On the coherence veryfication of the continuous variable state in Fock space
Almost all novel observable phenomena in quantum optics are related to the quantum coherence. The coherence here is determined by the relative phase inside a state. Unfortunately, so far all the relevant experimental results in quantum optics are insensitive to the phase information of the coherent state. Lack of phase information may cause serious consequences in many problems in quantum optics. For example, an ensemble of two mode squeezed states is a classical ensemble if the phase in each state is totally random; but it is a non-classical ensemble if the phase in each state is fixed. As a timly application, verification of this type of phase information in an ensemble of two mode squeezed states from the conventional laser is crucial to the validity of the continuous variavable quantum teleportation(CVQT) experiment. Here we give a simple scheme to distinguish two different ensemble of states: the Rudolph-Sanders ensemble, by which each squeezed states emitted has a uniform distribution from $0-2\pi$ on the phase value; and the van Enk-Fuchs ensemble, which emmits identical states with a fixed(but unknown) phase for every state. We believe our proposal can help to give a clear picture on whether the existing two mode squeezed states so far are indeed non-classical states which can be used as the entanglement resource.