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Physical Review A

Dynamics of a vortex ring encountering a spherical obstacle in Bose-Einstein condensates

Lihua Pan, Xiaojie Zhu, Qing-Li Zhu, Yongjun Liu, Jin An

Published Mar 22, 2022• 3 citations

Abstract

We investigate dynamics of a vortex ring encountering a coaxial spherical obstacle in Bose-Einstein condensates. For a perfect spherical obstacle, the vortex ring would first expand and then shrink when passing over the obstacle. For the case of a periodically modified spherical obstacle, the circular vortex ring is deformed to be gear shaped during the passing-over process. This gear-shaped vortex ring can evolve into a helical Kelvin-wave state, or split into several smaller vortex rings. In the latter situation, these split vortex rings would travel some distances forwards and then reconnect with each other, forming one new forward-moving Kelvin wave, or two Kelvin waves of different sizes, with the bigger one moving forwards and the smaller one moving backwards.

DOI: 10.1103/physreva.105.033313

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We investigate dynamics of a vortex ring encountering a coaxial spherical obstacle in Bose-Einstein condensates. For a perfect spherical obstacle, the vortex ring would first expand and then shrink when passing over the obstacle. For the case of a periodically modified spherical obstacle, the circular vortex ring is deformed to be gear shaped during the passing-over process. This gear-shaped vortex ring can evolve into a helical Kelvin-wave state, or split into several smaller vortex rings. In the latter situation, these split vortex rings would travel some distances forwards and then reconnect with each other, forming one new forward-moving Kelvin wave, or two Kelvin waves of different sizes, with the bigger one moving forwards and the smaller one moving backwards.

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.

Three coaxial quantized vortex rings in a Bose-Einstein condensate exhibit aperiodic leapfrogging dynamics. It is found that such circular vortex rings are dynamically unstable against deformation breaking axial rotational symmetry. The dynamics of the system is analyzed using the Gross-Pitaevskii and vortex-filament models. The dependence of the instability on the initial arrangement of the vortex rings is investigated. The system is found to be significantly unstable for a specific configuration of the three vortex rings.

We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: for smaller ratio, the knot travels faster. Finally, we show how vortex knots break up into vortex rings.

Abstract We experimentally investigate the periodic vortex shedding dynamics in a highly oblate Bose–Einstein condensate using a moving penetrable Gaussian obstacle. The shedding frequency f v is measured as a function of the obstacle velocity v and characterized by a linear relationship of f v = a(v − v c) with v c being the critical velocity. The proportionality constant a is linearly decreased with a decrease in the obstacle strength, whereas v c approaches the speed of sound. When the obstacle size increases, both a and v c are decreased. We discuss a possible association of a with the Strouhal number in the context of universal shedding dynamics of a superfluid. The critical vortex shedding is further investigated for an oscillating obstacle and found to be consistent with the measured f v. When the obstacle’s maximum velocity exceeds v c but its oscillation amplitude is not large enough to create a vortex dipole, we observe that vortices are generated in the low-density boundary region of the trapped condensate, which is attributed to the phonon emission from the oscillating obstacle.