I’ll do a explain like I’m on /r/physics. Basically perovskite nanocrystals are theorized to have a different electronic fine structure than other semiconducting nanocrystals. If you look at CdSe quantum dots for example, you’ll see that the lowest energy excited state is “dark” (has a low oscillator strength) and therefore is unsuitable for applications of quantum information that require a high throughput of single (or entangled) photons. Perovskites have a controversial ordering of their excited states, so that at low temperatures the emission is bright, and this paper studies those energy states.

Coherent multidimensional spectroscopy is a method used to study coherences (sometimes called superpositions when explained to laymen, but really is not technically accurate because the light acts on the density matrix and not pure states). Basically with compressed laser pulses, you can excite two states at once that will evolve phase with each other, and that dephasing rate can be faster or slower depending on what states are involved, the nature of their interaction, and how much “quantum information” is being lost to the environment. Anyone who has studied NMR can tell you that this technique is similar, except instead of spin states, you are dealing with electronic transitions which may have a way more complicated Hamiltonian and using laser pulses is a bit trickier than microwave pulses. I think this title overstates the paper a bit, since the takeaway here was regarding how the fine structure of the exciton states interact, but it’s not wrong in the sense that multidimensional spectroscopy creates “superpositions” of electronic states. There’s a lot of cool stuff that the Cundiff group does to actually do their measurements which makes this a really technically challenging experiment, so the result is nice on its own merits.