  We have investigated the vortex dynamics in a thin film of an iron-based
superconductor FeSe$_{0.5}$Te$_{0.5}$ by observing second-harmonic generation
(SHG) in the THz frequency range. We visualized the picosecond trajectory of
two-dimensional vortex motion in a pinning potential tilted by Meissner
shielding current. The SHG perpendicular to the driving field is observed,
corresponding to the nonreciprocal nonlinear Hall effect under the
current-induced inversion symmetry breaking, whereas the linear Hall effect is
negligible. The estimated vortex mass, as light as a bare electron, suggests
that the vortex core moves independently from quasiparticles at such a high
frequency and large velocity $\approx$300 km/s.
