As a quantum physicist: This might be an interesting experiment, but as far as the theory goes, this is exactly what is to be expected from standard quantum mechanics.
Quantum leaps being instantaneous would be a (possibly common) misconception.
The leap in a quantum leap is describing the notion of a discrete jump in measurement outcomes.
Okay, so you're a quantum physicist and you can answer my question!
My understanding of QM is that a quantum's system's state is suddenly and discontinuously changed by a measurement.
My understanding of this article is a bit confused, and I think that there are two possible things we could be seeing:
1. Quantum collapses of superpositions actually do take time ("This Changes Everything")
2. This particular quantum system is not actually being measured, but is oscillating in superposition in some odd way. ("Just a Particular System")
What's done in such an experiment is that we initialize a quantum state in a particular state (that this is possible is not actually obvious, but let's assume it's true) and then we make a lot of repeated measurements after different amounts of times.
So we're not talking about a single system, but instead about statistics about a set of measurements with systems that have been set up in the same initial state. (Each system only being measured once after a certain time after it's being set up).
The system is being measured, collapses DO take time, but this is not news to people who study certain branches of quantum information. The experiment confirming it though is a breakthrough.
Quantum leaps being instantaneous would be a (possibly common) misconception.
The leap in a quantum leap is describing the notion of a discrete jump in measurement outcomes.