  Combining advanced technologies of optics and antiferromagnetic spintronics,
we present a method to realize ultrafast spin transport. The optical Barnett
effect provokes quasiequilibrium Bose-Einstein condensates (BECs) of magnons
associated with the fully spin-polarized state in insulating antiferromagnets
(AFs). This optomagnonic Barnett effect enables us to exploit coherent magnons
of high frequency over the conventional ones of (sub-) terahertz associated
with the N\'eel magnetic order. We show that the macroscopic coherence of those
optical magnon BECs induces a spin current across the junction interface of
weakly coupled two insulating AFs, and this optomagnonic Josephson effect
realizes ultrafast spin transport. The period of the optomagnonic Josephson
oscillation is much shorter than the conventional one of the order of
picoseconds. Thus we propose a way to realize ultrafast spin transport in AFs
by means of the macroscopic coherence of optical magnon BECs.
