We present a representative set of analytic stationary-state solutions of the nonlinear Schrödinger 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.

• Received 26 June 2002

DOI:https://doi.org/10.1103/PhysRevA.66.063607