This chapter begins with a brief summary of the way states and observables are described in the classical theory, explaining the concepts of pure and mixed states and those relating to states of composite systems. The paper analyzes the existence of quantization maps associated with the orderings of operators in the coordinatemomentum representation. Wigner function and other quasidistributions are found in every decent book on quantum optics. Niels bohr used to say that if you are not confused by quantum mechanics, then you really do not understand it. Schleich, quantum optics in phase space they also contain description of homodyne detection, and the latter describes the tomographic reconstruction of. Modern in style and didactically skillful, quantum optics in phase space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable. The module introduces the quantisation of light, the concept of single light modes, the various quantum states of light and their description in phase space. We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. Matical tools needed for phasespace description of a very common. Regarding the negatives, there are several things this course deliberately avoids. Nonlinear optics nlo is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density p responds nonlinearly to the electric field e of the light.
Quantum optics in phase space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase. The title quantum optics covers a large range of possible courses, and so this introduction intends to explain what this course does and does not aim to provide. Quantum optics in phase space has been successful in preparing students and researchers for their quest of unravelling the mysteries of nature. Quantum optics in phase space also serves advanced researchers as a comprehensive reference book. In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Still, as every physics undergraduate learns early on, classical phase space is. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The phase space rep is di erent in character not equivalent to the above prominent in recent years for applications to quantum optics, quantum information theory, quantum tomography, also for questions re foundations of qm and classical mechanics cm qm as a deformation of cm, the nature of the qmcm interface, 4. Quantum mechanics in phase space world scientific series. Introductory quantum optics 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. Because a particle cannot simultaneously have a well defined position and. The phase space distribution fx, p of a quantum state is a quasiprobability distribution.
One of the most interesting facets of quantum optics is the way in which the use of phase space distributions has allowed an almost seamless unification of classical and quantum field theory, without sacrificing the quantum nature of optical fields. Classical optics is able to provide an understanding of either the corpuscular or wave aspects of quantum mechanics, reflected in phase space through the. Often, the theoretical treatments are accompanied by the corresponding experiments. In quantum optics, switch to creation and anihilation operators. Calculus for functions of noncommuting operators and general phase space methods in quantum mechanics. In the phasespace formulation, the phase space distribution may be treated as the fundamental, primitive description of the quantum system, without. An ideal detector should have response that is independent of radiation frequency and be small enough in comparison with the scale of field changes. Nov 03, 2011 in this tutorial, we introduce the basic concepts and mathematical tools needed for phase space description of a very common class of states, whose phase properties are described by gaussian wigner functions. Introduction to modern quantum optics download ebook pdf.
Controlling quantum interference in phase space with. Read download statistical methods in quantum optics 1 pdf. Wigners quasiprobability distribution function in phase space is a special weyl representation of the density matrix. Pdf statistical methods in quantum optics 1 download. Request pdf quantum optics in the phase space in this tutorial, we introduce the basic concepts and mathematical tools needed for phasespace description of a very common class of states.
Master equations in phasespace formulation of quantum optics. This course gives you access to basic tools and concepts to understand research articles and books on modern quantum optics. The main purpose of this tutorial is to introduce the reader to the phase space. During the second part of the 20th century experimental and theoretical progress developed together. Although optics in modern physics is part of quantum mechanics, it also has close ties to classical field theory. Matical tools needed for phase space description of a very. Request pdf quantum optics in the phase space in this tutorial, we introduce the basic concepts and mathematical tools needed for phase space description of a very common class of states.
In particular, universal twoqubit gates can be implemented deterministically through qubitqubit communication, mediated by a continuousvariable bus mode qubus, without direct. The phase space rep is di erent in character not equivalent to the above prominent in recent years for applications to quantum optics, quantum information theory, quantum tomography, also for questions re foundations of qm and classical mechanics cm qm as a deformation of cm, the nature of the qmcm interface. In other words, it is quantum mechanics applied to photons or light. The presentation is almost entirely concerned with the quantized electromagnetic. In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. Master equations in phasespace formulation of quantum. Berlin weinheim new york chichester brisbane singapore toronto. Quantum phase differencesum and su2su1,1 phase space quasidistributions. Request pdf quantum optics in the phase space in this tutorial, we introduce the basic concepts and mathematical tools needed for phase space description of a. The main purpose of this tutorial is to introduce the reader to the phasespace. It has been useful in describing quantum transport in quantum optics. Schleich illustrates the properties of quantum states with the help of the wigner phase space distribution function. Quantum optics qo is a field of research that uses semiclassical and quantum mechanical physics to investigate phenomena involving light and its interactions with matter at submicroscopic levels. Visualizing quantum mechanics in phase space arxiv.
The combination of phase space methods with cavity. Schleich illustrates the properties of quantum states with the help of the wigner. Schleichs quantum optics in phase space is a new contribution to physics travel literature, and it deserves praise as a guidebook. Quantum optics in phase space pdf quantum optics in phase space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase. The nonlinearity is typically observed only at very high light intensities values of atomic electric fields, typically 10 8 vm such as those provided by lasers. The canonical hamiltonian of quantum optics is the jaynescummings model, originally proposed to describe spontaneous emission 47, 111. As a celebration of the year of light, we present a brief history of the use of phase space distributions in optics.
Apr 11, 2012 in this tutorial, we introduce the basic concepts and mathematical tools needed for phase space description of a very common class of states, whose phase properties are described by gaussian wigner functions. Linear ray and wave optics in phase space 1st edition. If the quadratures are functions of time then the optical. It prompted the rapid exploitation of the phase space approach by c. Modern in style and didactically skillful, quantum optics in phase space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. In the phase space formulation, the phase space distribution may be treated as the fundamental, primitive description of the quantum system, without any reference to wave functions or density matrices. Each point in the optical phase space corresponds to a unique state of an optical system. From quantum optics to quantum technologies sciencedirect. Quantum optics in phase space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space.
It is also important in signal processing and the mathematics of algebraic deformation. Schleichquantum optics in phase spacewileyvch berlin weinheim new york chichester brisbane. Quantum optics in the phase spacea tutorial on gaussian states. The concept of phase space was developed in the late 19th century by. Quantum optics in cavities, phase space representations, and the classical limit of quantum mechanics. Thomas l curtright, cosmas k zachos submitted on 27 apr 2011, last revised 26 dec 2011 this version, v2. As a celebration of the year of light, we present a brief history of the use of phasespace distributions in optics. Quantum mechanics in phase space world scientific series in. Furthermore, the gaussian properties of these states may be preserved also during the dissipative evolution through noisy channels, both markovian and nonmarkovian. Quantum optics and laser experiments 6 physical picture of field parameter registration in the quantum case can be reduced to the problem of photon detection. Introductory quantum optics this book provides an elementary introduction to the subject of quantum optics, the study of the quantummechanical nature of light and its interaction with matter.
Today, it finds ap plications in current research in various branches of physics ranging from quantum optics11 and quantum chaos12 to nu clear. In this tutorial, we introduce the basic concepts and mathematical tools needed for phasespace description of a very common class of. May 23, 2017 in quantum optics, the optical phase space is a useful tool in which all quantum states of an optical system can be represented. Quantum optics is the study of the intrinsically quantum properties of light. Quantum optics in cavities, phase space representations. In this tutorial, we introduce the basic concepts and mathematical tools needed for phase space description of a very common class of states, whose phase properties are described by gaussian wigner functions. This cited by count includes citations to the following articles in scholar. Modern in style and didactically skillful, quantum optics. It is demostrated that, for hamiltonian systems in this representation the only welldefined quantization map. Quantum optics deals with processes and phenomena where the quantum states of the electromagnetic field are of central relevance.
Quantum optics in the phase space a tutorial on gaussian states. It originally provides a bridge between classical and quantum. Isbn 352729435x buy at amazon travel literature has its own vague rules and guidelines, flexible enough to include books that are little more than checklists of recommended museums, sights, and restaurants, along with careful descriptions of. For any such system, a plot of the quadratures against each other, possibly as functions of time, is called a phase diagram. Quantum optics describes modern highprecision experiments that often probe the very fundamentals of quantum mechanics.
However, they find that phase measuring experiments respond to a different operator. Master equations in phase space fotiulation of quantum optics g. The result is a remarkably concise yet comprehensive and accessible text and reference book an inspiring source of information. Agarwal department of physics and astronomy, university of rochester, rochester, eevtj york 146z7 received 12 august 1968. You will learn about quantization of light, formalism. Crt journal of experimental and theoretical physics established by e. Quantum optics in cavities, phase space representations, and. Giving wideranging references, it enables students to study and solve problems with modern scientific literature. Giving wideranging references, it enables students to. Quantum optics in the phase space a tutorial on gaussian states s. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information. Quantum optics in cavities, phase space representations, and the.
Modern in style and didactically skillful, quantum optics in phase space prepares students for their own research by presenting detailed derivations, many illustrations and a large set. The module considers the quantum effects of simple optical. Particularly notable was the series of papers with girish agarwal beginning in 1970 on phase space methods in statistical optics. Quantum optics in phase space presents the subject of quantum optics as transparently as possible. Special states from the truncated hilbert space of optical oscillator. Giving wideranging references, it enables students to study and solve problems with modern.
The authors consider the commonly employed phase operators due to susskind and glogower 1964 and their extension to unitary exponential phase operators. Pdf statistical methods in quantum optics 1 download full. Introduction it is well known that the uncertainty principle makes the concept of phase space in quantum mechanics problematic. Hybrid quantum computation in quantum optics arxiv vanity. At christma of 199s w6 e finall signey ad contrac ant michaed wals extremel y relieved. Diracs prescription for quantisation does not lead to a unique phase operator for the electromagnetic field.
172 405 567 885 202 1182 1224 742 738 828 203 649 273 1527 1519 688 1095 134 641 1286 333 74 756 427 224 1262 224 496 614 1361 931 1281 1200