Abstract Some of the most basic aspects of the interaction of atoms with light are considered, with emphasis on distinctly quantum-electrodynamical effects. Absorption and stimulated emission are associated with interference between incident and scattered fields. The JaynesCummings model, collapses and revivals, and dressed states are discussed along with related experimental studies in cavity quantum electrodynamics. Entangled states are associated with the interference of probability amplitudes for indistinguishable processes. The no-cloning theorem is reviewed. Von Neumann’s proof concerning hidden variable theories is examined and used to introduce Bell’s theorem and its proof. Resonance fluorescence spectra and photon anti-bunching correlations are calculated and compared with experiment. Photon polarization correlations in atomic cascades are calculated from the perspectives of both source fields and entanglement, and experimental studies of these correlations and Bell inequalities are reviewed.
Abstract Some of the most basic aspects of the interaction of atoms with light are considered, with emphasis on distinctly quantum-electrodynamical effects. Absorption and stimulated emission are associated with interference between incident and scattered fields. The JaynesCummings model, collapses and revivals, and dressed states are discussed along with related experimental studies in cavity quantum electrodynamics. Entangled states are associated with the interference of probability amplitudes for indistinguishable processes. The no-cloning theorem is reviewed. Von Neumann’s proof concerning hidden variable theories is examined and used to introduce Bell’s theorem and its proof. Resonance fluorescence spectra and photon anti-bunching correlations are calculated and compared with experiment. Photon polarization correlations in atomic cascades are calculated from the perspectives of both source fields and entanglement, and experimental studies of these correlations and Bell inequalities are reviewed.
Abstract This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.
In this chapter, we discuss a purely quantum approach to the interaction between an atom and the electromagnetic field. In this treatment, the atom and electromagnetic field form a single quantum system, whose evolution is handled globally within a unified formalism. This will thus have the merit of being fully consistent from the theoretical standpoint. But the main advantage in an entirely quantum approach is that it can treat the full range of matter–radiation interaction phenomena. In particular, it provides a rigorous description of the spontaneous emission of light by an excited atom , something that falls outside the scope of the semi-classical framework applied in Chapters 2 and 3, where the lifetime of an excited atomic state had to be fed in phenomenologically. It can describe other phenomena of the same type, such as parametric fluorescence by a nonlinear crystal subjected to pumping radiation (see Chapter 7), which underlies many recent developments in quantum optics. The fully quantum approach also has the merit of allowing a simple interpretation in terms of photons for the various matter–radiation interaction processes, such as absorption, stimulated emission, scattering, and also the basic processes of nonlinear optics. Indeed, it provides a unified framework for both stimulated and spontaneous processes. Finally, it can be used to tackle completely new situations where matter and radiation interact, which lie outside the scope of any semi-classical description, such as cavity quantum electrodynamics or the production of single-photon or entangled-photons states .
Abstract: An extensive review of the quantum theory of light-matter interaction is given in this chapter, beginning with its fundamental ideas and historical development. It covers the quantization of the electromagnetic field, atomic models, and important interaction Hamiltonians, including both semi-classical and completely quantum treatments. The role of vacuum fluctuations and fundamental processes like spontaneous and induced emission are examined. Quantum coherence, entanglement, decoherence, and its formal representation using master equations are also covered in this chapter. Modern applications such lasers, quantum sensors, and quantum communication systems are highlighted. The significance of light-matter interaction in furthering quantum science and technology is emphasized in the chapter's conclusion, which also discusses current research trends and future directions. Keywords: Laser, cryptography, Electromagnetic, Quantum, Atomic.
Abstract: An extensive review of the quantum theory of light-matter interaction is given in this chapter, beginning with its fundamental ideas and historical development. It covers the quantization of the electromagnetic field, atomic models, and important interaction Hamiltonians, including both semi-classical and completely quantum treatments. The role of vacuum fluctuations and fundamental processes like spontaneous and induced emission are examined. Quantum coherence, entanglement, decoherence, and its formal representation using master equations are also covered in this chapter. Modern applications such lasers, quantum sensors, and quantum communication systems are highlighted. The significance of light-matter interaction in furthering quantum science and technology is emphasized in the chapter's conclusion, which also discusses current research trends and future directions. Keywords: Laser, cryptography, Electromagnetic, Quantum, Atomic.
Density-matrix calculations provide the steady-state conditions for probe amplification or lasing between atomic levels with an uninverted population, but additional insight into the underlying physics is given by a probability amplitude approach. In this paper we derive the gain coefficient from the Feynman diagrams for a probe-laser incident on a resonantly pumped, V-type system using time-dependent perturbation theory in a dressed basis. The connection is made to density-matrix calculations for this model, which have been used recently to describe experiments in Rb [A. S. Zibrov et al., Laser Phys. 5, 553 (1995); Phys. Rev. Lett. 75, 1499 (1995)]. In the density-matrix calculation the overall gain is possible because the pump-induced coherence of a strongly driven transition leads to probe amplification, despite the lack of inversion on the probe transition. In our amplitude approach we associate a specific physical process with each of the scattering channels for the probe and show how amplification without inversion can be achieved. The amplitude calculation reveals a distinction between stepwise and two-quantum processes. Interference is shown to result from the two-quantum processes, constructive for the amplification channels and destructive for the absorption. Terms appearing in the gain coefficient are traced to different sources in the amplitude and density-matrix approaches. The physical origin of each term is discussed and compared for both approaches. Terms that arise from coherences in the density-matrix approach are shown to correspond to noninterfering stepwise contributions in the amplitude approach. In deriving these results, we find that the Feynman rules that we construct for forming the probability amplitude for an arbitrary scattering process of the electromagnetic field from the coupled atom-strong pump system are consistent with Rayleigh-Schr\"odinger perturbation theory in the quantum dressed basis. In addition, the spontaneously emitted photons become entangled with the probe field, correlating the emission spectrum with specific scattering channels.
Abstract This third edition, like its two predecessors, provides a detailed account of the basic theory needed to understand the properties of light and its interactions with atoms, in particular the many nonclassical effects that have now been observed in quantum-optical experiments. The earlier chapters describe the quantum mechanics of various optical processes, leading from the classical representation of the electromagnetic field to the quantum theory of light. The later chapters develop the theoretical descriptions of some of the key experiments in quantum optics. Over half of the material in this third edition is new. It includes topics that have come into prominence over the last two decades, such as the beamsplitter theory, squeezed light, two-photon interference, balanced homodyne detection, travelling-wave attenuation and amplification, quantum jumps, and the ranges of nonliner optical processes important in the generation of nonclassical light. The book is written as a textbook, with the treatment as a whole appropriate for graduate or postgraduate students, while earlier chapters are also suitable for final- year undergraduates. Over 100 problems help to intensify the understanding of the material presented.