Nonlinear dynamics of Josephson vortices in merging superfluid rings

Abstract

We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between the superflows. When the barrier is gradually eliminated, we observe essentially three-dimensional evolution of quantum vortices, which may include the development of the Kelvin-Helmholtz instability at the interface between the rings, in the framework of a weakly dissipative Gross-Pitaevskii equation. An initially more populated ring, carrying a persistent current, can drag an initially non-rotating less populated one into the same vortex state. The final state of the condensate crucially depends on an initial population imbalance in the double-ring set, as well as on the shape of the 3D trapping potential, oblate or prolate. In the prolate (axially elongated) configuration, robust 3D hybrid structures may appear as a result of the merger of persistent currents corresponding to different vorticities.

Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates

“…A more populated component with m 1 = 2 imposes its angular momentum onto the final state, provided that the initial imbalance takes values above some critical value P cr . However, the values of P cr found in [30] for the (2, 0) set are different from those ±P cr for the set of the merging rings with (m 1 , m 2 ) = (+1, −1), given by Equation (19). These differences are not surprising, as the set of (+1, −1) features an obvious symmetry with respect to the two components.…”

“…Note that the merging rings with vorticities (2, 0), which we investigated in Ref. [30], also evolve into the final state with the total angular momentum m = 0 or m = 2, while the single-charged state, with m = 1, was not realized even when the angular momentum per particle of the initial state was L p = 1. A more populated component with m 1 = 2 imposes its angular momentum onto the final state, provided that the initial imbalance takes values above some critical value P cr .…”

“…We concentrate here on simulations of dynamics of the merging rings with single-charged counter-propagating persistent currents, (m 1 , m 2 ) = (+1, −1), in a pancake-shaped toroidal trap. Note that a similar double-ring system, but loaded in a trap elongated in the z-direction, was investigated in [30]. As pointed out in that work, vortex dynamics and the relaxation process are strongly affected by the value of aspect ratio A, see Equation (9).…”

“…Figure 1 shows three different states produced by the ITP method for m 1 = 1, 2, 3 and P = 0 with high accuracy. Different directions of the flow in the top and bottom rings inevitably lead to the appearance of Josephson vortices (fluxons), with the number of fluxon cores N J = |m 1 − m 2 |, as pointed out in our previous work [30]. To produce additional description of the vortices, we need to consider the flow in both parts of the condensate.…”

“…In the case of non-zero particle-number (population) imbalance between the rings, the Josephson vortices rotate and bend. Splitting of Josephson vortices in the course of barrier reducing in the system with weak dissipation makes it possible to reach states with different final values of the total angular momenta of the merging rings, depending on the initial population imbalance between them [30].…”