Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the nonlinear Schrodinger equation

We present a representative set of analytic stationary-state solutions of the nonlinear Schrodinger equation for a symmetric double-square-well potential for both attractive and repulsive nonlinearity. In addition to the usual symmetry-preserving even and odd states, nonlinearity introduces quite exotic symmetry-breaking solutions-among them are trains of solitons with different number and sizes of density lumps in the two wells. We use the symmetry-breaking localized solutions to form, macroscopic quantum superposition states and. explore a simple model for the exponentially small tunneling splitting.