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Physical Review Research

Origin and evolution of the multiply quantized vortex instability

Sam Patrick, August Geelmuyden, Sebastian Erne, Carlo F. Barenghi, Silke Weinfurtner

Published Nov 14, 2022• 15 citations
Publisher

Abstract

We show that the dynamical instability of quantum vortices with more than a single unit of circulation results from a superradiant bound state inside the vortex core. We then reveal a striking behavior of the system in the nonlinear regime. Counter to the expectation that the instability should produce well-separated vortices, the system evolves into a bound state of corotating singularities orbiting within a few healing lengths of each other, undergoing modulations in separation. During these modulations, kinetic energy is traded back and forth between sound waves and vortical degrees of freedom.

DOI
10.1103/physrevresearch.4.043104

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We show that the dynamical instability of quantum vortices with more than a single unit of circulation results from a superradiant bound state inside the vortex core. We then reveal a striking behavior of the system in the nonlinear regime. Counter to the expectation that the instability should produce well-separated vortices, the system evolves into a bound state of corotating singularities orbiting within a few healing lengths of each other, undergoing modulations in separation. During these modulations, kinetic energy is traded back and forth between sound waves and vortical degrees of freedom.
We show that the dynamical instability of quantum vortices with more than a single quantum of angular momentum results from a superradiant bound state inside the vortex core. Our conclusion is supported by an analytic WKB calculation and numerical simulations of both linearised and fully non-linear equations of motion for a doubly-quantised vortex at the centre of a circular bucket trap. In the late stage of the instability, we reveal a striking novel behaviour of the system in the non-linear regime. Contrary to expectation, in the absence of dissipation the system never enters the regime of two well-separated phase defects described by Hamiltonian vortex dynamics. Instead, the separation between the two defects undergoes modulations which never exceed a few healing lengths, in which compressible kinetic energy and incompressible kinetic energy are exchanged. This suggests that, under the right conditions, pairs of vortices may be able to form meta-stable bound states.
Multiply quantized vortices (MQVs) within single-component Bose-Einstein condensates are unstable and decay rapidly. We show that MQVs can be stabilized by adding a small number of atoms of a second species to the vortex cores, and that these atoms remain in the vortex core as the system evolves. A consequence of the stabilization is that nearby corotating vortices can orbit in the opposite sense to their individual rotations when enough of the second species is present. This has implications concerning the imaging of vortices, as well as quantum turbulence and vortex nucleation in two-component condensates, such as those involving mixtures of 87Rb^{87}\mathrm{Rb}87Rb and 133Cs^{133}\mathrm{Cs}133Cs.
Quantum vortices with more than a single circulation quantum are usually unstable and decay into clusters of smaller vortices. One way to prevent the decay is to place the vortex at the center of a convergent (draining) fluid flow, which tends to force vortices together. It is found that while the primary splitting instability is suppressed in this way (and completely quenched for strong enough flows) a secondary instability can emerge in circular trapping geometries. This behavior is related to an instability of rotating black holes when superradiantly amplified waves are confined inside a reflective cavity. The end state of the secondary instability is dramatic, manifesting as a shock wave that propagates round the circular wall and nucleates many more vortices. Published by the American Physical Society 2024
Abstract We prepared a ring-shaped Bose–Einstein condensate with quantized circulation by imprinting a linear azimuthal phase. A doubly quantized vortex (DQV) can be generated and exist stably in the middle of the condensate cloud after the system is released into a rotationally symmetric harmonic trap. For an asymmetric trap with a small degree of anisotropy the generated DQV initially splits into two singly quantized vortices and revives again but eventually evolves into two unit vortices due to the dynamic instability. For the degree of anisotropy above a critical value, the DQV is extremely unstable and decays rapidly into two singlet vortices. The geometry-dependent lifetime of the DQV and vortex-induced excitations are also discussed intensively.
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)].
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.