What I miss in this article is what it implies that time is cloaked. What does is it mean and where can it be used for?
We all learn about causality. Things don't just happen without being there being some kind of reversible action. If an ice cube melts, that's a time reversible aspect of physics. Basically if you could run time backwards like a video in reverse, you would see the ice unmelt.
In another instance, imagine a block of ice in the middle of a star. There's no way that a chunk of ice can just appear in a star. Now, that's not to say its impossible for such a chunk to be there. But you can trace back a line of actions that led to it being there, ranging from the debris of the spacecraft that contained it to the launch pad on a planet orbiting nearby, to all of the patterns of matter and information encompassing the civilization that built and launched it in the first place.
So if I'm understanding this correctly, the temporal cloak effectively allows stuff to happen inside it that isn't detectable from the outside. To stretch my last analogy a bit, imagine you put such a temporal cloak around the entire civilization leading up to where the ice ends up in the star. To an outside observer, say some aliens doing a research study on our star, all of a sudden they would detect the block of ice in the star but not have any idea where it came from.
The problem with your analogy is that the debris from the spaceship, etc. would still be visible to an observer after the fact. A better analogy would be this:
The aliens point a camera at our entire civilization. Ignoring the fact that this cloak works on the order of monumentally smaller scales than civilizations and the time it takes to put an ice chunk in a star, we use the cloak while we put an ice chunk in a star. The aliens would see our civilization jump from a state with no ice chunk in a star to one with an ice chunk in a star. Assuming that their measuring devices are up to the task, they would still be able to find all the spaceship debris, etc.
here's the relevant bit:
Alternatively, it may be desirable to cloak the occurrence of an event over a finite time period, and the idea of temporal cloaking was proposed in which the dispersion of the material is manipulated in time to produce a "time hole" in the probe beam to hide the occurrence of the event from the observer. This approach is based on accelerating and slowing down the front and rear parts, respectively, of the probe beam to create a well controlled temporal gap in which the event occurs so the probe beam is not modified in any way by the event.
Time-space duality represents the analogy between diff raction and dispersion that arises from the mathematical equivalence between the equations describing the diff raction of a beam of light and the one-dimensional temporal propagation of a pulse through a dispersive medium [17,18]. Similar to a spatial lens that imparts a quadratic phase in space, a time-lens can be implemented that produces a quadratic phase shift in time [19{21]. This time-lens can, for example, magnify [22] or compress [23] signals in time and has an equivalent of the lens law. Time-lenses can be created with an electro-optic modulator [18] or via a parametric nonlinear optical process such as four-wave mixing (FWM) with a chirped pump wave [19,20]. In the latter case the signal wave is converted to an idler wave with a linear frequency shift in time (i.e., a quadratic phase in time) [21,22].
I understand this to mean that the passage of time in observed space can be slowed down relative to an observer, rather as happens when observing a body falling into a black hole.