"They did not create an entity that actually possesses "negative mass". They created configurations of energy states within a material that CAN BE CHARACTERIZED as a quasiparticle; there is no requirement that we think of it as a particle-like entity, it's just convenient from certain respects. In turn that quasiparticle behaves, in at least some respects, as if it were a particle with "negative mass", although from the sound of things, "negative inertia" would be a more accurate description of the phenomena they actually observed." - DarkLordKelvin
It needs imaginary mass, not just negative mass.
Edit: I confused the drive's requirements with tachyons.
Also, tachyons have imaginary mass. IIRC Alcubierre drive requires a negative energy density. And commonly they use a term called "exotic matter", which is an extremely vague term.