Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates

Abstract

In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional, two-component atomic Bose-Einstein condensates (BECs). The stationary states stem from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) and are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e., from the low-density linear limits to the high-density Thomas-Fermi regimes. We perform a Bogolyubov-de Gennes (BdG) spectral stability analysis to identify stable parametric regimes of these states. Upon SO(2)-rotation, the stable steady-states, one-, two-, three-, four-, and many dark-dark soliton breathing patterns are observed in the numerical simulations. Furthermore, analytic solutions up to three dark-bright solitons in the homogeneous setting, and three-component systems are also investigated.

14 pages, 12 figures

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• Domain Walls and Vector Solitons in the Coupled Nonlinear Schrodinger Equation
• Systematic solitary waves from their linear limits in two-component Bose-Einstein condensates with unequal dispersion coefficients
• Magnetic soliton molecules in binary condensates
• Roton-mediated soliton bound states in binary dipolar condensates