Abstract
Quenching an ultracold bosonic gas in a ring across the Bose–Einstein condensation phase transition is known, and has been experimentally observed, to lead to the spontaneous emergence of persistent currents. The present work examines how these phenomena generalize to a system of two experimentally accessible explicitly two-dimensional co-planar rings with a common interface, or to the related lemniscate geometry, and demonstrates an emerging independence of winding numbers across the rings, which can exhibit flow both in the same and in opposite directions. The observed persistence of such findings in the presence of dissipative coupled evolution due to the local character of the domain formation across the phase transition and topological protection of the randomly emerging winding numbers should be within current experimental reach.
Highlights
At the critical point of a second order phase transition, the symmetry of a system is spontaneously broken, with both relaxation time and correlation length diverging [1]
Consideration of the role of the quench timescale in finite-duration and linear quenches led to the universal Kibble–Zurek mechanism, which has been observed in a variety of complex systems [3], including liquid crystals [4], liquid helium [5, 6], superconducting loops [7,8,9,10], ion chains [11], Bose–Einstein condensates (BECs) [12,13,14,15,16,17,18,19,20,21], and, recently, in Rydberg lattices [22]
We explore the formation and structure of spontaneously generated supercurrents induced by an instantaneous crossing of the phase transition to the BEC state in a co-planar, side-by-side, double-ring geometry
Summary
At the critical point of a second order phase transition, the symmetry of a system is spontaneously broken, with both relaxation time and correlation length diverging [1]. The numerical work of reference [23] provided a detailed visualization of, and highlighted, the role of local phase formation and subsequent evolution to a stable persistent current in the context of a one-dimensional model Such Kibble–Zurek scaling only applies to finite duration quenches, the underlying phenomenon of spontaneous symmetry breaking and generation of defects are at the heart of any crossing through a second-order phase transition, including the numerically simpler instantaneous quenches, which provide crucial information for the formation dynamics of coherence in macroscopic systems and on the critical universal properties of the system. Identifying regimes which are optimal for experimental observation paves the way for the use of such geometries for the design of potential qubit operations
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