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arXiv:1002.2322 · Physical Review B

Dynamics of quantum dot superradiance

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Published Feb 8, 2010• 59 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.81.075308

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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 assemblies of either quantum dots or magnetic nanoclusters are studied. It is shown that such assemblies can produce coherent radiation. A method is developed for solving the systems of nonlinear equations describing the dynamics of such assemblies. The method is shown to be general and applicable to systems of different physical nature. Despite mathematical similarities of dynamical equations, the physics of the processes for quantum dots and magnetic nanoclusters is rather different. In a quantum dot assembly, coherence develops due to the Dicke effect of dot interactions through the common radiation field. For a system of magnetic clusters, coherence in the spin motion appears due to the Purcell effect caused by the feedback action of a resonator. Self-organized coherent spin radiation cannot arise without a resonator. This principal difference is connected with the different physical nature of dipole forces between the objects. Effective dipole interactions between the radiating quantum dots, appearing due to photon exchange, collectivize the dot radiation. While the dipolar spin interactions exist from the beginning, yet before radiation, and on the contrary, they dephase spin motion, thus destroying the coherence of moving spins. In addition, quantum dot radiation exhibits turbulent photon filamentation that is absent for radiating spins.
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.
We consider the model of quantum dots interacting with coherent radiation when the relaxation processes may be neglected. The system under investigation consists of two discrete energy levels of the quantum dots in the presence of strong electron-electron Coulomb interaction and the transitions between these levels in response to electromagnetic radiation. By using the suitable generalisation of the Hubbard model the system of equations describing the evolution of the state of quantum dot was derived.
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.
Light is often characterized only by its classical properties, like intensity or coherence. When looking at its quantum properties, described by photon correlations, new information about the state of the matter generating the radiation can be revealed. In particular the difference between independent and entangled emitters, which is at the heart of quantum mechanics, can be made visible in the photon statistics of the emitted light. The well-studied phenomenon of superradiance occurs when quantum-mechanical correlations between the emitters are present. Notwithstanding, superradiance was previously demonstrated only in terms of classical light properties. Here, we provide the missing link between quantum correlations of the active material and photon correlations in the emitted radiation. We use the superradiance of quantum dots in a cavity-quantum electrodynamics laser to show a direct connection between superradiant pulse emission and distinctive changes in the photon correlation function. This directly demonstrates the importance of quantum-mechanical correlations and their transfer between carriers and photons in novel optoelectronic devices.