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arXiv:cond-mat/0212528 · Physical Review A

Instabilities of off-centered vortices in a Bose-Einstein condensate

Tomoya Isoshima, Jukka Huhtamäki, Martti M. Salomaa

Published Sep 25, 2003• 8 citations
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Abstract

We study numerically the excitations of off-centered vortices in a Bose-Einstein condensate. The displacement of a single vortex and the separation of a doubly quantized vortex are considered. We find that the core-localized excitations of the precessing vortices continue to feature the property which implies that the vortices are unstable. The core-localized, dipolar, and quadrupolar excitations are found to deform continuously as functions of vortex displacements and intervortex separation.

DOI
10.1103/physreva.68.033611

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Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
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 derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.
The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23Na{}^{23}\mathrm{Na}23Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards division into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al., Phys. Rev. Lett. 89, 190403 (2002)].
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.