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We investigate how entangled coherent states and superpositions of lowintensity coherent states of non-Gaussian nature can be generated vianon-resonant interaction between either two linearly or circularly polarizedfield modes and an ensemble of X-like four-level atoms placed in an opticalcavity. We compare our results to recent experimental observations and arguethat the non-Gaussian structure of the field states may be present in thosesystems.

Non-Gaussian two-mode squeezing and continuous variable entanglement of linearly and circularly polarized light beams interacting with cold atoms