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 phenomena of non- reciprocal opacity, and the cavity spatial symmetry broken is the sufficient and necessary condition to achieve the nonreciprocal opacity when the relative phase of input fields is vanished. Moreover, we also include the effect of relative phase produced by 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 relative phase can promote the nonreciprocal opacity into a wider operating regime. Our findings show that although nonreciprocal opacity is analogy of optical diode effect and our system behaves like an optical isolator, it still can be operated in both forward or backward directions simultaneously.