Alcubierre Drive is the popular name given to the Kurosawa R-W33 engine used by all the human ships capable of FTL velocities. Although the engine was invented by a sino-japanese team lead by doctor Haiko Kurosawa in 2124, his work was fully based on the Miguel Alcubierre's research on FTL velocities and so the name of the second became more famous than that of the Japanese doctor.
Graphic that shows the functioning of the engine
The engine uses two opposite antimatter reactors that creates a bubble around the ship and deforms the space time in order to avance in FTL velocities without violating the Einstein's relativity theories.
One trip from Earth to Imvusa Ikhaya uses 50 times more energy than the world's total energy output in 2012.