Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials

Abstract

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a non-cubic nonlinearity, appropriate to describe the dimensionality crossover regime from one to three dimensional, we obtain branches of solutions in the form of single- and multiple-dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons' equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double well setting, which may lead to instabilities or decouple multiple dark soliton states.

35 pages, 12 figures

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• Matter-wave dark solitons in a double-well potential

Cited by in corpus (9)

• Gap solitons in elongated geometries: the one-dimensional Gross-Pitaevskii equation and beyond
• Josephson tunneling of dark solitons in a double-well potential
• Fluctuation and interaction induced instability of dark solitons in single and binary condensates
• Effective equations for matter-wave gap solitons in higher-order transversal states
• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• Dynamical Instability Induced by Zero Mode Under Symmetry Breaking External Perturbation
• PT-Symmetric potential impact on the scattering of a Bose-Einstein condensate from a Gaussian Obstacle
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Bifurcations, stability, and mode evolution in segregated condensate mixtures