Toward quantum state tomography of a single polariton state of an atomic ensemble

We present a proposal and a feasibility study for the creation and quantum state tomography of a single polariton state of an atomic ensemble. The collective non-classical and non-Gaussian state of the ensemble is generated by detection of a single forward-scattered photon. The state is subsequently characterized by atomic state tomography performed using strong dispersive light-atom interaction followed by a homodyne measurement on the transmitted light. The proposal is backed by preliminary experimental results showing projection noise limited sensitivity and a simulation demonstrating the feasibility of the proposed method for the detection of a non-classical and non-Gaussian state of the mesoscopic atomic ensemble. This work represents the first attempt at hybrid discrete-continuous variable quantum state processing with atomic memories.