Self-Adapted Josephson Oscillation of Dark-Bright Solitons under Constant Forces

TL;DR

This paper investigates the complex oscillation behaviors of dark-bright solitons in two-component Bose-Einstein condensates under constant forces, revealing self-adapted Josephson dynamics and phase diagrams.

Contribution

It introduces a novel theoretical framework describing nonlinear interaction effects on soliton oscillations, including explicit analytic expressions for Josephson parameters.

Findings

Identification of nonsinusoidal oscillations influenced by nonlinear interactions

Derivation of explicit Josephson equations with self-adapted parameters

Discovery of switching inertial mass regimes affecting soliton dynamics

Abstract

We study the propagation of dark-bright solitons in two-component Bose-Einstein condensates (BECs) with general nonlinear parameters, and explore how nonlinear interactions enrich the soliton dynamics giving rise to nonsinusoidal oscillations under constant forces. Treating the bright soliton as an effective barrier, we reveal that such oscillations are characterized by the Josephson equations with self-adapted critical current and bias voltage, whose explicit analytic expressions are derived using the Lagrangian variational method. The dynamical phase diagram in nonlinear parameter space is presented, identifying oscillation regions with different skewed sinusoidal dependence, and diffusion regions with irreversible soliton spreading due to instability of the barrier. Furthermore, we obtain periodic dispersion relations of the solitons, indicating a switch between positive and negative inertial masses, consistent with the oscillation behaviors. Our results provide a general and comprehensive theoretical framework for soliton oscillation dynamics and pave the way for investigating various nonlinear transports and their potential applications.