Tunneling of persistent currents in coupled ring-shaped 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.PACS numbers:

Josephson oscillations of chirality and identity in two-dimensional solitons in spin-orbit-coupled condensates

“…Note that the Josephson oscillations do not change the chemical potential in Eq. (35), which is borrowed from the respective single-layered solutions, that contain the factor of exp (−iμt ).…”

“…This regime, which is again possible solely in the nonlinear system, cf. exact solution (35) obtained in the linear limit (which actually corresponds to the system strongly dominated by the intercore coupling), takes place if the strength of the Josephson interaction exceeds a certain threshold value, κ > κ thr . The dependence of the threshold on the total norm in one layer, N, is shown in Fig.…”

“…Among other applications, the Josephson effect in superconductors may be used for design of qubits [27,28]. Josephson oscillations of angular momentum between annular BECs was investigated too [29][30][31][32][33][34][35][36][37][38]. In these contexts, chirality of the wave functions may play an important role [29], [39][40][41][42][43][44].…”

Orbital angular momentum dynamics of Bose-Einstein condensates trapped in two stacked rings

“…Weakly coupled condensates have been proposed as basic building blocks for quantum technologies [38][39][40][41]. In particular, the dynamics of BECs in tunnel-coupled ring potentials have been thoroughly explored in a variety of geometries such as stacked rings with [42,43] or without lattices [44][45][46][47][48], concentric rings [49,50], or coplanar rings [51,52].…”

Persistent current formation in double-ring geometries

“…Gaining control over the tunnelling of persistent currents in a double-ring geometry would closer emulate the geometry of the original theoretical scheme. Recently, several proposals for two parallel/stacked rings have shown that the winding number can tunnel between rings due to the creation of fluxons at their boundary [43], and at the single-particle level persistent current tunnelling has been predicted between arrays of adjacent rings and in similar configurations [44,45,46,47]. The aim of this work is to explore the full two-dimensional (2D) formation dynamics of spontaneous supercurrents in such a side-by-side geometry, and demonstrate the resulting (perhaps somewhat counter-intuitive) independence of the two connected rings, despite their density overlap and coupled dynamics.…”