Barnett / Vaccaro The Quantum Phase Operator

A Review
Erscheinungsjahr 2007
ISBN: 978-1-58488-761-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 504 Seiten

Reihe: Series in Optics and Optoelectronics

Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory.

Bringing together vital works that have been published on the subject, the book presents the ideas that led to the current theory of the phase operator and provides a complete picture of the progress that has followed since then. With introductions by the editors to put the papers in context and unify the content of the book, each section focuses on a different aspect of phase operators. The editors also chronologically organize the papers within the sections to highlight how scientific thought has evolved, if at all, over time.

A collection of important relevant material that is scattered throughout the literature, this volume chronicles the history of the various facets of the quantum phase operator, promoting a solid foundation in quantum theory.

Zielgruppe

Researchers in optics, quantum optics, optoelectronics, and mathematical physics; graduate students in optics and quantum optics.

Autoren/Hrsg.

Barnett, Stephen M.

Vaccaro, John A.

Inhaltsverzeichnis

PRECURSORS
The quantum theory of the emission and absorption of radiation
Amplitude and phase uncertainty relations
On the uncertainty relation for Lz and ø
On the commutator [Lz, ø]
Quantum mechanical phase and time operator
The quantum theory of light
Phase in quantum optics

THE PHASE OPERATOR

Unitary phase operator in quantum mechanics
Hermitian phase operator ? in the quantum theory of light

On the Hermitian optical phase operator
Phase properties of the quantized single-mode electromagnetic field
Quantum theory of rotation angles
Quantum optical phase

MATHEMATICAL ELABORATIONS

Wigner function for number and phase
Quantum optical phase and canonical conjugation
Limiting procedures for the optical phase operator
Consistency of quantum descriptions of phase
Canonical and measured phase distributions
Number-phase Wigner function on Fock space
Antinormal ordering of phase operators and the algebra of weak limits
Pegg-Barnett operators of infinite rank
Phase operators on Hilbert space

PHASE DYNAMICS AND UNCERTAINTIES

Phase properties of squeezed states of light
A new approach to optical phase diffusion
Quantum theory of optical phase correlations
Physical number phase intelligent and minimum uncertainty states of light
Phase optimized quantum states of light
Phase fluctuations and squeezing
Phase properties of linear optical amplifiers

THEORY OF PHASE MEASUREMENT
Phase measurements
On measuring extremely small phase fluctuations
Adaptive phase measurements of optical modes: Going beyond the marginal Q distribution
Phase measurements by projection synthesis
Quantum phase distribution by projection synthesis
Measuring the phase variance of light
Quantum phase distribution by operator synthesis
Single-shot measurement of quantum optical phase
Binomial states and the phase distribution measurement of weak optical fields

EXPERIMENTAL DEMONSTRATIONS

Experimental determination of number-phase uncertainty relations
Measurement of number-phase uncertainty relations for optical fields
Adaptive homodyne measurement of optical phase
Uncertainty principle for angular position and angular momentum
Minimum uncertainty states of angular momentum and angular position

TIME

Time in a quantum mechanical world
Complement of the Hamiltonian

REFERENCES

APPENDIX