Photon phase operator

Steven B. Berger

Masashi Ban

The phase operator for a two-mode photon system is defined in terms of the relative-number states, and its property is investigated in detail. The phase operator thus defined has a unitary exponential form. It is shown that the average value and fluctuation of the phase operator, where one mode is in some physical state, such as a coherent or a squeezed state, and the other is in a vacuum state, are equivalent to those obtained by means of the Pegg–Barnett phase operator for a single-mode photon. The average value and fluctuation of the phase operator are calculated for coherent and squeezed states of a two-mode photon system.

Lu Dao

Based on the uncertainty relation the squeezing effects of measured phase operators are introduced.Using the measured phase operator introduced by Barnett and Pegg,the squeezing effects of the measured phase operators are discussed in piling up states of photon numbers.

Stephen Mark Barnett, David Thomas Pegg, Joan A. Vaccaro

Hong-Yi Fan, Q. Y. Liu

Based on the quantization of one-photon electromagnetic field described in terms of the Riemann-Silberstein complex vector {\\bf F}, we construct the eigenvector set of {\\bf F}, this set is orthonormal and complete, with which we introduce the phase operator for one-photon state. It is shown that this phase operator manifestly exhibits phase behaviour.

Joachim Piprek