An approximate effective beamsplitter interaction between light and atomic ensembles

We present a method for designing a lossless beamsplitter interaction between an incident field mode and an atomic spin ensemble. This interaction is only approximately true for weak quantum non-demolition coupling between light and atomic ensemble and for a subset of particular fields and atomic states. We explore the accuracy of this approximation for various Gaussian states in an ideal pure state description. We also discuss possible applications of this interaction including entanglement concentration of entangled atomic ensembles.