Here's how Quanta breathlessly reported the result:
When quantum mechanics was first developed a century ago as a theory for understanding the atomic-scale world, one of its key concepts was so radical, bold and counter-intuitive that it passed into popular language: the “quantum leap.” Purists might object that the common habit of applying this term to a big change misses the point that jumps between two quantum states are typically tiny, which is precisely why they weren’t noticed sooner. But the real point is that they’re sudden. So sudden, in fact, that many of the pioneers of quantum mechanics assumed they were instantaneous.
A new experiment shows that they aren’t.This is mostly hype. While it is true that in the very early days of quantum mechanics some researchers (notably Niels Bohr) thought that quantum transitions were instantaneous, the fact that they aren't has been known for decades. What is new here is that this is the first time that this fact has been demonstrated experimentally. I don't want to detract from the technical accomplishment here in any way, it's a truly impressive experiment. But it's not the kind of conceptual breakthrough that the Quanta story implies. It's a totally expected result.
It is natural to conclude from the fact that energy states are quantized that the transition between them must happen instantaneously. Consider a system that transitions from energy state 0 to an adjacent energy state 1 (in some suitable units). It can't do it via a smooth transition between intermediate energy levels because these are physically impossible (that the whole point of quantum mechanics). So if a system is going to transition from 0 to 1 without occupying any energy state in between, the transition must be instantaneous, right?
Wrong. There is a different kind of "smooth" transition that a system can make between the 0 and 1 states, and that is via a superposition of the two states. Just as a particle can be in two different locations at the same time, it can be in two different energy states at the same time. To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states, i.e. it starts out entirely in state 0, and then transitions smoothly to being mostly in state 0 and a little bit in state 1, to being half in each state, to being mostly in 1 and a little bit in 0, to being entirely in 1. This has been known for decades, and is predicted by the math. You can even predict how fast the transition happens. For most common physical processes, like an atom absorbing or emitting a photon, the transition is really fast. But it's not instantaneous.
The tricky part is not figuring out that quantum transitions take time (well, OK, figuring it out is tricky too, but it's easy once you know how) but designing an experiment that demonstrates that the theory is correct. This is because any straightforward measurement of the energy of the system will always produce a result that shows the system is in one state or the other. The existence of superpositions can only be demonstrated indirectly, usually through interference effects. So to demonstrate the non-instantaneous nature of a quantum transition you have to do two things: first, you need to actually catch a system during a (typically very fast) transition and second, you need to come up with a way of getting the system to interfere with itself (or producing some other indirect effect that would not occur but for the existence of a superposition). That's what Minev et al. did.
The way they did it is really cool, but the advance here is an experimental one, not a theoretical one. They used a superconductor to produce a macroscopic quantum system that behaved like an atom in that it had a small number of discrete energy levels that it could transition between. Then they "tickled" this "atom" with microwaves and observed that the resulting response exhibited the kind of interference effects that would be expected if if were transitioning through superposition states. It's very cool, and a very impressive technical achievement, but it is in no way unexpected or surprising.