Femtosecond Dynamics of a Polariton Bosonic Cascade at Room Temperature. F. Chen, H. Zhou, H. Li, J. Cao, S. Luo, Z. Sun, Z. Zhang, Z. Shao, F. Sun, B. Zhou, H. Dong, H. Xu, H. Xu, A. Kavokin, Z. Chen and J. Wu in Nano Lett. 22:2023 (2022).  What the paper says!?

This is an important work which reports (I think) the first experimental realization of bosonic cascade. Namely, it reports on the

experimental realization of bosonic cascades, where stimulated transitions in a ladder of equidistant energy levels are expected to result in the generation of coherent radiation³¹ and nonclassical light.³²

Specifically:

In this letter, we visualize the femtosecond dynamics of stimulated transitions of exciton−polaritons between the condensates formed by whispering gallery modes (WGM) of a ZnO microwire

And:

We demonstrate a room temperature bosonic cascade based on a one-dimensional (1D) ZnO microcavity. In our experiments, polariton condensates subsequently occupy four neighboring quantum states in a quasi-equidistant energy spectrum.

There are previous works that showed the equidistant spacing (cf. here) but the bosonic cascading was not highlighted. Chinese diplomacy:

Attempts to the experimental realization of these effects with use of parabolic quantum wells embedded in planar microcavities³³ were not crowned by a decisive success so far.

They are

using the femtosecond angle-resolved spectroscopic imaging (FARSI) technique

which allows them to

boost up the time resolution down to femtoseconds

They measure $g^{(2)}$ and see that as the "demonstration" of bosonic cascade:

The mechanism of bosonic cascade is demonstrated by the extracted second-order time correlation factor g⁽²⁾(0) for all the LP branches.

The average is taken over time (so, over $t$), not over ensembles.

They supposedly describe the dynamics with QBME. They don't quote my 2004 papers (such as Ref. ) but they do quote, of course, the Liew et al. paper, so it's fine. However in the Supplementary, the dynamics is standard Boltzmann Equations, not QBME (see Eqs. (2)‒(8)). So it's unclear how they got their $g^{(2)}$! (bosonic cascade they could have in the mean field, but not hyperbunching). The theory part of the paper is, overall, a bit shaky and vague.

The cascade is advertised as involving four levels, but it starts on the 3rd one (not 4th), so it's really a 3-step cascade—one step only above the minimum (still good enough).

P3 branch can be originated from the fact that the P3 branch lies around the optimized wavelength range with the maximum Q-factor. The succeeding signals on P2 and P1 are in agreement with the theoretical model accounting for the cascading effect

The bosonic cascading seems compelling, but i) they don't detect the THz emission, which is arguably the interesting part, and ii) their $g^{(2)}(\tau) = \frac{\langle I(t)I(t+\tau)\rangle}{\langle I(t+\tau)\rangle\langle I(t)\rangle}$ integrates out time from something transient, so even in BE they could have superbunching, that has nothing to do with the QBME one, that they might not even include theoretically. Ironically, the higher bunching (small) from the pink-data in P1, which they cannot account for, might be the real bosonic superbunching, while 2 and 3 are just standard BE relaxation (also cascading, as I said).

The $g^{(2)}$ for the 4th one is <2 which I wouldn't worry about except that their theory also reproduces this! Then it's not clear why they say this «might be attributed». Theory should make it clear [if theory would be clear itself] and they explain as cothermal initial condition and insufficient time for the dynamics.

There's an awkward double use of "strong coupling" (also as strong interactions).

In conclusions: a nice, seminal experimental demonstration of bosonic cascades, but with various holes—and possibly, flaws—in its understanding and theoretical description.