This headline is deeply misleading. It is true that energy states are quantized. It does NOT follow that the transition between them is "instantaneous". The transition has always been known to be gradual, but the "gradualness" is not a smooth transition in the energy of the system, it's a smooth transition between being in one energy state to being in a superposition of two energy states to being entirely in the second energy state. That process plays out over (typically a very short but nonetheless non-zero) time. This has been known since the very beginning of QM.
What's news here is that this transition, which has always been predicted by theory, has been experimentally observed for the first time.
I have questions: you describe the change of states of particle as
"a smooth transition between being in one energy state to
being in a superposition of two energy states to being
entirely in the second energy state."
At the terminus of this transition, is the particle no longer in a superposition? IE there is now a 100% chance it's in the second state and 0% chance that it's in the original state?
If so, does that imply that the function of the particle's state (with respect to time) is discontinuous? Since there's a point at which it goes from being a superposition to exactly 0%.
The first answer is that a system is never 100% in any particular state because that would violate the uncertainty principle. When we speak of a system "definitely" being in a particular state that's an approximation/simplification. It actually means that the system is in a superposition of some range of states that for all intents and purposes we can treat as being the same, and the probability of it being in a state that cannot be treated the same for all intents and purposes is so close to zero we can ignore that.
The second answer is that whether or not a system is in a superposition depends on your point of view. A system can only ever be in a "single state" (according to the above approximation) with respect to some observable, and if it is in a single state with respect to that observable then it is necessarily in a superposition with respect to the complementary observable, e.g. a particle that is in a definite state with respect to position is necessarily in a superposition with respect to velocity.
So the whole process is everywhere and always continuous.
I was extremely confused by the proposition because yes, it's known that energy states are quantized but I've never heard of any popular literature before suggesting the transition itself was quantized. Intuitively it doesn't even make sense that it could be quantized.
I can't figure out what the antecedent of "this" is. But like I said, the fact that quantum jumps are not instantaneous is not and has never been controversial AFAIK.
UPDATE: It turns out that in the VERY early days of QM, some researchers (notably Niels Bohr) thought that quantum jumps were instantaneous. But it has been known and universally accepted that they are not for decades now.
What's news here is that this transition, which has always been predicted by theory, has been experimentally observed for the first time.