Josephson tunneling of dark solitons in a double-well potential

Abstract

We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.

submitted

References in corpus (16)

• Matter-wave interferometry in a double well on an atom chip
• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Stationary and non-stationary fluid flow of a Bose-Einstein condensate through a penetrable barrier
• Radio-frequency dressed state potentials for neutral atoms
• Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
• Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
• Excited states in the Thomas-Fermi limit: a variational approach
• Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
• Stability of excited states of a Bose-Einstein condensate in an anharmonic trap
• Formal analytical solutions for the Gross-Pitaevskii equation
• Beyond standard two-mode dynamics in Bosonic Josephson junctions
• Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials
• Matter-wave dark solitons in a double-well potential
• Stability of non-time-reversible phonobreathers

Cited by in corpus (4)

• Beating dark-dark solitons in Bose-Einstein condensates
• Tunneling, self-trapping and manipulation of higher modes of a BEC in a double well
• Spectral and Dynamical Properties of the Fractional Nonlinear Schrödinger Equation under Harmonic Confinement
• Dynamical control of particle jets from a driven condensate in a one-dimensional lattice with double-well potential