Breaking reciprocity by designed loss

In this paper, we show how designed loss in open quantum systems can break the reciprocity of field propagation, and how non-reciprocal and even unidirectional propagation can be achieved for different kinds of designed loss, both linear and nonlinear. In particular, we show how unidirectional propagation can be achieved for input states of certain symmetry in linear schemes, and demonstrate the possibility of building a single-mode optical insulator by combining two kinds of nonlinear designed losses, and the way to build a non-reciprocal asymmetric field distributor with a planar structure of dissipatively coupled waveguides. We discuss the feasibility of the considered schemes and suggest possible realizations