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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Vortex pairl creation and annihilation in a Bose-Einstein condensate

Woo Jin Kwon, Geol Moon, Yong-il Shin

Published Aug 1, 2015• 0 citations
Publisher

Abstract

We describe our recent experiments where we studied creation and annihilation of vortex pairs in a highly oblate Bose-Einstein condensate. We measured the critical velocity for vortex shedding and investigated the thermal relaxation of two-dimensional superfluid turbulence.
DOI
10.1109/cleopr.2015.7376016

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We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices, and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential decay of the vortex number is quantitatively well described by a rate equation consisting of one-body and two-body decay terms. In our measurement, we find that the local two-body decay rate is closely proportional to ${T}^{2}/\ensuremath{\mu}$, where TTT is the temperature and $\ensuremath{\mu}$ is the chemical potential.
In a recent experiment, Kwon et al. [Phys. Rev. A 90, 063627 (2014)] generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laser-induced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.
While quantized vortices and vortex lattices in Bose-Einstein condensates (BECs) have received much recent attention, the formation and dynamics of vortex dipoles have been nearly unexplored in experimental BECs. Vortex dipoles consist of a pair of vortices of opposite circulation moving under the influence of each other, and may be considered as metastable topological structures that carry linear momentum in a fluid. In this talk, a collaborative experimental and numerical study of the formation, dynamics, and lifetimes of vortex dipoles in BECs will be presented. In our work [1], single vortex dipoles were deterministically nucleated by causing highly oblate, harmonically trapped BECs to move past a repulsive obstacle above a supercritical flow velocity. Our measured critical velocity for vortex dipole shedding, and the subsequent dipole dynamics, are in good agreement with new numerical simulations. We find that vortex dipoles can survive for many seconds in the BEC without selfannihilation, and that multiply charged vortex dipoles can be formed with high enough flow velocities. References: 1. T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, and B.P. Anderson, preprint available at http://arxiv.org/abs/0912.3773.
In recent experiments, the relaxation dynamics of highly oblate, turbulent Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay rates in various sample conditions [Phys. Rev. A 90, 063627 (2014)] and, separately, the thermal friction coefficient $\ensuremath{\alpha}$ for vortex motion was measured from the long-time evolution of a corotating vortex pair in a BEC [Phys. Rev. A 92, 051601(R) (2015)]. We present a comparative analysis of the experimental results, and find that the vortex decay rate $\mathrm{\ensuremath{\Gamma}}$ is almost linearly proportional to $\ensuremath{\alpha}$. We perform numerical simulations of the time evolution of a turbulent BEC using a point-vortex model equipped with longitudinal friction and vortex-antivortex pair annihilation, and observe that the linear dependence of $\mathrm{\ensuremath{\Gamma}}$ on $\ensuremath{\alpha}$ is quantitatively accounted for in the dissipative point-vortex model. The numerical simulations reveal that thermal friction in the experiment was too strong to allow for the emergence of a vortex-clustered state out of decaying turbulence.
Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, besides the vortex drift-out process from the boundary, vortex-antivortex pair can annihilate in the bulk, but controversy remains on the number of vortices involved in the annihilation process. We find there exists a dynamical transition from four-body to three-body vortex annihilation processes with the time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical transition depends on the initial vortex pair density, and occurs when the sound waves generated in the vortex annihilation process surpass a critical energy. With the confinement along the third direction is relaxed in a quasi-2D BEC, the critical sound wave energy decreases due to the 3D vortex line curve and reconnection, shifting the dynamical transition to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.