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.