We report on criteria to detect entanglement between the light modes of twocrossed optical cavities by analyzing the transverse deflection patterns of anatomic beam. The photon exchange between the modes and the atoms occurs aroundthe overlapping nodes of associated standing waves, which generates thetwo-dimensional (2D) version of the Optical Stern-Gerlach (OSG) effect. In thisoptical cross-cavity setup, we show that the discrete signatures of the fieldsstates, left in the momentum distribution of the deflected atoms, may revealentanglement for a certain class of two-mode states. For a single photon, wepresent the possibility of quantifying entanglement by the rotation of themomentum distribution. For a larger number of photons, we demonstrate thatquantum interference precludes the population of specific momentum statesrevealing maximum entanglement between the light modes.
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