Non-Hermitian interaction of a discrete state with a continuum

Abstract

The interaction of a discrete state coupled to a continuum is a longstanding problem of major interest in different areas of quantum and classical physics. In Hermitian models, several dynamical decoupling schemes have been suggested, in which the discretecontinuum interaction can be substantially reduced and even suppressed. In this work we consider a discrete state interacting with a continuum via a time-dependent nonHermitian coupling with finite (albeit arbitrarily long) duration, and show rather generally that for a wide class of coupling temporal shapes, in which the real and imaginary parts of the coupling are related each other by a Hilbert transform, the discrete state returns to its initial condition after the interaction with the continuum, while the continuum keeps trace of the interaction. Such a behavior, which does not have any counterpart in Hermitian dynamics, can be referred to as non-Hermitian pseudo decoupling. Non-Hermitian pseudo decoupling is illustrated by considering a non-Hermitian extension of the Fano-Anderson model in a one-dimensional tight-binding lattice. Scuh a non-Hermitian model can describe, for example, photonic hopping dynamics in a tightbinding chain of optical microrings or resonators, in which non-Hermitian coupling can be realized by fast modulation of the real and imaginary (gain/loss) parts of the refractive index of the edge microring.