  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.
