Towards 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-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. 
S. L. Christensen, J. B. B\'eguin, H. L. S{\o}rensen, E. Bookjans, D.   Oblak, J. H. M\"uller, J. Appel and E. S. Polzik
quant-ph physics.atom-ph