Résumé
Coherent nonlinear dynamics in a double square well potential reveal the first example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to suggest experiments with Bose-Einstein condensates in engineered optical lattices or else with weakly coupled optical waveguide arrays.