Cavity output field nonreciprocal control via interference effects

We propose a scheme to investigate the coherent control of the output field in an asymmetrical cavity with and without atom interaction. We show that the system displays the phenomenon of nonreciprocal opacity and that broken cavity spatial symmetry is the sufficient and necessary condition to achieve nonreciprocal opacity when the relative phase of the input fields vanishes. Moreover, we also include the effect of the relative phase produced by the incoming fields and show how it realizes and modifies the nonreciprocal opacity in a symmetrical cavity. As a key result, we find that either the participation of atom-cavity interaction or the relative phase can promote the nonreciprocal opacity into a wider operating regime. Our findings show that, although nonreciprocal opacity is analogous to the optical diode effect and our system behaves like an optical isolator, it can still be operated in both forward and backward directions simultaneously.