Photon-induced self-trapping and entanglement of a bosonic Josephson junction inside an optical resonator

We study the influence of photons on the dynamics and the ground state of the atoms in a bosonic Josephson junction inside an optical resonator. The system is engineered in such a way that the atomic tunneling can be tuned by changing the number of photons in the cavity. In this setup the cavity photons are a means of control, which can be utilized both in inducing self-trapping solutions and in driving the crossover of the ground state from an atomic coherent state to a Schrodinger cat state. This is achieved, for suitable setup configurations, with interatomic interactions weaker than those required in the absence of a cavity. This is corroborated by the study of the entanglement entropy. In the presence of a laser, this quantum indicator attains its maximum value (which marks the formation of the catlike state and, at a semiclassical level, the onset of self-trapping) for attractions smaller than those of the bare junction.