Dynamics of multiple atoms in one-dimensional fields

TL;DR

This paper investigates the complex dynamics of multiple two-level atoms coupled to a one-dimensional electromagnetic field, highlighting the limitations of common approximations and exploring entanglement evolution.

Contribution

It provides a detailed comparison between exact numerical methods and approximate models for atom-field interactions, emphasizing collective effects.

Findings

Weak-coupling approximation may be less accurate with multiple atoms.

Collective atom-atom interactions significantly influence dynamics.

Entanglement dynamics depend on inter-atomic distances and frequencies.

Abstract

We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several inter-atomic distances and atomic frequencies.