Phase operator in quantum optics

Abstract

A quantum mechanical phase operator is presented in terms of the relative-number states and defined on the direct product space of the two Hilbert spaces. It is shown that for states belonging to a certain subspace of the direct product space, this phase operator gives the same results as are obtained using the Pegg-Barnett phase operator. Furthermore, the phase operator reduces to the measurable phase operator within the framework of the quantum detection theory in another subspace.