Winding up superfluid in a torus via Bose Einstein condensation

Abstract

Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point (“critical slowing down”). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains – fragments of broken symmetry – and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth – both experimentally measurable – follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition.

Vortices and vortex lattices in quantum ferrofluids

“…The experimental study of persistent superfluid flow in BECs confined to toroidal traps [43,[217][218][219][220][221][222][223][224][225][226][227] has matured significantly over the last decade. As such, ring shaped BECs in toroidal traps have been the subject of many experimental and theoretical investigations [228][229][230][231][232][233] focusing on persistent currents [217,220,234], weak links [218,221], formation of matter-wave patterns by rotating potentials [235], solitary waves [230,236], and the decay of the persistent current via phase slips [219,237,238]. In these studies the transference of angular momentum from optical fields [217,221] or stirring with an optical potential [221,222] is used to generate persistent flow.…”

Formation of helical ion chains

“…In the three dimensional case and the helix formation, the relation between the winding number distribution and quench rate can be obtained by an argument which was used to derive the KZ scaling of the winding number of Bose-Einstein-Condensate (BEC) wavefunction obtained by a nonequilibrium quench in a radially symmetric toroidal trap [53]. This argument is also used to predict the winding numbers in strongly coupled holographic superconductors described by gauge-gravity duality [54].…”

The Kibble–Zurek mechanism in a subcritical bifurcation

“…The Kibble-Zurek (KZ) mechanism was initially established for second-order phase transitions [1][2][3][4] under which many experiments tested its validity in different systems such as liquid crystals [5][6][7], 3 He [2,[8][9][10]], 4 He [11], Bose-Einstein condensates [12][13][14][15][16], Josephson tunnel junctions [17][18][19][20][21][22], superconducting films [23] and ferroelectric materials [24] among others. This framework has also been proven to be adequate to shed light on supercritical and subcritical out-of-equilibrium bifurcations performed in optical Kerr-like systems [25] and in thermo-convective systems [26][27][28][29][30][31].…”