Nonlocal entanglement of coherent states, complementarity, and quantum erasure

We describe a nonlocal method for generating entangled coherent states of a two-mode field wherein the field modes never meet. The proposed method is an extension of an earlier proposal C. C. Gerry, Phys. Rev. A 59, 4095 1999 for the generation of superpositions of coherent states. A single photon injected into a Mach-Zehnder interferometer with cross-Kerr media in both arms coupling with two external fields in coherent states produces entangled coherent states upon detection at one of the output ports. We point out that our proposal can be alternatively viewed as a “which path” experiment, and in the case of only one external field, we describe the implementation of a quantum eraser.