...In the form of aluminium oxynitride, a crystalline transparent ceramic currently being tested out under the trade name of ALON as a possible armour plating.
sorry about the double up (first link), as you said the Alcubierre drive is still hypothetical, but it is a start and shows the current thinking and direction of FTL research.
another interesting NFTL(not as fast as light) drive is the nuclear pulse engine, while still hypothetical it is with in the bounds of current technology to produce.
Since I'm currently running a time-travel campaign, I thought it might be interesting to generate DTI's files on the events of Star Trek IV. In part, they read:
Nichols, Marcus PhD. Chem, UCLA 1969 In 1985, Dr. Mark Nichols solved the issue of making aluminum oxynitride transparent while working as San Francisco branch manager of Plexicorp. AlNO had been developed a few years earlier in an opaque white form. Nichols credited his inspiration to a Dr. Scott from the University of Edinburgh, though nobody has been able to track down the mysterious Dr. Scott. In 2286, DTI was notified that during the Whalesong Crisis, when James T. Kirk and his comand crew went back in time to 1985, Captain Montgomery Scott gave Nichols the nudge that allowed him to make this breakthrough. As Capt. Scott testified that Nichols had actually been the one to make the breakthrough in the unaltered timeline, this is classed as a Predestination Paradox. AlNO is the basis for today's Transparent Aluminum.