Photophysics of single silicon vacancy centers in diamond: implications for single photon emission. E. Neu, M. Agio and C. Becher in Opt. Express 20:19956 (2012).  What the paper says?

This investigate the emission of single SiV centers (14 of them) and various aspects (including photostability, bleaching, blinking, etc., in some detail), but we are more interested in their analysis of the population dynamics to "explore the underlying level scheme".

The Authors extend (they say "verify") a hypothesis in a previous paper that an intensity-dependent de-shelving occurs. This is a scheme of their idea, that proposes "an intensity dependent de-shelving path":

In practice, it appears that the new path thus opened is not directly part of the model itself, but enters indirectly by altering some of the parameters $k_{ij}$. They otherwise still rely on the bi-exponential model of everybody (their Eq. (2)). The parameters there are constrained by the underlying model for the levels (their Eqs.(3-6)). They find a way to justify relaxing such constrains to get a better fit with what remains the bi-exponential shape. Assuming such effective parameters, they obtain better fits of their power-dependent data (their Fig. 4) It would be interesting to work out a model that actually inserts a genuine cascade in the de-shelving.

The deviation of $g^{(2)}(0)$ from zero is described by convolution with a Gaussian and addition of a background (this could be compared to our loss of antibunching).

There is a discussion of how pumping rates can bypass Einstein's coefficients:

the color center is excited to vibrationally excited states that typically relax within picoseconds to the vibrational ground state in the excited state (state 2). Thus, the intermediate pumping levels do not accumulate population, therefore efficiently suppressing stimulated emission and thus saturation on the pumping transition.