# Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip

## TL;DR

This paper demonstrates that flipping the coupling from Hermitian to non-Hermitian in a discrete-continuum quantum system enables time reversal of the discrete states, even with non-unitary dynamics, under certain conditions.

## Contribution

It introduces a novel method of achieving time reversal in open quantum systems by non-Hermitian coupling manipulation, expanding the control over subsystem dynamics.

## Key findings

- Time reversal is possible with non-Hermitian coupling flips.
- Exact reversal requires frequency degeneracy or large mismatch.
- Periodic switching can freeze the subsystem dynamics.

## Abstract

Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states, or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.