We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.

Interference of atomic de Broglie waves tunneling from a vertical array of macroscopically populated traps has been observed. The traps were located in the antinodes of an optical standing wave and were loaded from a Bose-Einstein condensate. Tunneling was induced by acceleration due to gravity, and interference was observed as a train of falling pulses of atoms. In the limit of weak atomic interactions, the pulse frequency is determined by the gravitational potential energy difference between adjacent potential wells. The effect is closely related to the ac Josephson effect observed in superconducting electronic systems.

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.

Phase transitions are ubiquitous in nature, ranging from protein folding and denaturisation, to the superconductor-insulator quantum phase transition, to the decoupling of forces in the early universe. Remarkably, phase transitions can be arranged into universality classes, where systems having unrelated microscopic physics exhibit identical scaling behaviour near the critical point. Here we present an experimental and theoretical study of the Bose-Einstein condensation phase transition of an atomic gas, focusing on one prominent universal element of phase transition dynamics: the spontaneous formation of topological defects during a quench through the transition [1, 2, 3]. While the microscopic dynamics of defect formation in phase transitions are generally difficult to investigate, particularly for superfluid phase transitions [4, 5, 6, 7], Bose-Einstein condensates (BECs) offer unique experimental and theoretical opportunities for probing such details. Although spontaneously formed vortices in the condensation transition have been previously predicted to occur [8, 9], our results encompass the first experimental observations and statistical characterisation of spontaneous vortex formation in the condensation transition. Using microscopic theories [10, 11, 12, 13, 14, 15, 16, 17] that incorporate atomic interactions and quantum and thermal fluctuations of a finite-temperature Bose gas, we simulate condensation and observe vortex formation in close quantitative agreement with our experimental results. Our studies provide further understanding of the development of coherence in superfluids, and may allow for direct investigation of universal phase-transition dynamics.

We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our highly oblate trap geometry. For sufficiently rapid flow velocities we find that clusters of like-charge vortices aggregate into long-lived dipolar flow structures.

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas BoseEinstein condensates. Our condensates are produced in a superposition of two internal states of 87 Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of two. PACS number(s): 03.75. Fi, 67.90.+z, 67.57.Fg, 32.80.Pj The dynamics of quantized vortices in superfluid helium and superconductors have been fascinating and important research areas in low-temperature physics [1]. Continued study of vortex dynamics may, for example, lead to a better understanding of energy dissipation in these systems [2]. Work on optical vortices has also become an active area of research [3]. More recently, demonstrations of the creation of quantized vortices in dilute-gas Bose-Einstein condensates (BEC) [4,5] have proven to be striking examples of the similarities between the condensed matter, optical, and dilute-gas quantum systems. Because of the observational capabilities of dilute-gas BEC experiments and the ability to manipulate the quantum wavefunction of the condensates, these systems provide a unique approach to the study of quantized vortices and their dynamics. This paper reports direct observations and measurements of singly quantized vortex core precession in a BEC.Numerous theoretical papers have explored the expected stability and behavior of vortices in BEC [6][7][8][9][10][11][12][13]. One interesting predicted effect is vortex core precession about the condensate axis [6,[8][9][10][11][12]. Radial motion of the core within the condensate can also occur, and may be understood as being due to energy dissipation and damping processes.Core precession may be described in terms of a Magnus effect -a familiar concept in fluid dynamics and superfluidity [1]. An applied force on a rotating cylinder in a fluid leads to cylinder drift (due to pressure imbalances at the cylinder surface) that is orthogonal to the force. Analogously, a net force on a vortex core in a superfluid results in core motion perpendicular to both the vortex quantization axis and the force. In the condensate vortex case, these forces can be due to density gradients within the condensate, for example, or the drag due to thermal atoms. The density-gradient force may be thought of as one component of an effective buoyancy: just as a bubble in a fluid feels a force anti-parallel to the local pressure gradient, a vortex core in a condensate will feel a force towards lower condensate densities. The total effective buoyancy, however, is due less to displaced mass (the "bubble") than it is to dynamical effects of the velocity-field asymmetry, which in turn is a consequence...

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length . We show that, for the divergencefree portion of the superfluid velocity field, the kinetic-energy spectrum over wave number k may be decomposed into an ultraviolet regime (k ) À1 ) having a universal k À3 scaling arising from the vortex core structure, and an infrared regime (k ( À1 ) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent À1=3 for vortices of the same sign of circulation leads to an infrared kinetic-energy spectrum with a Kolmogorov k À5=3 power law, which is consistent with the existence of an inertial range. The presence of these k À3 and k À5=3 power laws, together with the constraint of continuity at the smallest configurational scale k % À1 , allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous, compressible, two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic-energy distribution, once we introduce the concept of a clustered fraction consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical twodimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.

We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.