Breaking reciprocity by designed loss

Abstract

In this paper we show how designed loss in open quantum systems can break reciprocity of the state propagation, and how the non-reciprocal and even unidirectional propagation can be achieved for different kinds of designed loss, both linear and nonlinear ones. In particular, we show how a unidirectional propagation can be achieved for states of certain symmetry in linear schemes, demonstrate possibility of building a single-mode optical insulator by combining two kinds of nonlinear designed losses, and the way to build non-reciprocal circulator with a planar structure of dissipatively coupled waveguides. We discuss feasibility of the considered schemes and suggest possible realizations. I. INTRODUCTIONRecently, non-reciprocal propagation of electromagnetic field became a popular research theme. Non-reciprocity is important for quite a wide of practical tasks, from field distributors and circulators to lasing and high-precision sensing [1][2][3][4][5][6]. Current interest to realization of non-reciprocal systems, and especially isolators, is born of necessity to extent methods commonly applied for longer wavelength (radio, microwaves, etc.) toward optical region and possibility to integrate non-reciprocal systems into photonic circuitry. Traditional realizations implementing magneto-sensitive media are either hard to realize on the basis of existing integration platforms, or difficult even to realize for optical wavelength, or both [4,5]. So, a plethora of novel schemes for breaking reciprocity has appeared in recent years. There are schemes exploiting time-modulation [7,8], nonlinearities [9][10][11] and interaction with few-level systems, such as atom-like structures [4,[12][13][14], optomechanics [15], topological properties of structured media [5,16,17].Some quite interesting results were also obtained by considering loss. Recently it was shown that even common single-photon energy losses in conjunction with the usual (i.e., unitary) coupling can also be a tool for devising non-reciprocal multi-mode structures [18,19]. Even more interesting results are obtained with designed loss, i.e., for example, when different systems are coupled to the same loss reservoir inducing dissipative coupling between them, or when loss is made to be nonlinear. For instance, designed collective linear loss can lead to unidirectional propagation and amplification [20,21].Here we present another interesting feature of designed loss: it is ability to break reciprocity without conjoining with the simultaneous unitary coupling. We discuss a general recipe for doing so with the designed loss allowing for several stationary states, provide several examples and outline ways for possible practical realizations, in particular, with integrable planar waveguide systems. Notice that schemes relying only on the designed loss might be easier to realize in practice that schemes combining unitary and dissipative coupling, since one does not need adjusting different types of coupling. We show how the designed nonlinear loss can break reciprocity ev...