Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase slips are induced by vortex excitations created by a rotating weak link. We analyze the influence of a localized condensate density depletion and atomic superflows, governed by the rotating barrier, on the energetic and dynamical stability of the vortices in the ring-shaped condensate. We simulate in a three-dimensional dissipative mean-field model the dynamics of the condensate using parameters similar to the experimental conditions. Moreover, we consider the dynamics of the stirred condensate far beyond the experimentally explored region and reveal surprising manifestations of complex vortex dynamics.

We study formation and stabilization of vortex rings in atomic Bose-Einstein condensates. We suggest a novel approach for generating and trapping of vortex rings by 'optical tweezers'-two bluedetuned optical beams forming a toroidal void in the bulk of a magnetically or optically confined condensate cloud. We demonstrate that matter-wave vortex rings trapped within the void are energetically and dynamically stable. Our theoretical findings suggest the possibility for generation, stabilization, and nondestructive manipulation of quantized vortex rings in experimentally feasible trapping configurations. Despite the multitude of methods to generate vortex rings in inhomogeneous trapped BECs, they turn out to be unstable (see e.g. [6]), which substantially restricts their lifetime and complicates experimental observation. In practice, the vortex ring either drifts to an edge of the condensate, where it immediately decays into elementary excitations, or shrinks and annihilates within the condensate bulk. To the best of our knowledge, a stable vortex ring in a trapped condensate has not been demonstrated either theoretically or experimentally.In this paper, we propose an experimentally feasible trapping configuration that can be used to create, stabilize, and manipulate a vortex ring in a controllable and nondestructive manner. Our method for the vortexring stabilization is based on a simple physical observation: when a superfluid flow involves fewer atoms, the energy cost to nucleate a vortex ring decreases because of a smaller contribution to the kinetic energy of the superfluid. Thus, the spatial position of the vortex core in a toroidal 'anti-trap' with the locally depressed atomic density is energetically preferable. In contrast to such anti-trapping configuration, a vortex ring in a toroidal trap was found to be unstable [9]. Here we propose to use repulsive blue-detuned laser beams to create a toroidal void in the bulk of the BEC cloud held in a large-scale magnetic or optical trap, which can be used to trap and guide a vortex ring. We demonstrate both energetic and dynamical stability of the vortex rings for realistic experimental parameters.Model -Dynamical properties of an ultracold dilute atomic BEC can be accurately described by the meanfield Gross-Pitaevskii equation (GPE):i ∂Ψ(r, t) ∂t = − 2 2M ∆ +Ṽ (r) + U 0 |Ψ(r, t)| 2 Ψ (r, t),(1) where ∆ is a Laplacian operator, U 0 = 4π 2 as M is coupling strength, M is the mass of the atom, a s is the s-wave scattering length. The norm of the condensate wave function

We reveal that Hopf solitons can be stabilized in rotating atomic Bose-Einstein condensates. The Hopfion is a matter-wave vortex complex which carries two independent winding numbers. Such a topological solitonic structure results from a superfluid flow of atoms simultaneously quantized in poloidal and toroidal directions. In the framework of a dissipative mean-field model we observe different unstable evolution scenarios of the Hopfions. We demonstrate energetic and dynamical stability of the Hopf solitons under experimentally feasible conditions.

In the framework of the stochastic projected Gross-Pitaevskii equation we investigate finite-temperature dynamics of a bosonic Josephson junction (BJJ) formed by a Bose-Einstein condensate of atoms in a two-well trapping potential. We extract the characteristic properties of the BJJ from the stationary finite-temperature solutions and compare the dynamics of the system with the resistively shunted Josephson model. Analyzing the decay dynamics of the relative population imbalance we estimate the effective normal conductance of the junction induced by thermal atoms. The calculated normal conductance at various temperatures is then compared with predictions of the noise-less model and the model of ballistic transport of thermal atoms.