Quantum phase operator and statistics of the optical field

Weifeng Wu, Hong-Yi Fan

Masashi Ban

Lawrence N. Mertz

The phase operator is deemed to be the same as the position operator. Statistical rather than Heisenberg uncertainty must then couple the quadrature field operators.

Stephen Mark Barnett, PAUL M. RADMORE

Abstract This chapter considers methods for describing the quantum statistics of a single mode of the electromagnetic field. Some of these methods may be extended to multimode fields, and this is discussed in the last section of the chapter. The moment generating function is developed for studying the photon number statistics of a single field mode. The quantum properties of optical phase are described using the optical phase operator. The characteristic functions and quasi-probability distributions provide a complete statistical description of the field. These rely on the properties the coherent states and the Glauber displacement operator.

I. A. Deryugin, A. A. Vishenskii, Vitaliy N. Kurashov

Berthold‐Georg Englert, Krzysztof Wódkiewicz

The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of the recorded raw data a set of operational quantities that correspond to the intrinsic quantum-mechanical observable. This general approach is illustrated by the example of an operational measurement of the position and the momentum of a particle, as well as by an analysis of the operational detection of the phase of an optical field. For the latter we identify the intrinsic phase operator and report its explicit form.