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

Electromagnetically induced transparency (EIT) has been often 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 realisations in any medium will have to contend with inhomogeneous broadening. Here we reappraise an earlier scheme [Munro et al. Phys. Rev. A 71, 033819 (2005)] 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. Our modelling shows that single mode waveguide structures of length 200 μm in single-crystal diamond containing a dilute ensemble of NV− of only 200 centres are sufficient for quantum non-demolition measurements using EIT-based weak nonlinear interactions. PACS numbers: 42.50.Gy,42.50.-p, 42.50.Ex