# Metastable decoherence-free subspaces and electromagnetically induced transparency in interacting many-body systems

## TL;DR

This paper explores complex dynamics in interacting many-body systems under electromagnetically induced transparency, revealing a metastable decoherence-free subspace that enables slow relaxation, entangled state preparation, and effective non-equilibrium dynamics.

## Contribution

It introduces the concept of a metastable decoherence-free subspace in interacting Rydberg atom systems and derives the effective dynamics within this subspace.

## Key findings

- Identification of a metastable decoherence-free subspace with linearly growing dimension
- Derivation of effective non-equilibrium dynamics with coherent and dissipative interactions
- Potential for preparing entangled dark states and implementing unitary operations

## Abstract

We investigate the dynamics of a generic interacting many-body system under conditions of electromagnetically induced transparency (EIT). This problem is of current relevance due to its connection to non-linear optical media realized by Rydberg atoms. In an interacting system the structure of the dynamics and the approach to the stationary state becomes far more complex than in the case of conventional EIT. In particular, we discuss the emergence of a metastable decoherence free subspace, whose dimension for a single Rydberg excitation grows linearly in the number of atoms. On approach to stationarity this leads to a slow dynamics which renders the typical assumption of fast relaxation invalid. We derive analytically the effective non-equilibrium dynamics in the decoherence free subspace which features coherent and dissipative two-body interactions. We discuss the use of this scenario for the preparation of collective entangled dark states and the realization of general unitary dynamics within the spin-wave subspace.