From NASA: Potentially, A Breakthrough (Understatement of The Century)

[True Blue Door]

9. Actually that's a separate subject.

For one, the absolute best that could be accomplished with something like this, if it proves to be real, would be a fraction of lightspeed. That's still massive, and opens up not only the solar system but the nearby stars. But it isn't warp drive.

But at least one member of the same NASA team that I'm aware of is involved in experiments to see if a microscopic warp bubble can be generated. The theory for warp has been shown to be sound, but there's no experimental evidence of its reality yet.

So far, according to his preliminary findings, what he's found is an effect that resembles what Alcubierre's warp theory predicts, but that he cannot yet rule out other explanations for the result. Here's a talk the NASA researcher gave last year about where he was in the experimental process with confirming the existence of warp: