1103/c6wx-zc9x

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We experimentally and numerically study the collapse dynamics of a quantum vortex in a two-dimensional atomic superfluid following a fast interaction ramp from repulsion to attraction. We find the conditions and timescales for a superfluid vortex to radially converge into a quasistationary density profile, demonstrating the spontaneous formation of a vortex solitonlike structure in an atomic Bose gas. We record an emergent self-similar dynamics caused by an azimuthal modulational instability, which amplifies initial density perturbations and leads to the eventual splitting of a solitonic ring profile or direct fragmentation of a superfluid into disordered, but roughly circular arrays of Townes solitonlike wave packets. These dynamics are qualitatively reproduced by simulations based on the Gross-Pitaevskii equation. However, a discrepancy in the magnitude of amplified density fluctuations predicted by our mean-field analysis suggests the presence of effects beyond the mean-field approximation. Our study sets the stage for exploring out-of-equilibrium dynamics of vortex quantum matter quenched to attractive interactions and their universal characteristics.
We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.
The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].
We study the process of scattering of two-dimensional dark solitons, and their vortex-antivortex pairs as a specific case, by a single quantum vortex in a Bose-Einstein condensate with repulsive interaction between atoms. An asymptotic theory describing the dynamics of such solitonlike structures in a smoothly inhomogeneous flow of ultracold Bose gas is developed. An analytical expression for the angle of scattering of two-dimensional dark solitons (including vortex pairs) by a single-phase singularity is obtained in the limit of large impact parameters. All theoretical concepts are confirmed by numerical calculations performed directly within the Gross-Pitaevskii equation. It is shown that for small impact parameters, the considered solitonlike structures interact inelastically with the core of a single quantum vortex, scattering over large angles and radiating sound waves.
A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.
Spatiotemporal evolution of a confined Bose-Einstein condensate is studied by numerically integrating the time-dependent Gross-Pitaevskii equation. Self-interference between the successively expanding and reflecting nonlinear matter waves results in spiral atomic density profile, which subsequently degenerates into an embedding structure: The inner part preserves memory of the initial states while the outer part forms a sequence of necklacelike rings. The phase plot reveals a series of discrete concentric belts. The large gradients between adjacent belts indicate that the ring density notches are dark solitons. In the dynamical process, a scenario of vortex-antivortex pairs are spontaneously created and annihilated, whereas the total vorticity keeps invariant.
Experiments on attractive Bose-Einstein condensates (BECs) have unlocked many intriguing out-of-equilibrium dynamics through the interplay between matter-wave dispersion and nonlinear attractive interaction. Competition between these effects leads to fascinating phenomena such as wave collapse, modulational instability, and formation of multidimensional bright solitons. This chapter reviews experimental studies on attractive condensates, with a primary focus on alkali atoms featuring two-body contact interactions. We review recent experimental advances in optical trapping and interaction control techniques, which have enabled new studies on attractive condensates in three and also in lower dimensions. Specifically, we discuss pioneering and recent experimental observations on the dynamics and stability of attractive BECs, including the formation of bright solitons, their collisions, and excitations in quasi-one-dimensional traps. Recent observations of the elusive two-dimensional Townes solitons and vortex solitons are also discussed in this Chapter. We then highlight an experimental technique revealing the nonclassical signatures of modulational instability in an attractive condensate.