Single photon quantum non-demolition measurements in the presence of inhomogeneous broadening

Electromagnetically induced transparency (EIT) has often been proposed for generating nonlinear optical effects at the single photon level; in particular, as a means to effect a quantum non-demolition measurement of a single-photon field. Previous treatments have usually considered homogeneously broadened samples, but realizations in any medium will have to contend with inhomogeneous broadening. Here we reappraise an earlier scheme (Munro et al 2005 Phys. Rev. A 71 033819) with respect to inhomogeneities and show an alternative mode of operation that is preferred in an inhomogeneous environment. We further show the implications of these results on a potential implementation in diamond-containing nitrogen-vacancy colour centres