Nonlinear phase-dynamics in a driven Bosonic Josephson junction

We study the collective dynamics of a driven two mode Bose-Hubbard model in the Josephson interaction regime. The classical phase-space is mixed, with chaotic and regular components, that determine the dynamical nature of the fringe-visibility. For weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative-phase $\varphi$ between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the inter-site potential barrier stabilizes the $\varphi=\pi$ 'inverted pendulum' coherent state, and protects the fringe visibility.