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The generation of an entangled coherent state is one of the most importantingredients of quantum information processing using coherent states. Recently,numerous schemes to achieve this task have been proposed. In order to generatetravelling-wave entangled coherent states, cross phase modulation, optimized byoptical Kerr effect enhancement in a dense medium in an electromagneticallyinduced transparency (EIT) regime, seems to be very promising. In thisscenario, we propose a fully quantized model of a double-EIT scheme recentlyproposed [D. Petrosyan and G. Kurizki, {\sl Phys. Rev. A} {\bf 65}, 33833(2002)]: the quantization step is performed adopting a fully Hamiltonianapproach. This allows us to write effective equations of motion for twointeracting quantum fields of light that show how the dynamics of one fielddepends on the photon-number operator of the other. The preparation of aSchr\"odinger cat state, which is a superposition of two distinct coherentstates, is briefly exposed. This is based on non-linear interaction viadouble-EIT of two light fields (initially prepared in coherent states) and on adetection step performed using a $50:50$ beam splitter and two photodetectors.In order to show the entanglement of a generated entangled coherent state, wesuggest to measure the joint quadrature variance of the field. We show that theentangled coherent states satisfy the sufficient condition for entanglementbased on quadrature variance measurement. We also show how robust our scheme isagainst a low detection efficiency of homodyne detectors.Comment: 15 pages, 9 figures; extensively revised version; added Section

Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime