  We consider tunneling of quasiparticles through a rectangular quantum well,
subject to periodic driving. The quasiparticles are the itinerant charges in
two-dimensional and three-dimensional semimetals having a quadratic band
touching (QBT) point in the Brillouin zone. We assume a non-adiabatic limit
where the Floquet theorem is applicable to analyze the time-periodic
Hamiltonian. By deriving the Floquet scattering matrices, we chalk out the
transmission and shot noise spectra of the QBT semimetals. The spectra show
Fano resonances, which we identify with the (quasi)bound states of the systems.
