Are any laboratories trying to develop faster than light travel?

Not that I know of. There is no physical basis for such a phenomenon, and no one has been able to show that a simple back of the envelope calculation of the energy requirements is incorrect when it comes to accelerating a human to speeds near that of light.

I know for a fact, however, that at Area 31 (Baskin and Robins Ice Cream parlor!) just outside NASA's Goddard Space Flight Center in Maryland this topic does come up from time to time.