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CRC Press eBooks

Super-radiance of multi-spin systems

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev, I. V. Sokolov, Evgenii Dmitrievich Trifonov

Published Mar 29, 2018• 0 citations
Publisher

Abstract

This chapter is devoted mainly to the description and theoretical interpretation of super-radiance experiments in a multi-proton spin system. It considers the simplest case of multi-spin super-radiance in a cavity. The spin magnetic moment in a static magnetic field is a perfect realization of the 'two-level' atomic model. In fact, this physical system was the origin of this model, and was extended to a wide class of resonant phenomena, including super-radiance. A refined description of super-radiance of magnetic spins in solids will probably have to take into account the dependence of the relaxation rate on the magnitude of the magnetization, using as a basis the concept of spin temperature. The chapter shows the limitations of the method of Bloch equations for describing NMR effects in solids, as mentioned earlier in the literature. It attempts to observe super-radiance in the radiofrequency domain was reported by P. Bosiger and their group, using a nuclear subsystem of Al atoms in ruby crystals.

DOI
10.1201/9780203737880-8

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For nearly two decades, starting from the prediction of super-radiance by R. H. Dicke in 1954, the subject was generally considered as being mainly of theoretical significance. The situation changed in 1973 when Skribanowitz, Herman, MacGillivray and Feld performed experiments with low-pressure HF gas, and realized conditions where the phase memory time of the radiation centres was longer than the cooperative spontaneous emission time. This chapter describes the numerous super-radiance experiments. It demonstrates that conditions for the experimental realization of super-radiance do exist, that is under appropriate circumstances super-radiance is not suppressed by de-phasing or inhomogeneous relaxation. The experiments can be divided into two classes with respect to the time scale of the relaxation processes. In gases, the relaxation times are typically in the nanosecond range, whereas in solids these processes are faster, by at least one or two orders of magnitude. The chapter gives a description of some of these experiments both in gases and in solids.

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This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the main features of super-radiance using some simplified models. It presents a review of experimental work on super-radiance. The book also presents a generalization of the Wigner–Weisskopf approach to the N -atom system using a diagram method of non-stationary perturbation theory. It discusses several correlation functions for the field and the polarization, which characterize the coherence properties of super-radiation. The book uses the semiclassical approach to investigate the influence of de-phasing processes on radiation efficiency, or in other words, the influence of homogeneous and inhomogeneous broadening of the spectral line on the dynamics and spectrum of super-radiance. It considers the boundary value problem for the transmission and reflection of short pulses, taking into account the local field correction. Two effects are of special interest: the population-dependent frequency shift and the possibility of mirror-less bistability of ultra-short electromagnetic pulses.

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General properties of super-radiance--cooperative spontaneous emission of multi-atomic systems are explained on the basis of some simple models. First we consider spontaneous emission of two atoms separated from each other by a distance less than the wavelength. Then the kinetics of super-radiance of N-atomic system in a small volume are described. The main attention we put into super-radiance photon statistics. We show the Poissonian statistics for the main part of super-radiance pulse and demonstrate the special conditions when it can be Sub-Poissonian one.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 4, 1999•202 citations
This chapter is devoted mainly to the description and theoretical interpretation of super-radiance experiments in a multi-proton spin system. It considers the simplest case of multi-spin super-radiance in a cavity. The spin magnetic moment in a static magnetic field is a perfect realization of the 'two-level' atomic model. In fact, this physical system was the origin of this model, and was extended to a wide class of resonant phenomena, including super-radiance. A refined description of super-radiance of magnetic spins in solids will probably have to take into account the dependence of the relaxation rate on the magnitude of the magnetization, using as a basis the concept of spin temperature. The chapter shows the limitations of the method of Bloch equations for describing NMR effects in solids, as mentioned earlier in the literature. It attempts to observe super-radiance in the radiofrequency domain was reported by P. Bosiger and their group, using a nuclear subsystem of Al atoms in ruby crystals.
For nearly two decades, starting from the prediction of super-radiance by R. H. Dicke in 1954, the subject was generally considered as being mainly of theoretical significance. The situation changed in 1973 when Skribanowitz, Herman, MacGillivray and Feld performed experiments with low-pressure HF gas, and realized conditions where the phase memory time of the radiation centres was longer than the cooperative spontaneous emission time. This chapter describes the numerous super-radiance experiments. It demonstrates that conditions for the experimental realization of super-radiance do exist, that is under appropriate circumstances super-radiance is not suppressed by de-phasing or inhomogeneous relaxation. The experiments can be divided into two classes with respect to the time scale of the relaxation processes. In gases, the relaxation times are typically in the nanosecond range, whereas in solids these processes are faster, by at least one or two orders of magnitude. The chapter gives a description of some of these experiments both in gases and in solids.
This chapter considers super-radiance on an elementary level in the sense that the main notions and concepts of the phenomenon will be treated as they evolved in the course of the early studies starting with the classical works by R. H. Dicke. It considers super-radiance from a system with dimensions small compared with the wavelength of the emission that is the Dicke model. The chapter discusses the results to be obtained are also applicable to the single-mode super-radiance of an extended system. It then considers mainly the cooperative spontaneous emission of a collection of N identical atoms confined within a small volume. If the audience wish to investigate the super-radiance of an extended system, the dimensions of which exceed the emission wavelength, the semiclassical method is more convenient. In essence, the semiclassical approach discussed in the chapter combines the quantum mechanical treatment of the atomic system that uses the density matrix formalism with the classical treatment of the radiation field.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the main features of super-radiance using some simplified models. It presents a review of experimental work on super-radiance. The book also presents a generalization of the Wigner–Weisskopf approach to the N -atom system using a diagram method of non-stationary perturbation theory. It discusses several correlation functions for the field and the polarization, which characterize the coherence properties of super-radiation. The book uses the semiclassical approach to investigate the influence of de-phasing processes on radiation efficiency, or in other words, the influence of homogeneous and inhomogeneous broadening of the spectral line on the dynamics and spectrum of super-radiance. It considers the boundary value problem for the transmission and reflection of short pulses, taking into account the local field correction. Two effects are of special interest: the population-dependent frequency shift and the possibility of mirror-less bistability of ultra-short electromagnetic pulses.
This chapter introduces a three-level atomic model and discusses two other coherent atomic phenomena; namely, coherent Raman scattering and lasing without inversion. Lasing without inversion may take place in three-level resonant atomic systems and, like super-radiance, results from atomic coherence. Super-radiation is initiated by spontaneous fluctuations of the polarization in the medium. The semiclassical method is a powerful tool that is useful for the treatment of propagation effects in super-radiance as well as in such coherent emission processes as self-induced transparency, photon echo and others. The use of the Maxwell—Bloch equations allows one to consider these phenomena in elongated systems. Fortunately, the semiclassical approach is readily applicable to low-density systems that are to gases. However, one has to exercise greater care when applying it to coherent emission in solids. In high-density systems there is a strong mixing of the field and atomic states in the vicinity of resonance.
We discuss the coherent behavior of a polarized, nuclear or electron, spin system for which the magnetic dipole radiation emitted in the radio-frequency region, has approximately quadratic dependence on the number of spins. An effective method of describing these phenomena is provided by computer simulation of a microscopic model of the spin system. Important aspects of this numeric simulation are described, together with a comparison with the theoretical predictions. The behavior of the transverse component of the magnetic moment, M+(t){M}^{+}(t)M+(t), in super-radiant conditions is studied. In addition, the role of dipole-dipole interactions in super-radiation phenomena is investigated in detail. It is shown that some important features of super-radiation cannot be described with the Bloch equations.
General properties of super-radiance--cooperative spontaneous emission of multi-atomic systems are explained on the basis of some simple models. First we consider spontaneous emission of two atoms separated from each other by a distance less than the wavelength. Then the kinetics of super-radiance of N-atomic system in a small volume are described. The main attention we put into super-radiance photon statistics. We show the Poissonian statistics for the main part of super-radiance pulse and demonstrate the special conditions when it can be Sub-Poissonian one.