Vortex lattices: from the hydrodynamic to the quantum hall regime

In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image...

Using a focused laser beam we stir a Bose-Einstein condensate of 87Rb confined in a magnetic trap and observe the formation of a vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to four vortices are simultaneously present. We have also measured the lifetime of the single vortex state after turning off the stirring laser beam.

In this paper we systematically study the double layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunnelling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit one novel phase transition, which is consequence of competition between inter-layer coherent hopping and inter-layer density-density interaction. ...

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a co-rotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structural phase transitions and domain formation as this ratio is varied.

We study the formation and stability of a single vortex state in a weakly-interacting Bose-Einstein condensate that is confined in a rotating harmonic potential. Our results are consistent with the fact that any single off-center vortex is unstable. Furthermore, a vortex state located at the center of the cloud first becomes locally stable as the rotational frequency increases. Finally our study implies the existence of hysteresis effects.

In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pai...

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodolo...

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional. Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method. Fou...

We investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an $N$-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (fo...

Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODE) for dynamics of one and two individual vortices in the rotating BECs with those of the partial differential equation (PDE). In particular, we characterize orbitally stable vortex configurations in a symmetric harmonic trap due to a cubic repulsive interaction and the steady rotation. The ODE system is analyzed in details and the PDE ...