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arXiv:1404.1739 · AIP conference proceedings

Coherent radiation by quantum dots and magnetic nanoclusters

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Published Jan 1, 2014• 0 citations
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Abstract

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.

DOI
10.1063/1.4870198

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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.
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 peculiarities of coherent spin radiation by magnetic nanomolecules is investigated by means of numerical simulation. The consideration is based on a microscopic Hamiltonian taking into account realistic dipole interactions. Superradiance can be realized only when the molecular sample is coupled to a resonant electric circuit. The feedback mechanism allows for the achievement of a fast spin reversal time and large radiation intensity. The influence on the level of radiation, caused by sample shape and orientation, is analysed. The most powerful coherent radiation is found to occur for an elongated sample directed along the resonator magnetic field.
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.
In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be represented as an atom with zero kinetic energy, and that all excitonic effects except dipole-dipole interactions may be disregarded. We use Jaynes-Cummings-Paul model with applications to quantum systems based on a time-dependent Hamiltonian and entangled states. We obtain a system of equations describing the interaction and present a method to solve the equations analytically for a single mode field within the Rotating-Wave Approximation. As an example of the applicability of this approach, we solve the system of two two-level quantum dots in a lossless cavity with two modes of electromagnetic field. We furthermore study the evolution of entanglement by defining and computing the concurrency.
A model is presented for a system of N two-level excitons interacting with each other via optical near fields represented as localized photons. In a low exciton density limit, quantum dynamics of the dipole moments or quantum coherence between any two energy levels is linear. As the exciton density becomes higher, the dynamics becomes nonlinear, and the system has several kinds of quasi-steady states of the dipole distribution depending on the system parameters. These quasi-steady states are classified with the help of the effective Hamiltonian that is derived from the renormalization of degrees of freedom of localized photons with a unitary transformation. Among them there exist a “ferromagnetic” state (dipole-ordered state), in which all electric dipoles are aligned in the same direction, and an “anti-ferromagnetic” state, where all dipoles alternatingly change the direction. In addition, we show that an arbitrary state can be transformed into a dipole-ordered state by manipulating initial values of the population differences appropriately. For example, if we initially prepare a dipole-forbidden state, which is similar to the “anti-ferromagnetic” state and cannot be coupled with propagating far fields, and if we manipulate the distribution of the population differences properly, the initial state evolves into a dipole-ordered state. The radiation property of such dipole-ordered states is examined in detail. Neglecting energy dissipation by radiation, we find that some of the ordered states show strong radiation equivalent to Dicke's superradiance. Then by introducing a radiation reservoir, the dissipative master equation is derived. Solving the equation with and without quantum correlations, we numerically show that multiple peaks in the radiation profile can survive in both cases. The mechanism of this phenomenon is discussed, and a brief comment on an application to photonic devices on a nanometer scale is given.