Preparing hell state by using dissipative process in directly coupled cavities

In this study, we propose a theoretical scheme for generating and stabilizing a maximally entangled state of two atoms trapped in two directly coupled cavities. Herein, two-level atoms arc coupled to the two quantized cavity fields with large detuning and that each atom is subjected to non-resonant driving by two weak classical fields. By introducing nonlocal bosonic modes, we find that the two identical atoms arc resonantly coupled to one of the collective optical cavity modes, whereas they arc coupled to the other collective optical cavity mode with large detuning. The target steady state can be prepared using the combined effect between the unitary dynamics of the classical fields and the dissipative process of the collective optical cavity modes in the drcsscd-statc subspaccs. The steady state can be prepared without requiring any special initial state. The numerical simulation shows that the Bell state can be obtained with high fidelity and that our scheme is robust to fluctuations of the system parameters.