Entanglement of amplitude and optical phase involved in the EPR eigenstate

By noticing that although single-mode Susskind-Glogower phase operator does not commute with photon number operator, two-mode nonlinear phase operator commutes with number-difference operator. We reveal that the common eigenstate [eta\ of two-particles' relative coordinate and total momentum involves the entanglement between phase and amplitude. We also reveal entanglement between number difference and amplitude inherent in the state \D, \eta\], where \D, \eta\] = integrald alpha /2 pi\eta = \eta\(ei alpha)]e(-iD alpha) is a deductive state of \eta].