Vortex reconnections in atomic condensates at finite temperature

Abstract

The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length/time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the ZarembaNikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further show reconnections to be insensitive to the inhomogeneity in the background density. In this paper we present results of an investigation of vortex reconnections in finite-temperature trapped Bose-Einstein condensates. We model the problem in the context of the Zaremba-Nikuni-Griffin (ZNG) formalism [26,27], where the Gross-Pitaevskii equation (GPE) is generalized by the inclusion of the thermal cloud mean field, and a dissipative or source term which is associated with a collision term in a semiclassical Boltzmann equation for the thermal cloud. The main feature of this model is that the condensate and thermal cloud interact with each other self-consistently; for a strongly nonlinear dynamical event like a vortex reconnection, a simpler and less accurate approach may give misleading answers.The governing ZNG equations areandIn this formalism φ = φ(r, t) is the condensate wavefunction, f = f (r, p, t) is the phase-space distribution function of thermal atoms, V ext = mω 2 r 2 /2 is the harmonic potential which confines the atoms (assumed, for simplicity, to be spherically-symmetric), ω is the trapping frequency, m the atomic mass, and g = 4πh 2 a s /m, with a s being the s-wave scattering length. Equation (1) generalises the GPE for a T = 0 condensate by the addition of the thermal cloud mean-field potential 2gñ and the dissipation/source term −iR(r, t). The condensate density is n c (r, t) = |φ(r, t)| 2 and the thermal cloud density is recovered from f (r, p, t) via an integration over all momenta,ñ(r, t) = (2πh) −3 dpf (p, r, t). The mean-field potential acting on the thermal cloud is U eff = V ext (r) + 2g[n c (r, t) +ñ(r, t)]. The quantities C 22 [f ] and C 12 [φ, f ] are collision integrals defined in arXiv:1404.4557v2 [cond-mat.quant-gas]

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Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

“…Vortex pair annihilation is one of the key issues in the study of 2D quantum turbulence [32][33][34][35][36][37][38][39][40]. Many aspects of the pair annihilation process [41,42], such as the roles of vortex-phonon interactions [43,44], and thermal dissipation [45], have never been directly addressed in experiments.…”

Local and nonlocal dynamics in superfluid turbulence

“…Moreover, the tests against experiments mentioned above 28-30 , guarantee that the numerical resolution is sufficient, and put the distinction between v loc s and v non s on solid ground. It is known from experiments 24 and from more microscopic models 23,25,26 that colliding vortex lines reconnect with each other. An algorithmic procedure is introduced to reconnect two vortex lines if they become sufficiently close to each other.…”