High visibility experimental demonstration of the relative-phase operator

Summary form only given. A single-mode quantum-phase operator cannot be simultaneously Hermitian and work in an unrestricted Hilbert-space, recently, work on finding the operator corresponding to the relative phase between two harmonic oscillators has been undertaken. In particular we suggested an experimental implementation of a generalization of the relative-phase operator derived by Luis and Sanchez-Soto (1993). The states defined by Luis and Sanchez-Soto are a two-mode generalization of the Pegg-Barnett single-mode phase eigenstates. The present experiment employed a scheme based on CW excitation of a type-II spontaneous parametric down-conversion crystal. The frequency degenerate photon pairs were generated colinearly in a single spatial mode. Due to the direct creation of the orthogonally polarized photon pairs, we can easily achieve a higher spatial mode-function overlap than in the previous experiment. A delay line between the horizontal and vertical basis was used in order to compensate for the linear dispersion, which makes the two orthogonally-polarized photons overlap in time, this together with the use of the CW excitation ensure a good temporal mode-function overlap.