The quantum phase problem: a critical review

Phase properties of squeezed states of light

Simple physical ideas lead us to identify the phase of a single mode of the electromagnetic field as the quantity conjugate to the photon number. This in turn leads to the form of the phase probability distribution. The phase operator cannot be represented in the conventional infinite dimensional Hilbert space but can be expressed by means of a finite-dimensional state space together with a suitable limiting procedure. We introduce the Hermitian optical phase operator and describe its most important properties.

Quantum Optical Phase

Exact phase calculations for general squeezed states are presented. Results are given for different phase definitions, using number-state expansions. It is shown that the calculations based on the measured-phase-operator formalism leads to contrasting behavior compared with those based on the Susskind–Glogower, Lerner–Lynch, and Hermitian-phase-operator formalisms.

Phase properties of squeezed states

Publisher Summary This chapter discusses the quantum phase properties of nonlinear optical phenomena. Optical fields produced in nonlinear optical processes have specific phase properties, which depend on the nonlinear process in which the field is produced, and on the state of the field before it undergoes the nonlinear transformation. The phase properties of a two-mode field are constructed from the single-mode phases. The chapter focuses on the real fields that can be generated in practice in various nonlinear optical processes. The phase properties can be described based on two different formalisms that include the Pegg–Barnett Hermitian phase formalism and the formalism based on s-parametrized phase distributions. Using the examples of real field, the chapter discusses the similarities and differences that are encountered when various phase distributions are applied to describe a particular field state.

Hong-Yi Fan

Papers

An exact calculation of the expectation values of phase operators in squeezed states