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arXiv:1408.6073 · Laser Physics

Coherent dynamics of radiating atomic systems in pseudospin representation

Vyacheslav I. Yukalov

Published Aug 15, 2014• 12 citations
arXivHTMLPDF

Abstract

The aim of this review is twofold. Firstly, a general approach is presented which can provide a unified description of the dynamics of radiating systems of different natures. Both atomic systems and spin assemblies can be treated within the same mathematical method, which is based on a pseudospin (or spin) representation of the evolution equations. The approach is applicable to all stages of radiation dynamics, including the most difficult initial quantum stage, where coherence is not yet developed. This makes it possible to study the process of coherent self-organization from the chaotic quantum stage. Secondly, the approach is illustrated by applying it to the description of several coherent phenomena. Different types of superradiance are characterized: pure superradiance, triggered superradiance, pulsing and punctuated superradiance. The theory of such interesting effects as triggering dipolar waves, turbulent photon filamentation, collective liberation of light, pseudospin atomic squeezing, and operator entanglement production is presented.

DOI
10.1088/1054-660x/24/9/094015

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The aim of this review is twofold. Firstly, a general approach is presented which can provide a unified description of the dynamics of radiating systems of different natures. Both atomic systems and spin assemblies can be treated within the same mathematical method, which is based on a pseudospin (or spin) representation of the evolution equations. The approach is applicable to all stages of radiation dynamics, including the most difficult initial quantum stage, where coherence is not yet developed. This makes it possible to study the process of coherent self-organization from the chaotic quantum stage. Secondly, the approach is illustrated by applying it to the description of several coherent phenomena. Different types of superradiance are characterized: pure superradiance, triggered superradiance, pulsing and punctuated superradiance. The theory of such interesting effects as triggering dipolar waves, turbulent photon filamentation, collective liberation of light, pseudospin atomic squeezing, and operator entanglement production is presented.
The main part of this review is devoted to the comprehensive description of coherent radiation by nuclear spins. The theory of nuclear spin superradiance is developed and the experimental observations of this phenomenon are considered. The intriguing problem of how coherence develops from initially incoherent quantum fluctuations is analysed. All main types of coherent radiation by nuclear spins are discussed, which are: free nuclear induction, collective induction, maser generation, pure superradiance, triggered superradiance, pulsing superradiance, punctuated superradiance, and induced emission. The influence of electron-nuclear hyperfine interactions and the role of magnetic anisotropy are studied. Conditions for realizing spin superradiance by magnetic molecules are investigated. The possibility of nuclear matter lasing, accompanied by pion or dibaryon radiation, is briefly touched.
In this paper we attempt to unify the theoretical treatment of a variety of cooperative interaction phenomena occurring in resonantly interacting radiation-matter systems. The system consists of a multimode optical field interacting with NNN resonant atoms in a region of large spatial extent. The field and atoms may or may not be coupled to reservoirs. We derive a set of coupled master equations for the reduced matter and radiation density operators of the composite system in the first Born approximation, using a method due to Bogoliubov. These equations describe within a single framework phenomena involving superradiant emission and coherent propagation. In the first place, our theory generalizes existing formulations of the superradiance problem by treating the radiation field as part of the dynamical system rather than as a reservoir. Hence, our equations describe stimulated interaction effects, which are entirely absent in the usual superradiance master equations. Moreover, our equations contain terms describing the self-consistent interaction of an average field with a set of polarizable atoms, as in the coupled Bloch and Maxwell equations of the theory of coherent pulse propagation, and enable us to describe fluctuations, arising from incoherent emission, about the average behavior described by the Bloch-Maxwell theory. We solve formally the dynamical equation for the radiation density operator and obtain a displaced multivariate Gaussian distribution centered on the solution of the Maxwell wave equation, which has as parameters the first and second moments of the matter density operator. Then we derive and discuss the field and atomic-moment equations, both in the wave-number and position representations. The moment equations enable us to show the relationship between descriptions of superradiant damping based on the Bloch equations and those based on the existence of correlated atomic states, including both as special cases. We introduce reduced matter moments, which allow us to separate incoherent- and coherent-emission effects and enable us to discuss the question of the closure of the moment equations. Then we consider cases where the behavior of the atomic system is dominated by a strong coherent pump wave or where the atoms are in a symmetric correlated state and show how the slowly-varying-envelope approximation simplifies the radiation-moment equations in these two cases. In the former case, we obtain an approximate theory which consists, in lowest order, of the Bloch-Maxwell equations with radiative-damping terms, plus an equation describing the time development of the correlation function for field fluctuations. Returning to our general formalism, we relate the usual parameters of the theory of radiative decay and of resonant interactions to the more general quantities appearing in our spatial analysis. Finally, we discuss the importance of the stimulated-emission terms appearing in our theory and describe several extensions, including the introduction of inhomogeneous broadening.
The possibility of realizing the superradiant regime of electromagnetic emission by the assembly of quantum dots is considered. The overall dynamical process is analyzed in detail. It is shown that there can occur several qualitatively different stages of evolution. The process starts with dipolar waves triggering the spontaneous radiation of individual dots. This corresponds to the fluctuation stage, when the dots are not yet noticeably correlated with each other. The second is the quantum stage, when the dot interactions through the common radiation field become more important, but the coherence is not yet developed. The third is the coherent stage, when the dots radiate coherently, emitting a superradiant pulse. After the superradiant pulse, the system of dots relaxes to an incoherent state in the relaxation stage. If there is no external permanent pumping, or the effective dot interactions are weak, the system tends to a stationary state during the last stationary stage, when coherence dies out to a low, practically negligible, level. In the case of permanent pumping, there exists the sixth stage of pulsing superradiance, when the system of dots emits separate coherent pulses.
The relation is studied between the entanglement production and collective radiation by an ensemble of atoms. Entanglement production is quantified by means of a general measure introduced earlier by the author. Primary emphasis is placed on the entanglement generated by pseudospin density matrices. The problem of collective atomic radiation can be described by the pseudospin evolution equations. These equations define the evolutional entanglement generated by the related density matrices. Under conditions of superradiant emission, the entanglement production exhibits sharp peaks at the delay time, where the intensity of radiation is maximal. The possibility of regulating the occurrence of such peaks by punctuated superradiance is discussed, which suggests the feasibility of {\it punctuated entanglement production}.
A semiclassical radiation theory is developed in which the spontaneous emission field of a two-level atom is a quantum entity represented by atomic operators acting in the Hilbert space of the atomic states. The theory is applied to an investigation of the coherence properties of spontaneous emission. It is found that incoherent and coherent components can be identified in the emission field, the former dominating in the early stages of the decay from the excited state and the latter dominating in the later stages or in the emission from a weakly excited atom. The single-atom coherence properties are shown to lead to well-known superradiance phenomena in the spontaneous emission from an assembly of similar atoms. The paper does not use the theory of quantum electrodynamics; it builds on knowledge at the undergraduate level of classical radiation theory and the quantum mechanics of atoms.
The aim of this communication is to present in a concentrated form the main ideas of a method, developed by the author, for treating strongly nonequilibrium collective phenomena typical of the interaction of radiation with matter, as well as to give a survey of several applications of the method. The latter is called the Scale Separation Approach since its basic techniques rely on the possibility of separating different space-time scales in nonequilibrium statistical systems. This approach is rather general and can be applied to diverse physical problems, several of which are discussed here. These problems are: Superradiance of nuclear spins, filamentation in resonant media, semiconfinement of neutral atoms, negative electric current, and collective liberation of light.