Methods in theoretical quantum optics is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas if quantum optics. This book is ideal for students who have already explored the basics of the quantum theory of light and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics, but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.

Methods in Theoretical Quantum Optics (Oxford Series in Optical and Imaging Sciences)

Science & Math

Barnett, Stephen M.

Radmore, Paul M.

Chemistry

Clarendon Press

This work presents the mathematical methods widely used by workers in the field of quantum optics. It deals with the physical assumptions which lead to the models and approximations employed, but the text is meant to give a firm grounding in those techniques needed to derive analytical solutions to problems. Based on teachings by the authors, most of the text has been tested on students.

Reference

Words, Language & Grammar

Recent experimental progress has enabled cold atomic gases to be studied at nano-kelvin temperatures, creating new states of matter where quantum degeneracy occurs - Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This book presents the phase space theory approach for treating the physics of degenerate quantum gases, an approach already widely used in quantum optics. However, degenerate quantum gases involve massive bosonic and fermionic atoms, not massless photons. The book begins with a review of Fock states for systems of identical atoms, where large numbers of atoms occupy the various single particle states or modes. First, separate modes are considered, and here the quantum density operator is represented by a phase space distribution function of phase space variables which replace mode annihilation, creation operators, the dynamical equation for the density operator determines a Fokker-Planck equation for the distribution function, and measurable quantities such as quantum correlation functions are given as phase space integrals. Finally, the phase space variables are replaced by time dependent stochastic variables satisfying Langevin stochastic equations obtained from the Fokker-Planck equation, with stochastic averages giving the measurable quantities. Second, a quantum field approach is treated, the density operator being represented by a distribution functional of field functions which replace field annihilation, creation operators, the distribution functional satisfying a functional FPE, etc. A novel feature of this book is that the phase space variables for fermions are Grassmann variables, not c-numbers. However, we show that Grassmann distribution functions and functionals still provide equations for obtaining both analytic and numerical solutions. The book includes the necessary mathematics for Grassmann calculus and functional calculus, and detailed derivations of key results are provided.

Phase Space Methods for Degenerate Quantum Gases (International Series of Monographs on Physics)

Dalton, Bryan J.

Jeffers, John

Physics

Oxford University Press

Spin angular momentum of photons and the associated polarization of light has been known for many years. However, it is only over the last decade or so that physically realizable laboratory light beams have been used to study the orbital angular momentum of light. In many respects, orbital and spin angular momentum behave in a similar manner, but they differ significantly in others. In particular, orbital angular momentum offers exciting new possibilities with respect to the optical manipulation of matter and to the study of the entanglement of photons. Bringing together 44 landmark papers, Optical Angular Momentum offers the first comprehensive overview of the subject as it has developed. It chronicles the first decade of this important subject and gives a definitive statement of the current status of all aspects of optical angular momentum. In each chapter the editors include a concise introduction, putting the selected papers into context and outlining the key articles associated with this aspect of the subject.

Optical Angular Momentum (Optics & Optoelectronics)

Allen, L.

Padgett, Miles J.

CRC-Press

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