Advances in the experimental atomic optics allow confining Bose-Einstein condensate inside of two long parallel atomic waveguides. Proximity of the waveguides to each other allows tunneling of atoms between them, which is schematically depicted on the figure. Due to the tunneling and extended spatial dimension along the waveguides this system forms long Bose-Josephson junction. It can sustain stable persistent circulating supercurrent, which by analogy with the superconducting case we call atomic or Bose-Josephson vortex. Bose-Josephson vortex is a topological soliton solution degenerate with respect to two possible directions of circulation. It is possible to find an exact analytic solution describing Bose-Josephson vortex stationary atomic Josephson vortex [1]. Josephson vortex exists only below certain critical tunneling strength (Josephson coupling), where the dark soliton is absolutely unstable. By tuning the Josephson coupling above or below its critical value the Josephson vortex can be reversibly interconverted with dark soliton. Transitions between dark soliton and Josephson vortex are spontaneous and correspond to breaking (vortex) and restoration (dark soliton) of the time reversal symmetry. The Josephson vortex can be controllably displaced along the junction by imposing tunneling current created by misbalance of chemical potentials between the waveguides [2]. In quasi-one-dimension, motion of an atomic Josephson vortex is strongly coupled to the current circulation through the phase-slip effect. This leads to a destruction of the circulation for the vortex speeds above a certain value determined by the Josephson coupling. In contrast to the standard approach to Josephson vortices in superconductors within the Sine-Gordon formalism, a description of the coupling between the center-of-mass motion and the circulation necessarily involves both density and phase variations. The Josephson vortex can be created with the phase imprinting technique directly or indirectly by, first, creating the dark soliton and then by adiabatic decrease of the Josephson coupling transforming the dark soliton to the Josephson vortex. The Josephson vortex can be detected by absorption imaging due a specific feature it produces in the column density of released from the waveguides atomic clouds. Josephson vortex can be used a mobile qubit [2] and also for controlled and coherent transfer of BEC atoms between two separated reservoirs [1].

References

1. Atomic Josephson vortices , V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 73, 013627 (2006)
2. Josephson vortex between two atomic Bose-Einstein condensates , V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 71, 011601 (2005)