Quantum-Optical States in Finite-Dimensional Hilbert Space. I. General Formalism

  1. Myron W. Evans
  1. Adam Miranowicz1,2,
  2. Wiesław Leoński2 and
  3. Nobuyuki Imoto1

Published Online: 13 MAR 2002

DOI: 10.1002/0471231479.ch3

Modern Nonlinear Optics, Part I, Volume 119, Second Edition

Modern Nonlinear Optics, Part I, Volume 119, Second Edition

How to Cite

Miranowicz, A., Leoński, W. and Imoto, N. (2002) Quantum-Optical States in Finite-Dimensional Hilbert Space. I. General Formalism, in Modern Nonlinear Optics, Part I, Volume 119, Second Edition (ed M. W. Evans), John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471231479.ch3

Author Information

  1. 1

    CREST Research Team for Interacting Carrier Electronics, School of Advanced Sciences, The Graduate University for Advanced Studies (SOKEN). Hayama, Kanagawa, Japan

  2. 2

    Nonlinear Optics Division, Institute of Physics, Adam Mickiewicz University, Poznań Poland

Publication History

  1. Published Online: 13 MAR 2002
  2. Published Print: 28 SEP 2001

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. I. Prigogine3,4 and
  2. Stuart A. Rice5

Series Editor Information

  1. 3

    Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas, USA

  2. 4

    International Solvay Institutes, Université Libre de Bruxelles, Brussels, Belgium

  3. 5

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

ISBN Information

Print ISBN: 9780471389309

Online ISBN: 9780471231479

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Keywords:

  • finite-dimensional (FD) Hilbert space;
  • infinite-dimensional (ID) Hilbert space;
  • finite-dimensional (FD) quantum-optical states;
  • coherent states;
  • discrete Wigner function

Summary

This chapter presents two essentially different constructions of harmonic oscillator states in a finite-dimensional (FD) Hilbert space. The authors propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, they bring together several known FD quantum-optical states, including FD coherent states, FD phase coherent states, FD displaced number states, FD Schrödinger cats, and FD squeezed vacuums. The discrete Wigner function is applied in order to demonstrate intriguing properties of the various states.