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Oxford University Press eBooks

Photons as population changers

Bruce W. Shore

Published Sep 15, 2020• 0 citations
Publisher

Abstract

Chapter 5 presents the views of photons that have accompanied experimental uses of lasers to manipulate the quantum states of atoms and other systems. It discusses not only the Einstein rate equations appropriate for incoherent radiation but also the Rabi oscillations that accompany coherent excitation, and the Jaynes-Cummings model that demonstrates the discreteness of photons.

DOI
10.1093/oso/9780198862857.003.0005

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This book describes the changing views of the physics community toward photons, and how photons are viewed today in several contexts. The first portion, a ninechapter Memoir with few equations and many definitions, explains the changing view of physicists toward radiation and its wave-particle photons, written for those with interest but possibly without technical background. It gives operational definitions that have been used for photons and their association with quantum-state manipulations that include Quantum Information, astronomical sources and crowds of photons, the boxed fields of cavity Quantum Electrodynamics It defines, qualitatively, the historical photons of Planck, Einstein, Compton, and Bohr, the later photons of Dirac, Feynman, and Glauber, and the photon constituents of the Standard Model of Particle Physics. It points to contemporary photons as causers of change to atoms, as carriers of messages, and as subject to controllable creation and alteration. A second portion, of three tutorial appendices, explains the mathematical background of quantum theory and radiation needed by those whose profession involves photonics and who therefore want more detailed understanding of the Memoir portion: quantum theory and the Schrodinger equation for quantum-state manipulation; Maxwell equations for electromagnetism with wave modes that become photons through a quantization postulate, possibly exhibiting quantum entanglement; and the coupling of atoms and fields to create quasiparticles that are seen as slow and stored light pulses. As with other Memoirs, the present book has idiosyncrasies of the author. Most notably, on the opening page of each chapter, and at the end of the book, is a cartoon drawn by the author, as a grad student, that reflects the changing views of a PhD aspirant toward the grad school experience as he progressed through the graduate school of MIT in the 1950s.

Oxford University Press eBooks•Sep 15, 2020•3 citations
Chapter 5 presents the views of photons that have accompanied experimental uses of lasers to manipulate the quantum states of atoms and other systems. It discusses not only the Einstein rate equations appropriate for incoherent radiation but also the Rabi oscillations that accompany coherent excitation, and the Jaynes-Cummings model that demonstrates the discreteness of photons.
The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it has been found that during the quiescent intervals of collapsed Rabi oscillations the atom and field exist in a macroscopic superposition state (a Schrödinger cat). This discovery offers the opportunity to use the JCM to elucidate the basic properties of quantum correlation (entanglement) and to explore still further the relationship between classical and quantum physics. The relative simplicity of the JCM and the ease with which it can be extended through analytic expressions or numerical computation continues to motivate attention, as evidenced by the growing abundance of publications. We here present an overview of the theory of the JCM and some of the many extensions and generalizations that have appeared.
Coherent manipulations of atoms using laser light The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.
Theory of the interaction between atom and radiation field: three pictures in quantum mechanics description two-level atom and the optical Bloch equation quantized description of the radiation field Dicke Hamiltonian and Jaynes - Cummings model quantum theory of a small system coupling to a reservoir. The quantum properties of light: coherence of light squeezed states of light resonance fluorescence superfluorescence optical bistability effects of virtual photon processes. Quantum properties of the atomic behaviour under the interaction of the radiation field: collapses and revivals of the atomic populations squeezing effects of the atomic operators coherent trapping of the atomic population quantum characteristics of a two-atom system under the interaction of radiation field autoionization of the atom in a laser field motion of the atom in a laser field laser cooling.
Abstract We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light–matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes–Cummings model results for the quantum Rabi oscillation of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light–matter interactions for these cases. Our results match well with the seminal experimental data obtained in this regard by Brune et al (1996 Phys. Rev. Lett. 76 1800). We also have studied the population dynamics in this regard by applying the generalized Einstein rate equations.
This book describes the changing views of the physics community toward photons, and how photons are viewed today in several contexts. The first portion, a ninechapter Memoir with few equations and many definitions, explains the changing view of physicists toward radiation and its wave-particle photons, written for those with interest but possibly without technical background. It gives operational definitions that have been used for photons and their association with quantum-state manipulations that include Quantum Information, astronomical sources and crowds of photons, the boxed fields of cavity Quantum Electrodynamics It defines, qualitatively, the historical photons of Planck, Einstein, Compton, and Bohr, the later photons of Dirac, Feynman, and Glauber, and the photon constituents of the Standard Model of Particle Physics. It points to contemporary photons as causers of change to atoms, as carriers of messages, and as subject to controllable creation and alteration. A second portion, of three tutorial appendices, explains the mathematical background of quantum theory and radiation needed by those whose profession involves photonics and who therefore want more detailed understanding of the Memoir portion: quantum theory and the Schrodinger equation for quantum-state manipulation; Maxwell equations for electromagnetism with wave modes that become photons through a quantization postulate, possibly exhibiting quantum entanglement; and the coupling of atoms and fields to create quasiparticles that are seen as slow and stored light pulses. As with other Memoirs, the present book has idiosyncrasies of the author. Most notably, on the opening page of each chapter, and at the end of the book, is a cartoon drawn by the author, as a grad student, that reflects the changing views of a PhD aspirant toward the grad school experience as he progressed through the graduate school of MIT in the 1950s.