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On Macroscopic Quantum Coherence with Synchronized Atoms and Molecules: Superradiance

Gombojav O. Ariunbold

Published Sep 17, 2022• 1 citation
Publisher

Abstract

The collective behavior of quantum particles is one of the most intriguing phenomena in quantum optics. In particular, superradiance refers to spontaneous collective emissions from a group of quantum particles behaving collectively as a whole due to the buildup of macroscopic quantum coherence. An important question is whether macroscopic quantum coherence is constructed by means of a quantum synchronization (i.e., a quantum analog of classical synchronization) or not. The purpose of this article is to draw attention to this question from the author’s perspective. A few selected studies relevant to synchronized atoms and molecules are discussed. The author concludes that collective behaviors of quantum particles may be formulated as quantum synchronizations, but extensive studies are still needed to confirm this hypothesis.

DOI
10.3390/pr10091885

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The collective behavior of quantum particles is one of the most intriguing phenomena in quantum optics. In particular, superradiance refers to spontaneous collective emissions from a group of quantum particles behaving collectively as a whole due to the buildup of macroscopic quantum coherence. An important question is whether macroscopic quantum coherence is constructed by means of a quantum synchronization (i.e., a quantum analog of classical synchronization) or not. The purpose of this article is to draw attention to this question from the author’s perspective. A few selected studies relevant to synchronized atoms and molecules are discussed. The author concludes that collective behaviors of quantum particles may be formulated as quantum synchronizations, but extensive studies are still needed to confirm this hypothesis.
Synchronization phenomena in multiple polarizations through quantum effects of photon fields have been observed as superradiance. These phenomena are often observed in macroscopic and classical systems. In contrast, superradiance is cooperative spontaneous emission, that is, a synchronization phenomenon in microscopic and quantum systems. In this study, we consider two emitters in a free photon field and investigate their exact phase dynamics. By analogy with the Kuramoto model, we illustrate clearly that the interaction of synchronization in superradiance originates from spontaneous emission owing to the quantum effects of photon fields. In contrast to superradiance in-phase, subradiance in antiphase is also possible. We illustrate the parameter diagram that determines whether in-phase or antiphase oscillation occurs. In addition, we find that a temporal transition occurs from the in-phase to antiphase synchronization owing to the energy dissipation. The results of this study will stimulate further research on synchronization phenomena in microscopic and quantum systems.
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.
The basic features of coherent spontaneous emission, including its dependence on the square of the number of participating emitters, are reviewed. Analogies with magnetic resonance phenomena are exploited, and we explain the need to go beyond such analogies in order to treat optical emission. Some recent results in the theory of optical superradiance are discussed. The radiative decay process is treated as a quantum-classical interpolation problem, and explicit solutions are given. In addition to its time dependence, we give the angular distribution of radiated power and the expected intensity fluctuations, and we estimate the maximum number of emitters which can cooperate in a superradiant event. Dicke's “coherence brightening” criterion is discussed from the point of view of the present paper. A “failure” of the criterion is exhibited and explained. Two of the purely quantum aspects of superradiance are isolated and discussed briefly.
Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.
This article reviews the present status of superradiance in atoms and molecules. The introductory section describes the important physical properties of superradiant emission, and presents the important experimental features. A simple theoretical formulation, based on the coupled Maxwell-Schrödinger equations, is described. Simple expressions for observable output parameters are given, valid in experimentally relevant regimes. These results are compared with superradiance experiments performed at a wide range of wavelengths in numerous laboratories since 1973. While the principal features of superradiance are generally agreed upon, details of the initiation of the radiation process and of the observed ringing are still under study.