Quantum coherence and speed limit in the mean-field Dicke model of superradiance

TL;DR

This paper investigates quantum coherence in the mean-field Dicke model of superradiance, showing that coherence correlates with radiation intensity and influences the system's evolution speed, providing insights for quantum optics and condensed matter physics.

Contribution

It introduces a method to quantify single-atom quantum coherence via radiation intensity and explores its effect on the quantum speed limit in superradiant systems.

Findings

Single-atom $l_1$-norm of coherence equals the square root of normalized radiation intensity.

Quantum coherence accelerates the evolution of superradiant systems.

Probing coherence through radiation intensity can be useful in experiments.

Abstract

Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom $l_1$-norm of coherence is given by the square root of the normalized average intensity of radiation emitted by the superradiant system. This validates quantum coherence as a useful figure of merit towards the understanding of superradiance phenomenon in the mean-field approach. In particular, this result suggests probing the single-atom coherence through the radiation intensity in superradiant systems, which might be useful in experimental realizations where is unfeasible to address atoms individually. Furthermore, given the nonlinear unitary dynamics of the time-dependent single-atom state that effectively describes the system of $N$ atoms, we analyze the quantum speed limit time and its interplay with the $l_1$-norm of coherence. We verify the quantum coherence speeds up the evolution of the superradiant system, i.e., the more coherence stored on the single-atom state, the faster the evolution. These findings unveil the role played by quantum coherence in superradiant systems, which in turn could be of interest for communities of both condensed matter physics and quantum optics.