Engineering Ponderomotive Potential for Realizing $\pi$ and $\pi/2$ Bosonic Josephson Junctions

We study the ponderomotive potential of a bosonic Josephson junction periodically modulated by a high-frequency electromagnetic field. Within the small population difference approximation, the ponderomotive drive induces the well-known Kapitza pendulum effect, stabilizing a $\pi$-phase mode. We discuss the parameter dependence of the dynamical transition from macroscopic quantum self-trapping to $\pi$-Josephson oscillations. Furthermore, we examine the situation where the small population difference approximation fails. In this case, an essential momentum-shortening effect emerges, leading to a stabilized $\pi/2$-phase mode under certain conditions. By mapping this to a classical pendulum scenario, we highlight the uniqueness and limitations of the $\pi/2$-phase mode in bosonic Josephson junctions.