Su­per­lu­mi­nal in­ter­ac­tions 
The fact that photons emitted from an electric-dipole active atom
  cannot be spatially localized better than to the near-field zone of
  the atom is seen as the origin of genuine superluminality.

http://www.ncbi.nlm.nih.gov/pubmed/11309086
Question: What are superluminal interactions? No detailed information available on the web. I know that electromagnetic waves cannot be spatially localized better that to the near-field zone of the location where they are created. 
 A: "Superluminal Interactions" is a fancy way (and, IMO if you look at the Latin roots, a not too accurate way) of saying "faster than lightspeed interactions". 
It is the notion that objects or events at a spacelike separation in spacetime from one another can influence each other's physics or transfer information.
In flat, Minkowskian spacetime, the "proper time" $\Delta \tau$ separating two points ('events") in spacetime (in SI units) is 
$$\Delta \tau = \sqrt{(c\,\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2-(\Delta z)^2}\,c^{-1}$$
where $\Delta t$ is the difference between the time co-ordinates and $\Delta x,\,\Delta y,\,\Delta z$ the differences between the spatial co-ordinates of the two events.
Events with $(c\,\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2-(\Delta z)^2 < 0$ are called "spacelike separated", $\Delta \tau$ would be imaginary any signal / interaction between the two would have to travel faster than lightspeed. Those with $(c\,\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2-(\Delta z)^2 > 0$ are called "timelike" separated and those on the same light cone with $(c\,\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2-(\Delta z)^2 = 0$ are sometimes called "lightlike" separated.
Closely linked to this notion (indeed its opposite) is the notion of locality (this is a word you should also look up): that only timelike separated events can influence one another. All physically valid theories are believed by most working physicists to be local, which is one of the reasons why relativity and quantum mechanics (particularly the ideas explored in relation to Bell's inequality) sit so uneasily together. Most physicists are unwilling to give up the notion of locality, so most interpret these results as saying that "counterfactual definiteness" or "counterfactual reality" (the idea that one can talk meaningfully about what an experimental outcome is "going to be" before the experiment is done) is meaningless in the relevant situations.
If spacelike separated events can influence one another, then there exists a Lorentz-transformed (boosted) inertial frame of reference wherein their order in time is swapped. That is, if there is a causal relationship between the two, say "$A$" gives rise to or causes "$B$", then there are inertial reference frames wherein the time order of $A$ and $B$ is reversed and therefore causality is violated. This is why most physicists believe "Superluminal Interactions" mean any theory allowing them is all going to end badly!
So, in summary, you should look up "locality" in relation to physical theories,  "violation of causality",  "Bell's theorem" and counterfactual definiteness" to further understand your notion of "Superluminal Interactions".
Afternote: I am not sure an article accepted by the Journal of Microscopy can be relied upon to discuss "superluminal interaction". This notion is well outside the usual ken of ideas dealt with in a journal like this (no slur meant to the Journal, there are some excellent articles on cutting edge microscopy therein). I would have to look carefully at the article to judge the soundness of their claims, but it sounds like something to be highly skeptical of.
