Generation of pair coherent state using weak cross-Kerr media

We firstly give a nonlocal method for generating pair coherent state with two traveling wave fields in distinct districts. The experimental scheme proposed is based on a two-mode photon number matching process, which employs weak cross-Kerr media and on/off detection. Then we discuss the details for implementing this scheme, showing that it is robust against the low quantum efficiency of photon detectors and offers nearly perfect pair coherent states. Finally, we show how a two-mode Schrödinger cat state and a generalized two-mode correlated photon number state can be prepared via this matching process.