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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multipole claster superfluorescence: the generalized Dicke model

А. А. Калачев, Самарцев Виталий Владимирович

Published Jan 24, 2006• 0 citations
Publisher

Abstract

The peculiarities of superfluorescence in systems consisting of a few neighbor particles (clusters), when exchange or/and electrostatic multipole interactions between particles become significant, are investigated theoretically. It is shown that interaction between particles in the cluster leads to superpuassonian statistics of emitted photons and the intensity I of quadrupole superfluorescence on the double frequency depends on the number N of active centers as I~Nα, where α> 2. In particular, α = 3 , when N >> 1. Possible schemes of cluster construction in nuclei systems are considered and prospects of observation of multipole gamma superfluorescence are discussed.

DOI
10.1117/12.675140

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Physical Review A•Nov 1, 1975•43 citations
The peculiarities of superfluorescence in systems consisting of a few neighbor particles (clusters), when exchange or/and electrostatic multipole interactions between particles become significant, are investigated theoretically. It is shown that interaction between particles in the cluster leads to superpuassonian statistics of emitted photons and the intensity I of quadrupole superfluorescence on the double frequency depends on the number N of active centers as I~Nα, where α> 2. In particular, α = 3 , when N >> 1. Possible schemes of cluster construction in nuclei systems are considered and prospects of observation of multipole gamma superfluorescence are discussed.
The processes of cooperative luminescence and superfluorescence (SF) in nanoclusters, which consist of a few neighbor particles, interacting with each other by exchange or/and electrostatic forces, are investigated theoretically. It is shown that there are two types of cooperative SF depending on the ratio between the linear size of a nanocluster and cooperative interaction range. The experiments on cooperative luminescence in Ytterbium-doped silica fibers are analyzed. It is shown that the intensity of cooperative SF in such a system should be proportional to the forth degree of Ytterbium concentration.
The features of superfluorescence (SF) in nanoclusters, which consist of a few neighboring particles interacting with each other by exchange or/and electrostatic forces, are investigated theoretically. It is shown that there are two types of cooperatively SF depending on the ratio between the linear size of a nanocluster and the cooperative interaction range. Experiments on cooperative luminescence in Ytterbium-doped silica fibers are analyzed. It is shown that the intensity of cooperative SF in such a system should be proportional to the fourth degree of Ytterbium concentration.
Recent advances in optical studies of condensed matter systems have led to the emergence of a variety of phenomena that have conventionally been studied in the realm of quantum optics. These studies have not only deepened our understanding of light–matter interactions but have also introduced aspects of many-body correlations inherent in optical processes in condensed matter systems. This paper is concerned with the phenomenon of superradiance (SR), a profound quantum optical process originally predicted by Dicke in 1954. The basic concept of SR applies to a general N body system, where constituent oscillating dipoles couple together through interaction with a common light field and accelerate the radiative decay of the whole system. Hence, the term SR ubiquitously appears in order to describe radiative coupling of an arbitrary number of oscillators in many situations in modern science of both classical and quantum description. In the most fascinating manifestation of SR, known as superfluorescence (SF), an incoherently prepared system of N inverted atoms spontaneously develops macroscopic coherence from vacuum fluctuations and produces a delayed pulse of coherent light whose peak intensity ∝N2. Such SF pulses have been observed in atomic and molecular gases, and their intriguing quantum nature has been unambiguously demonstrated. In this review, we focus on the rapidly developing field of research on SR phenomena in solids, where not only photon-mediated coupling (as in atoms) but also strong Coulomb interactions and ultrafast scattering processes exist. We describe SR and SF in molecular centers in solids, molecular aggregates and crystals, quantum dots, and quantum wells. In particular, we will summarize a series of studies we have recently performed on semiconductor quantum wells in the presence of a strong magnetic field. In one type of experiment, electron-hole pairs were incoherently prepared, but a macroscopic polarization spontaneously emerged and cooperatively decayed, emitting an intense SF burst. In another type of experiment, we observed the SR decay of coherent cyclotron resonance of ultrahigh-mobility 2D electron gases, leading to a decay rate that is proportional to the electron density. These results show that cooperative effects in solid-state systems are not merely small corrections that require exotic conditions to be observed; rather, they can dominate the nonequilibrium dynamics and light emission processes of the entire system of interacting electrons.
Spontaneous decay is a phenomenon that has been described for the first time by Dirac, Wigner and Weisskopf, at the early ages of the development of quantum electrodynamics. The theory is applicable to a multi-body system only when atoms don’t interact during their decay. Dicke introduces in his seminal paper the case where this assumption doesn’t hold. The results he obtains not only tell that the system emits pulses, but the pulse duration now depends on 1/N, where N is the number of participating atoms to the process. The pulses temporal profile is described by a squared hyperbolic secant function. The resulting emission intensity scales as N^2. The atomic system radiates more intensively than the ordinary fluorescent emission, this is the reason why the process is called superradiance, or by a generalization to extended systems, superfluorescence. The superradiant emission has preferential escape directions, depending on the atomic sample shape. Superradiance is a collective process and it takes place when the group of excited atoms is left unper- turbed during the formation of of the macroscopic dipole. A fundamental difference compared to the spontaneous and stimulated emission processes is that all atoms act together as a single entity and it isn’t possible to identify single atoms involved. This remarkable behaviour is manifest when the atomic coherence of the system, while influenced by environmental interactions that cause dephasing in atoms, persists for a sufficient interval of time. Typical dephasing mechanisms, such as collisions in gases or lattice phonon interactions in crystals, make its experimental observation difficult. A possible solution to this problem is the use of optical crystals doped with rare-earths that are characterized by long and narrow levels lifetimes.
We discuss from first principles the cooperative decay of a system of two-level atoms, initially prepared in an uncorrelated excited state with population inversion NNN, and we give the conditions under which the superfluorescence effect occurs. Describing the atomic system in terms of collective variables, we derive a master equation for the reduced atomic density operator, which gives rise both to a damping and to a time-dependent frequency shift in the dynamics of collective modes. The coupled equations of motion are solved with a self-consistent approach. It is found that the system goes through a nonexponential decay if the maximum length of the active volume is smaller than a "cooperation range" and larger than a "threshold length," in agreement with the one-mode theory. The radiation burst has a time width proportional to ${N}^{\ensuremath{-}1}$, and its intensity is proportional to N2{N}^{2}N2. Specializing to a pencil-shaped volume, we find that only two atomic modes need to be considered; in this case, the average emitted radiation is all condensed in the two diffraction patterns of the opposite axial modes.