The stationary solutions of G-P equations in double square well

TL;DR

This paper derives analytical stationary solutions for the Gross-Pitaevskii equation in a double-well potential, revealing symmetry breaking phenomena and the emergence of solutions from bifurcations and isolated points.

Contribution

It provides new analytical solutions for the GPE in double-well traps and explores symmetry breaking and solution bifurcations in BECs.

Findings

Symmetry preserving solutions relate to linear Schrödinger eigenstates.

Symmetry breaking solutions can emerge from bifurcations or isolated points.

Moving nodes are observed in symmetry breaking solutions.

Abstract

We present analytical stationary solutions for the Gross-Pitaevskii equation (GPE) of a Bose-Einstein condensate (BECs) trapped in a double-well potential. These solutions are compared with those described by [Mahmud et al., PRA \textbf{66}, 063607 (2002)]. In particular, we provide further evidence that symmetry preserving stationary solutions can be reduced to the eigenstates of the corresponding linear Schr\"{o}dinger equation. Moreover, we have found that the symmetry breaking solutions can emerge not only from bifurcations, but also from isolated points in the chemical potential-nonlinear interaction diagram. We also have found that there are some moving nodes in the symmetry breaking solutions.