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 pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
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 pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
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 pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
Motivated by recent experimental and theoretical studies of few-particle vortex clusters in Bose–Einstein condensates, we consider the ordinary differential equations of motion and systematically examine settings for up to N = 6 vortices. We analyze the existence of corresponding stationary state configurations and also consider their spectral stability properties. We compare our particle model results with the predictions of the full partial differential equation system. Whenever possible, we propose generalizations of these results in the context of clusters of N vortices. Some of these we can theoretically establish, especially for the N -vortex polygons, while others we state as conjectures, e.g. for the N -vortex line equilibrium.
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 of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
While quantized vortices and vortex lattices in Bose-Einstein condensates (BECs) have received much recent attention, the formation and dynamics of vortex dipoles have been nearly unexplored in experimental BECs. Vortex dipoles consist of a pair of vortices of opposite circulation moving under the influence of each other, and may be considered as metastable topological structures that carry linear momentum in a fluid. In this talk, a collaborative experimental and numerical study of the formation, dynamics, and lifetimes of vortex dipoles in BECs will be presented. In our work [1], single vortex dipoles were deterministically nucleated by causing highly oblate, harmonically trapped BECs to move past a repulsive obstacle above a supercritical flow velocity. Our measured critical velocity for vortex dipole shedding, and the subsequent dipole dynamics, are in good agreement with new numerical simulations. We find that vortex dipoles can survive for many seconds in the BEC without selfannihilation, and that multiply charged vortex dipoles can be formed with high enough flow velocities. References: 1. T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, and B.P. Anderson, preprint available at http://arxiv.org/abs/0912.3773.