I'm not so sure the energy requirements are all that high. Alcubierre suggested that the sort of exotic matter needed would actually be fairly easy to create. NASA's been running experiments hoping to measure it with inconclusive results:
> In 2012, a NASA laboratory announced that they had constructed an interferometer that they claim will detect the spatial distortions produced by the expanding and contracting spacetime of the Alcubierre metric. The work has been described in Warp Field Mechanics 101, a NASA paper by Harold Sonny White.[5][6] Alcubierre has expressed skepticism about the experiment, saying "from my understanding there is no way it can be done, probably not for centuries if at all".
> In 2013, the Jet Propulsion Laboratory published results of a 19.6-second warp field from early Alcubierre-drive tests under vacuum conditions.[33] Results have been reported as "inconclusive".[34]
https://en.wikipedia.org/wiki/Alcubierre_drive#Experiments
> In 2012, a NASA laboratory announced that they had constructed an interferometer that they claim will detect the spatial distortions produced by the expanding and contracting spacetime of the Alcubierre metric. The work has been described in Warp Field Mechanics 101, a NASA paper by Harold Sonny White.[5][6] Alcubierre has expressed skepticism about the experiment, saying "from my understanding there is no way it can be done, probably not for centuries if at all".
> In 2013, the Jet Propulsion Laboratory published results of a 19.6-second warp field from early Alcubierre-drive tests under vacuum conditions.[33] Results have been reported as "inconclusive".[34]