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QUANTUM OPTICS, FROM ONE MODE TO MANY MODES

Claude Fabre

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

These lectures form a general introduction to the domain of Quantum Optics, with a special emphasis on the notion of field eigenmodes that are necessary to describe the quantum effects in light and define the photons: possibility of changing the basis of field eigenmodes and choosing the most appropriate one, definition of intrinsic properties, independent of the choice of basis. Are successively studied the single mode quantum effects, the quantum correlations existing in bimodal systems, and some interesting features of highly multimode systems such as the optical images.

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These lectures form a general introduction to the domain of Quantum Optics, with a special emphasis on the notion of field eigenmodes that are necessary to describe the quantum effects in light and define the photons: possibility of changing the basis of field eigenmodes and choosing the most appropriate one, definition of intrinsic properties, independent of the choice of basis. Are successively studied the single mode quantum effects, the quantum correlations existing in bimodal systems, and some interesting features of highly multimode systems such as the optical images.
This book provides an introduction to quantum optics for experimental physicists and for college students who have studied quantum mechanics. Its distinguishing feature is its emphasis on multimode fields with correlating different-frequency modes, notably on their phenomenological description and on the practical methods of generating them. The phenomena described in this book provide an opportunity to study nonrelativistic quantum electrodynamics and to master many important concepts of theoretical physics.
This book offers a complete revision for its introduction to the quantum theory of light, including notable developments as well as improvements in presentation of basic theory and concepts, with continued emphasis on experimental aspects. The author provides a thorough overview on basic methods of classical and quantum mechanical measurements in quantum optics, enabling readers to analyze, summarize, and resolve quantum optical problems. The broad coverage of concepts and tools and its practical, experimental emphasis set it apart from other available resources. New discussions of timely topics such as the concept of the photon and distinguishability bring the entire contents up to date. Key Features: Provides a complete update of a classic textbook for the field. Features many new topics, including optical coherence, coherent and incoherent imaging, turbulence-free interferometry. Includes new chapters for intensity fluctuation correlation and thermal light ghost imaging, and biphoton imaging. Offers a complete overhaul of the introductory theory to give a more coherent and thorough treatment. Expands on discussions of optical tests of quantum theory, Popper’s experiment, Einstein’s locality questions, and the delayed choice quantum eraser.
Summary form only given. We find that the quantum statistics of multimode squeezed fields are easily obtained and simply understood via an eigenmode description. The eigenmode description of squeezed light is based on our finding that the squeezing matrix /spl Gamma/ can always be diagonalized by a physical transformation of the fields - either a change of basis or linear unitary evolution. Each eigenmode possesses single-mode squeezing statistics, and the corresponding eigenvalue is the effective squeezing parameter for that mode. The squeezing eigenmodes are completely uncoupled from one another (at the quantum level) and represent independent channels (pixels) useful for carrying noise-sensitive data. We show how an eigenmode description of a squeezed field allows one to easily calculate noise statistics of the field upon diffraction and/or propagation through any sequence of lossless linear optical elements. We further show that the eigenmodes define the shape of the local oscillator which must be used in order to obtain the smallest quantum noise in balanced homodyne or heterodyne measurements. Finally, we use the theory to model pulsed optical parametric downconversion in a /spl chi//sup (2)/ medium with a classical pump field of arbitrary bandwidth, allowing for the possibility of phase and/or group velocity mismatch.
In linear optics, the concept of a mode or eigenmode is well established. Often these modes correspond to a set of fields that are mutually orthogonal with intensity profiles that are invariant as they propagate through a given optical system. More generally, using an eigenmode decomposition, one can define a set of orthogonal modes with respect to an optical measure given that is linear in the intensity of the fields or Hermitian in the fields themselves. However, if the intensity of the light is sufficiently large, the dipole response of an optical medium includes nonlinear terms that cause the eigenmode decomposition to break down. In this work, we introduce the eigenmode decomposition in the presence of these nonlinear source terms by introducing small perturbation fields whose interaction is mediated by some high-intensity background field. Unlike the eigenmodes of linear optics, these novel modes correspond to a set of orthogonal fields that are, in general, distributed across multiple wavelengths. Here, we study the definition and interaction of these eigenmodes for classical electromagnetic fields and multiphoton fields. In the context of classical fields, with our eigenmodes established, we highlight the influence of the high-intensity background field on the symmetry of the eigenmodes. At the multiphoton level, we show that the description of multiphoton fields is simplified by using the propagation eigenmodes while remaining equivalent to the standard approach.
This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schrödinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.