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CRC Press eBooks

Quantum electrodynamical approach

M. G. Benedict, A. M. Ermolaev, В. А. Малышев, I. V. Sokolov, Evgenii Dmitrievich Trifonov

Published Mar 29, 2018• 0 citations
Publisher

Abstract

The quantum electrodynamical (QED) theory of the spontaneous decay of a single excited two-level atom was generalized and applied to the super-radiance problem by several authors. This chapter considers the evolution of the system of atom plus field, applying an approach equivalent to the master equation method. It uses the diagram representation of the quantum perturbation theory for the density matrix of the system. The diagram method provides an effective tool for the derivation of the master equations. The chapter presents the quantum theory of super-radiance of an extended three-dimensional polyatomic system within the Markov and the rotating wave approximations and neglecting retardation. It discusses the spatial properties of super-radiance, including the angular correlation of photons, which have been mentioned in earlier works by R. H. Dicke and V. Ernst and P. Stehle.

DOI
10.1201/9780203737880-4

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The elementary theory of super-radiance

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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.

CRC Press eBooks•Mar 29, 2018•0 citations

Introduction

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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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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.

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Spontaneous emission from a system of $N$ identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state $|{z}_{0}〉$.

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Spontaneous radiative coupling of atomic energy levels

David A. Cardimona, Carlos R. Stroud

Density-matrix equations of motion derived from Heisenberg picture source-field quantum electrodynamics contain damping constants and frequency shifts which are not associated with a single radiative transition but which instead couple two separate transitions together. In the absence of degeneracies in the atomic levels, these coupling terms are normally neglected when the rotating-wave approximation is invoked. These terms cannot be neglected when there are degeneracies or near degeneracies. In this paper, we interpret the generalized frequency shifts, show how they can be renormalized and included in shifts of atomic energy levels and altered damping constants, and discuss their experimental significance.

Physical Review A•May 1, 1983•34 citations
The quantum electrodynamical (QED) theory of the spontaneous decay of a single excited two-level atom was generalized and applied to the super-radiance problem by several authors. This chapter considers the evolution of the system of atom plus field, applying an approach equivalent to the master equation method. It uses the diagram representation of the quantum perturbation theory for the density matrix of the system. The diagram method provides an effective tool for the derivation of the master equations. The chapter presents the quantum theory of super-radiance of an extended three-dimensional polyatomic system within the Markov and the rotating wave approximations and neglecting retardation. It discusses the spatial properties of super-radiance, including the angular correlation of photons, which have been mentioned in earlier works by R. H. Dicke and V. Ernst and P. Stehle.
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.
Spontaneous emission from a system of NNN identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state ∣z0〉|{z}_{0}〉∣z0​〉.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.
Density-matrix equations of motion derived from Heisenberg picture source-field quantum electrodynamics contain damping constants and frequency shifts which are not associated with a single radiative transition but which instead couple two separate transitions together. In the absence of degeneracies in the atomic levels, these coupling terms are normally neglected when the rotating-wave approximation is invoked. These terms cannot be neglected when there are degeneracies or near degeneracies. In this paper, we interpret the generalized frequency shifts, show how they can be renormalized and included in shifts of atomic energy levels and altered damping constants, and discuss their experimental significance.