-We consider a generalization of recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that an interplay of initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more or less than the initially filled one. Moreover, presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in PT symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to PT symmetric lasers and Jahn-Teller systems are pointed out.Introduction. -Recently, an intriguing quantum optical model for resonant cavities coupled by a chiral mirror has been proposed [1]. The chiral mirror is a planar metamaterial array of asymmetric split rings, through which transmission of circularly polarized electromagnetic waves becomes different in the opposite direction without violating Lorentz reciprocity principle [2]. The transmission matrix of such a mirror is a two dimensional non-Hermitian matrix. The proposed quantum optical system is then described by a non-Hermitian Hamiltonian. As a special class of non-Hermitian systems, parity-time (PT ) symmetric systems have been attracted much attention [3][4][5]. More recently, it is shown that hybridized metamaterials can simulate effectively spontaneous symmetry breaking in PT -symmetric non-Hermitian quantum systems [6]. Nonreciprocal light transmission in PT -symmetry broken phase using whispering-gallery microcavities has been observed very recently [7].

We examine quantum dynamics of surface plasmons weakly coupled to optical soliton photons in a metal-dielectric-nonlinear Kerr medium interface. We consider a photon-number-dependent coupling model which is a heuristic extension of the classical soliton excitation of surface plasmons in the quantum limit. The coupling coefficient additionally depends on the distance between the dielectric and the metal. We propose a practical scheme to control the number of surface plasmons by a Gaussian variation of the metal-dielectric spatial separation. Our numerical simulations show that the curvature of the Gaussian distance profile can be used for controlling the number of surface plasmons.