In a recent experiment, Kwon et. al (arXiv:1403.4658 [cond-mat.quant-gas]) generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laserinduced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.

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]

We study the dynamics of vortices in finite temperature atomic Bose-Einstein condensates, focussing on decay rates, precession frequencies and core brightness, motivated by a recent experiment (Freilich et al. Science 329, 1182(2010) in which real-time dynamics of a single vortex was observed. Using the ZNG formalism based on a dissipative Gross-Pitaevskii equation for the condensate coupled to a semi-classical Boltzmann equation for the thermal cloud, we find a rapid nonlinear increase of both the decay rate and precession frequency with increasing temperatures. The increase, which is dominated by the dynamical condensate-thermal coupling is also dependent on the intrinsic thermal cloud collisional dynamics; the precession frequency also varies with the initial radial coordinate. The integrated thermal cloud density in the vortex core is for the most part independent of the position of the vortex (except when it is near the condensate edge) with its value increasing with temperature. This could potentially be used as a variant to the method of Coddington et al. (Phys. Rev. A 70, 063607 (2004)) for experimentally determining the temperature.

We investigate a procedure to generate turbulence in a trapped Bose-Einstein condensate which takes advantage of the decay of multicharged vortices. We show that the resulting singly-charged vortices twist around each other, intertwined in the shape of helical Kelvin waves, which collide and undergo vortex reconnections, creating a disordered vortex state. By examining the velocity statistics, the energy spectrum, the correlation functions and the temporal decay, and comparing these properties with the properties of ordinary turbulence and observations in superfluid helium, we conclude that this disordered vortex state can be identified with the 'Vinen' regime of turbulence which has been discovered in the context of superfluid helium. arXiv:1704.06759v1 [cond-mat.quant-gas]

We simulate the dissipative evolution of a vortex in a trapped finite-temperature dilute-gas Bose-Einstein condensate using first-principles open-systems theory. Simulations of the complete stochastic projected GrossPitaevskii equation for a partially condensed Bose gas containing a single quantum vortex show that the transfer of condensate energy to the incoherent thermal component without population transfer provides an important channel for vortex decay. For the lower temperatures considered, this effect is significantly larger that the population transfer process underpinning the standard theory of vortex decay, and is the dominant determinant of the vortex lifetime. A comparison with the Zaremba-Nikuni-Griffin kinetic (two-fluid) theory further elucidates the role of the particle transfer interaction, and suggests the need for experimental testing of reservoir interaction theory. The dominance of this particular energetic decay mechanism for this open quantum system should be testable with current experimental setups, and its observation would have broad implications for the dynamics of atomic matter waves and experimental studies of dissipative phenomena.