Chaos to Synchronization and Dissipative Quantum Scarring in Open Coupled top-Dicke model in a Lossy Cavity

We present a variant of the Dicke model, termed as the open coupled-top Dicke model, which enables the exploration of rich non-equilibrium phenomena, particularly the fate of quantum scars in an open environment. This model can effectively be realized by coupling a two-species Bose-Josephson junction to a lossy cavity. Photon loss induces spontaneous synchronization via projection onto a dissipation-free subspace, along with transient chaos followed by restoration of synchronization and coherence. We identify two distinct scarring phenomena in the presence of dissipation. One remains protected, exhibiting persistent revivals, while the scar associated with the superradiant phase displays a dissipation-induced slow decay of the survival probability. Remarkably, for sufficiently small spin magnitude, the chaos-assisted macroscopic quantum tunneling is linked to the latter type of scarring. The results can be readily tested in ongoing cavity QED experiments and have broader applicability in other platforms.