Nonlinear dynamics in double square-well potentials

The first example of the coexistence of Josephson oscillations with a self-trapping regime is found in the context of the coherent nonlinear dynamics in a double square-well potential. We prove the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated Gross–Pitaevskii equation, which explains this macroscopic bistability. We illustrate and confirm the effect with numerical simulations. This property allows suggesting experiments with Bose–Einstein condensates in engineered optical lattices or with weakly coupled optical waveguide arrays.