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arXiv:2204.14269 · Physical Review A

Generation of Josephson vortices in stacked toroidal Bose-Einstein condensates

Nataliia Bazhan, Anton Svetlichnyi, Dominik Pfeiffer, Daniel Derr, G. Birkl, A. I. Yakimenko

Published Oct 10, 2022• 17 citations
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Abstract

Coupled coaxially stacked toroidal condensates with persistent currents suggest an appealing physical platform for investigation of various phenomena related to interacting superflows from Josephson effects in the regime of weak interactions to the quantum Kelvin-Helmholtz instability for merging rings. We suggest experimentally accessible methods to prepare states with different topological charges in two coupled coaxial ring-shaped atomic Bose-Einstein condensates. Our results open up the way to direct observation of rotational Josephson vortices in atomic Bose-Einstein condensates.

DOI
10.1103/physreva.106.043305

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•Apr 17, 2019•6 citations
Coupled coaxially stacked toroidal condensates with persistent currents suggest an appealing physical platform for investigation of various phenomena related to interacting superflows from Josephson effects in the regime of weak interactions to the quantum Kelvin-Helmholtz instability for merging rings. We suggest experimentally accessible methods to prepare states with different topological charges in two coupled coaxial ring-shaped atomic Bose-Einstein condensates. Our results open up the way to direct observation of rotational Josephson vortices in atomic Bose-Einstein condensates.
Abstract Considerable progress in experimental studies of atomic gases in a toroidal geometry opens up novel prospects for the investigation of fundamental properties of superfluid states and creation of new configurations for atomtronic circuits. In particular, a setting with Bose–Einstein condensates loaded in a dual-ring trap suggests a possibility to consider the dynamics of tunneling between condensates with different angular momenta. Accordingly, we address the tunneling in a pair of coaxial three-dimensional (3D) ring-shaped condensates separated by a horizontal potential barrier. A truncated (finite-mode) Galerkin model and direct simulations of the underlying 3D Gross–Pitaevskii equation are used for the analysis of tunneling superflows driven by an initial imbalance in atomic populations of the rings. The superflows through the corresponding Bose–Josephson junction are strongly affected by persistent currents in the parallel rings. Josephson oscillations of the population imbalance and angular momenta in the rings are obtained for co-rotating states and non-rotating ones. On the other hand, the azimuthal structure of the tunneling flow demonstrates formation of Josephson vortices (fluxons) with zero net current through the junction for hybrid states , built of counter-rotating persistent currents in the coupled rings.
Precise control of topologically protected excitations, such as quantum vortices in atomtronic circuits, opens new possibilities for future quantum technologies. We theoretically investigate the dynamics of Josephson vortices (rotational fluxons) induced by coupled persistent currents in a system of coplanar double-ring atomic Bose-Einstein condensates. We study the Josephson effect in an atomic Josephson junction formed by coaxial ring-shaped condensates. Tunneling superflows, initiated by an imbalance in atomic populations between the rings, are significantly influenced by the persistent currents in the inner and outer rings. This results in pronounced Josephson oscillations in the population imbalance for both corotating and nonrotating states. If a linear acceleration is applied to the system, our analysis reveals peculiar azimuthal tunneling patterns and dynamics of Josephson vortices which leads to nonzero net tunneling current and shows sensitivity to the acceleration magnitude. When multiple Josephson vortices are present, asymmetric vortex displacements that correlate with both the magnitude and direction of acceleration can be measured, offering the potential for quantum sensing applications.
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.
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.
Persistent current, or "flow without friction", as well as quantum vortices are the hallmarks of superfluidity. Recently a very long-lived persistent flow of atoms has been experimentally observed in Bose-Einstein condensates trapped in a ring-shaped potential. This enables fundamental studies of superfluidity and may lead to applications in high-precision metrology and atomtronics. We overview our recent theoretical studies of the generation of the persistent current in a stirred toroidal atomic Bose-Einstein condensate, and discuss our new investigation of the hysteresis in the atomtronic circuit.
The stacks of Bose-Einstein condensates coupled by long Josephson junctions present a richphenomenology feasible to experimental realization and specially suitable for technologicalapplications as the nonlinear-optics and superconducting analogs have already proved. Among this,we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates cancarry tunneling superflows whose dynamical stability depends on the quasimomentum. Across thestacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yieldtransverse Josephson vortices with a generic non-integer circulation in units ofh/m. Additionally, thesuperpositions of degenerate linear Bloch waves can suppress the supercurrents and give rise tofamilies of nonlinear standing-wave states with strong(transverse)spatial localization. Stable states ofthis type can also be found infinite size systems.