Anomalous phase ordering of a quenched ferromagnetic superfluid

Abstract

Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as t 1/3 . This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin waves are noninteracting, the transport occurs through a dynamic coupling to other degrees of freedom of the system. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.

Damped point-vortex model for polar-core spin vortices in a ferromagnetic spin-1 Bose-Einstein condensate

“…Fitting v Bog to v ex , we extract a small but non-zero wavevector k ≈ 2π × 0.1ξ −1 s , which shifts the speed slightly from the sound (k = 0) speed. In [69], which studied the phase ordering dynamics following a quench to the easy-plane phase, it was found that out-of-equilibrium F z and phase(F ⊥ ) excitations remain after all PCVs have annihilated, leading to anomalously slow thermalization. However the origin of the excitations was not identified.…”

“…The damping arises due to a coupling of the PCV coordinates to extrinsic modes, resulting in a loss of energy from the point-vortex phase space. We also identify the excitations produced following PCV annihilation, which likely play an important role in the anomalous phase ordering identified in [69]. A linear Zeeman field results in the ground state condensate magnetization rotating out of the transverse plane to partially align with the Zeeman field [70].…”

Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate

“…In particular advanced studies concern nonthermal fixed points 9 – 13 . The vast majority of works is devoted to two- and three-dimensional spin-1 ferromagnetic condensates 14 – 27 , but also for one-dimensional spinor 28 – 30 or binary Bose condensates 31 – 33 , including driven-dissipative systems 34 – 36 .…”