  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-atoms 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 detection of a non-classical and
non-Gaussian state of the mesoscopic atomic ensemble. This work represents the
first attempt of hybrid discrete-continuous variable quantum state processing
with atomic ensembles.
