Efficient and fast manipulation of antiferromagnets has to date remained a challenging task, hindering their application in spintronic devices. For ultrafast operation of such devices, it is highly desirable to be able to control the antiferromagnetic order within picoseconds - a timescale that is difficult to achieve with electrical circuits. Here, we demonstrate that bursts of spin-polarized hot-electron currents emerging due to laser-induced ultrafast demagnetization are able to efficiently excite spin dynamics in antiferromagnetic Mn$_2$Au by exerting a spin-transfer torque on femtosecond timescales. We combine quantitative superdiffusive transport and atomistic spin-model calculations to describe a spin-valve-type trilayer consisting of Fe$|$Cu$|$Mn$_2$Au. Our results demonstrate that femtosecond spin-transfer torques can switch the Mn$_2$Au layer within a few picoseconds. In addition, we find that spin waves with high frequencies up to several THz can be excited in Mn$_2$Au.
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