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

TL;DR

This paper reexamines EIT-based quantum non-demolition measurements in inhomogeneously broadened media, proposing an alternative approach suitable for diamond NV centers, and demonstrates feasibility with small-scale waveguide structures.

Contribution

It presents a new mode of operation for EIT-based QND measurements in inhomogeneous environments, specifically tailored for diamond NV centers, expanding practical implementation options.

Findings

Inhomogeneous broadening affects EIT-based QND schemes.

An alternative operational mode is more effective in inhomogeneous media.

Small diamond waveguides with 200 NV centers can enable QND measurements.

Abstract

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 \textit{et al.} Phys. Rev. A \textbf{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 $200 \mu\mathrm{m}$ 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.