On the Quantum Phase Operator for Coherent States

Abstract

In papers by Lynch [Phys. Rev. A41, 2841(1990] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase φ0 of the Pegg-Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Mandel [Phys. Rev. A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase taking post-selection conditions into account.

Generalized Weyl quantization on the cylinder and the quantum phase

“…Also, the existing experiments on the fluctuations of phase in coherent photon states seem to confirm the PB theory [34,35,36,37,38,39]. Nevertheless, the results are still under discussion and in fact, can hardly be considered as conclusive [40,41]. Consequently, yet other approaches to the problem of defining phase operator are possible.…”

Operator formalism for the Wigner phase distribution

“…We have already shown in the previous section, using the Fock state representation (6), that ρ † w (θ) = ρ w (θ) i.e., that the Wigner phase operator is hermitian. In this section, we will enumerate some more of the important properties of the Wigner phase operator.…”

“…Recently, there has been some debate over whether the Pegg-Barnett phase is the actual phase observed in experiments [6]. An alternative approach to defining a plausible quantum phase is, as the radial integral of one of the various phase space quasi-probability distributions [7,8].…”

“…Recently, there has been some debate over whether the Pegg-Barnett phase is the actual phase observed in experiments [6].…”

Uncertainty relations in quantum optics. Is the photon intelligent?

“…Remark The Heisenberg -Robertson uncertainty relation for the phase φ and the number of photons n or for the angle θ and the angular momentum L z were considered by many authors and formulae analogous to (2.42) have been found [30,40,43,[65][66][67]. The problem of physically acceptable definition of the uncertainty in angle θ or in phase φ was considered by D. Judge [65], H.S.…”