Breakdown of the cross-Kerr scheme for Photon Counting
  We show, in the context of single photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarisability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single photon applications. Our results are presented in the context of a transmon in a one dimensional microwave waveguide, but the conclusions also apply to optical systems. 
Bixuan Fan, Anton F. Kockum, Joshua Combes, G\"oran Johansson, Io-chun   Hoi, Christopher Wilson, Per Delsing, G. J. Milburn...
quant-ph