Stokes--anti-Stokes Correlations in Raman Scattering from Diamond Membranes

We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in diamond membranes. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon, that is, the phonon excited by the S process is consumed in the aS process. We show that the intensity cross-correlation $g_{\rm S,aS}^{(2)}(0)$, which describes the simultaneous detection of Stokes and anti-Stokes photons, decreases steadily with laser power as $1/{\rm P_L}$. Contrary to many other material systems, diamond exhibits a maximum $g_{\rm S,aS}^{(2)}(0)$ at very low pump powers, implying that the Stokes-induced aS photons outnumber the thermally generated aS photons. On the other hand, the coincidence rate shows a quadratic plus cubic power dependence, which indicates a departure from the Stokes-induced anti-Stokes process.