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arXiv:1409.6260 · Physical Review A

Vortices in a toroidal Bose-Einstein condensate with a rotating weak link

A. I. Yakimenko, Y. M. Bidasyuk, Michael Weyrauch, Yevhenii Kuriatnikov, S. I. Vilchinskiĭ

Published Mar 5, 2015• 45 citations
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Abstract

Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.

DOI
10.1103/physreva.91.033607

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We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the current-phase relation of the weak link, a feature which is difficult to implement in superconducting or superfluid helium circuits.
Motivated by a recent experiment [Beattie, Moulder, Fletcher, and Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013)], we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a two-component condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe stable superflow if the spin-population imbalance is above some well-defined threshold value. Below the stability threshold the persistent currents with higher-order circulation decay in quantized steps, and the vortex lines escape from the center of the ring through dynamically created ``weak links'' in the condensate annulus. These regions with reduced density of one spin component are filled by atoms of the other component. The vortices then leave the ring-shaped high-density region of the condensate and finally decay into elementary excitations.
We study the relation between Josephson dynamics and topological excitations in a dilute Bose-Einstein condensate confined in a double-well trap. We show that the phase slips responsible for the self-trapping regime are created by vortex rings entering and annihilating inside the weak-link region or created at the center of the barrier and expanding outside the system. Large amplitude oscillations just before the onset of self-trapping are also strictly connected with the dynamics of vortex rings at the edges of the inter-well barrier. Our results extend and analyze the dynamics of the vortex-induced phase slippages suggested a few decades ago in relation to the "ac" Josephson effect of superconducting and superfluid helium systems.
We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose–Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta.
We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.