Nonlinear Dynamics in Double Square Well Potential

TL;DR

This paper explores the nonlinear dynamics of Bose-Einstein condensates in double square well potentials, revealing coexistence of Josephson oscillations and self-trapping, supported by analytical and numerical evidence.

Contribution

It analytically demonstrates the simultaneous existence of multiple stationary solutions explaining macroscopic bistability in such systems.

Findings

Coexistence of Josephson oscillations and self-trapping regimes.

Analytical proof of symmetric, antisymmetric, and asymmetric solutions.

Numerical simulations confirm the theoretical predictions.

Abstract

Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.