Current-Phase Relation of a Bose-Einstein Condensate Flowing Through a Weak Link

Abstract

We study the current-phase relation of a Bose-Einstein condensate flowing through a repulsive square barrier by solving analytically the one dimensional Gross-Pitaevskii equation. The barrier height and width fix the current-phase relation $j(\delta \varphi )$, which tends to $j\sim \cos (\delta \varphi /2)$ for weak barriers and to the Josephson sinusoidal relation $j\sim \sin (\delta \varphi )$ for strong barriers. Between these two limits, the current-phase relation depends on the barrier width. In particular, for wide enough barriers, we observe two families of multivalued current-phase relations. Diagrams belonging to the first family, already known in the literature, can have two different positive values of the current at the same phase difference. The second family, new to our knowledge, can instead allow for three different positive currents still corresponding to the same phase difference. Finally, we show that the multivalued behavior arises from the competition between hydrodynamic and nonlinear-dispersive components of the flow, the latter due to the presence of a soliton inside the barrier region.

6 pages, 5 figures

References in corpus (9)

• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• The Josephson effect throughout the BCS-BEC crossover
• Effect of a potential step or impurity on the Bose-Einstein condensate mean field
• DC Josephson Effect with Fermi gases in the Bose-Einstein regime
• Transition from phase slips to the Josephson effect in a superfluid 4He weak link
• Critical velocity of superfluid flow through single barrier and periodic potentials
• Transcritical flow of a Bose-Einstein condensate through a penetrable barrier
• The stationary solutions of G-P equations in double square well

Cited by in corpus (23)

• Driving phase slips in a superfluid atom circuit with a rotating weak link
• Experimental realization of Josephson junctions for an Atom SQUID
• Resistive flow in a weakly interacting Bose-Einstein condensate
• Interferometric measurement of the current-phase relationship of a superfluid weak link
• Strongly correlated superfluid order parameters from dc Josephson supercurrents
• Contact resistance and phase slips in mesoscopic superfluid atom transport
• Saturation of black hole lasers in Bose-Einstein condensates
• Josephson junction dynamics in a two-dimensional ultracold Bose gas
• Josephson oscillations and self-trapping of superfluid fermions in a double-well potential
• Dynamic high-resolution optical trapping of ultracold atoms
• Instability of the superfluid flow as black-hole lasing effect
• Superfluid flow past an obstacle in annular Bose--Einstein condensates
• Quantum Vortices in Curved Geometries
• Shapiro steps in strongly-interacting Fermi gases
• Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers
• Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates
• Quantum Scattering States in a Nonlinear Coherent Medium
• Stability Criterion for Superfluidity based on the Density Spectral Function
• Parity Symmetry Breaking and Topological Phases in a Superfluid Ring
• Acceleration-induced transport of quantum vortices in joined atomtronic circuits
• Increasing the stability of a superfluid in a rotating necklace potential
• Theoretical description of atomtronic Josephson junctions in an optical lattice
• Tunneling Hamiltonian analysis of DC Josephson currents in a weakly-interacting Bose-Einstein condensate