Antiferromagnets (AFMs) have the potential to push spintronic devices from the static or gigahertz frequency range to the terahertz (THz) range for the sake of the high-speed processing. The insensitivity of AFMs to magnetic fields also makes it hard to manipulate spin currents. Here we show the optical generation of ultrafast spin current in an AFM/heavy metal heterostructure at zero external magnetic field and at room temperature by detecting the THz emission. In addition, it is generally believed that the magnon generation efficiency is the same as the magnon annihilation efficiency in a ferromagnetic insulator by a charge current in a heavy metal/ferromagnetic insulator bilayer. However, we found that the magnon creation and annihilation efficiency are asymmetric, evidenced by an observation of a unidirectional spin Hall magnetoresistance effect.