Non-Markovian Dynamics of a Single Excitation within Many-Body Dissipative Systems

TL;DR

This paper investigates the complex non-Markovian dynamics of a single excitation in many-body dissipative systems, revealing how initial states influence system-environment interactions and demonstrating superradiance in structured reservoirs.

Contribution

It introduces a framework for analyzing non-Markovian effects in many-body systems with symmetric couplings, highlighting the impact of initial states and steady-state independence from the reservoir.

Findings

Initial atomic states significantly affect dynamics.

System can become decoupled from the environment.

Superradiant behavior predicted in structured reservoirs.

Abstract

We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir under specific system symmetries. In the regime of multiple atoms coupled to a single reservoir with identical couplings, we identify remarkable effects, notably that the initial configuration of the atomic excited state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady state amplitudes of the excited states become independent of the choice of the reservoir. The framework introduced is applied to a structured photonic reservoir associated with a photonic crystal, where we show it reproduces previous theoretical and experimental results and it predicts superradiant behaviour within the single-excitation regime.