as the authors (Lijun Wang and peers) note: "Our experiment is not at odds with Einstein’s special relativity. The experiment can be well explained using existing physics theories that are consistent with Relativity. In fact, the experiment was
designed based on calculations using existing physics theories."

It is impossible to get an object to go faster than the speed of light by adding energy to the object...but it may be possible to manipulate spacetime in a way which will allow an object to inhabit an inertial rest frame within a spacetime expanding many times the speed of light. You've probably heard of the Alcubierre warp drive? The following references are provided by David who just may have discovered something which could make a warp drive very possible.
David's "Inertia manipulation through metric patching"
http://home.aol.com/zcphysicsms/inertmanip.htm
David's "The New Warp Drive"
http://home.aol.com/zcphysicsms/alternatewarp.htm
David also explains Alcubierre's Drive and several modifications at this site which also covers General Relativity (which the research is based on).
For a good text explanation of Alcubierre's idea
John Cramer (There is a great picture of the spacetime which looks like Santa's Sleigh).
http://www.npl.washington.edu/AV/altvw81.html