**Photophysics of quantum emitters in hexagonal boron-nitride nano-flakes**. M. K. Boll, I. P. Radko, A. Huck and U. L. Andersen in Opt. Express **28**:7475 (2020).

They characterize four emitters (A, B, C & D) from the same sample (hBN nano-flake), using $g^{(2)}(\tau)$ as a probe of relaxation dynamics. They correlate each photon arrival event from the raw data with all the other registered photons to compute $g^{(2)}(\tau)$ instead of a histogram of time delays (start-stop method) which becomes inaccurate at long times. They thus obtain a nice series of across-timescales, self-consistently normalized data.

They find nice shapes with rounded antibunching at small times and bunching shoulders. They explain the latter with *two* (as opposed to usually one) shelving states. They also study blinking. This is their basic picture (their Fig. 2):

The actual ground and excited states consist of a manifold of vibrational states, as pictured. But this plays no role at room temperature.

Their rate equations connect the two shelving-states to the ground state, i.e., is *not* a cascade:

They find the need for more than one-shelving state at higher powers, but not more than two is needed. Their system is already overfitted, especially as they also include background noise.

An interesting observation is that their $g^{(2)}(\tau)$ at small times, i.e., around $\tau=0$, does not exhibit the linear $\tau$ dependence of their model (and that of similar deshelving^{[1]}).

This is what they say about it:

We did not find, however, such "rounded shapes" in our analysis of how antibunching is spoilt.^{[2]} Could it be because their shelving model misses some aspects of photon liquefaction (there is a genuine cascade somewhere)?

## References

- ↑
__Correlations in light emitted by three-level atoms__. D. T. Pegg, R. Loudon and P. L. Knight in Phys. Rev. A **33**:4085 (1986).
- ↑
__Loss of antibunching__. J. C. López Carreño, E. Zubizarreta Casalengua, B. Silva, E. del Valle and F. P. Laussy in Phys. Rev. A **105**:023724 (2022).