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Journal of Applied Physics

Vortices in an annular Josephson ladder

K. H. Lee

Published Mar 26, 2015• 3 citations
Publisher

Abstract

We present numerically the static vortex configurations in an annular Josephson ladder subject to a transverse magnetic field. When the applied magnetic field is small, the supercurrents flow only along the angular direction. In that case, the phases of the inner and outer rings are coupled each other with the same winding numbers of vorticity. Such a phase-locking remains until the magnetic field reaches a certain high value over which Josephson vortices begin to appear between the two rings. The flux imbalance of the inner and outer rings leads to the different winding numbers of vorticity and the appearance of vortices in some plaquettes. The vortex configurations for a given magnetic field are found not to be unique but to exhibit other excited states of vortices with the higher energies and lower probabilities of occurrence.

DOI
10.1063/1.4916335

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We present numerically the static vortex configurations in an annular Josephson ladder subject to a transverse magnetic field. When the applied magnetic field is small, the supercurrents flow only along the angular direction. In that case, the phases of the inner and outer rings are coupled each other with the same winding numbers of vorticity. Such a phase-locking remains until the magnetic field reaches a certain high value over which Josephson vortices begin to appear between the two rings. The flux imbalance of the inner and outer rings leads to the different winding numbers of vorticity and the appearance of vortices in some plaquettes. The vortex configurations for a given magnetic field are found not to be unique but to exhibit other excited states of vortices with the higher energies and lower probabilities of occurrence.
We consider two concentric rings formed by bosonic condensates of exciton-polaritons. A circular superfluid flow of polaritons in one of the rings can be manipulated by acting upon the second annular polariton condensate. The complex coupling between the rings with different topological charges triggers nucleation of stable Josephson vortices (JVs) which are revealed as topological defects of the angular dependence of the relative phase between rings. Being dependent on the coupling strength, the structure of the JV governs the difference of the mean angular momenta of the inner and the outer rings. At the vanishing coupling the condensates rotate independently demonstrating no correlations of their winding numbers. At the moderate coupling, the interaction between two condensates tends to equalize their mean angular momenta despite the mismatch of the winding numbers demonstrating the phenomenology of a drag effect. Above the critical coupling strength the synchronous rotation is established via the phase slip events.
We theoretically investigate the properties of ultracold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The nonrotating ground-state phases are investigated across the superfluid-supersolid phase transition, revealing a particle imbalance between the two rings and a preferential density modulation in the outer ring in the absence of rotation. Near the phase transition on the superfluid side, applying rotation can induce density modulations in either ring, depending on the angular momentum and barrier strength. For low angular momentum, such rotation-induced density modulation forms in the outer ring, while for high angular momentum and weak barriers, it emerges in the inner ring. Rotation can lead to persistent currents and the nucleation of a vortex residing either at the center (central vortex) or at the ring junction (Josephson vortex). Josephson vortices can also form at the junctions of the localized density sites induced by rotation in the inner ring, a behavior that is unique to our system. By switching off the trap and allowing the system to expand, distinct interference patterns emerge, which can be analyzed to identify and distinguish between various vortex configurations, and thus can be observed in current state-of-the-art experiments.
We investigate the problem of vortex trapping in cyclically coupled Bose-Josephson junctions. Starting with NNN independent Bose-Einstein condensates we couple the condensates through Josephson links and allow the system to reach a stable circulation by adding a dissipative term in our semiclassical equations of motion. The central question we address concerns the probability of trapping a vortex with winding number mmm. Our numerical simulations reveal that the final distribution of winding numbers is narrower than the initial distribution of total phases, indicating an increased probability for no-vortex configurations. Specifically, the final width of the distribution of winding numbers for NNN sites scales as $\ensuremath{\lambda}{N}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}=0.47\ifmmode\pm\else\textpm\fi{}0.01$ and $\ensuremath{\lambda}<0.67$ (the value predicted for the initial distribution). The actual value of $\ensuremath{\lambda}$ is found to depend on the strength of dissipation. The nonlinearity of the problem also manifests itself in the result that it is possible to obtain a nonzero circulation starting with zero total phase around the loop.
The three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive BECs subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold, and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamical evolutions under large atomic interaction strengths. The former exhibits simultaneously symmetrical splitting in the transverse plane, while the latter displays periodically expand-merge cycles in the longitudinal direction.
A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.
We study theoretically the phase diagram of vortex states in 3A^{3}\mathit{A}3A in a weak magnetic field H\ensuremath{\sim}H0{H}_{0}H0​(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}H0{H}_{0}H0​, while for H\ensuremath{\gg}H0{H}_{0}H0​ the lattice of vortex pairs (Sepp\"al\"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8Tc{T}_{c}Tc​) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5H0{H}_{0}H0​ and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.