Two-Component Nonlinear Schrodinger Models with a Double-Well Potential

TL;DR

This paper models two-component nonlinear Schrödinger equations with a double-well potential, analyzing symmetry-breaking bifurcations in Bose-Einstein condensates, and confirms analytical predictions with numerical simulations.

Contribution

It introduces a two-component nonlinear Schrödinger model with a double-well potential, analyzing bifurcations and stationary states, extending previous single-component studies.

Findings

Numerous symmetry-breaking bifurcations depend on chemical potentials.

Analytical predictions via a two-mode approximation are confirmed numerically.

Unstable branches lead to specific outcomes in direct simulations.

Abstract

We introduce a model motivated by studies of Bose-Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap.The analysis is focused on symmetry-breaking bifurcations in the system, starting at the linear limit and gradually increasing the nonlinearity. Depending on values of the chemical potentials of the two species, we find numerous states, as well as symmetry-breaking bifurcations, in addition to those known in the single-component setting. These branches, which include all relevant stationary solutions of the problem, are predicted analytically by means of a two-mode approximation, and confirmed numerically. For unstable branches, outcomes of the instability development are explored in direct simulations.