  Second-order processes introduce nonlinearities in quantum dynamics,
unlocking a totally unexpected area of control operations. Here we show that
the well-known Landau-Zener-St\"uckelberg-Majorana (LZSM) transition can be
driven by a virtual process in a three-level system whereby two photons from a
drive with linearly-modulated phase create excitations onto the third level
while avoiding completely the first level. We implement this experimentally in
a transmon qubit achieving a population transfer of $98\%$, limited by
relaxation. We predict and observe experimentally the doubling of the LZSM
velocity. The observation of this effect is made possible by the nearly-exact
cancellation of the two-photon ac Stark shift when the third transition is
included. Furthermore, we demonstrate considerable robustness to offsets in
frequency and amplitude, both in theory and experimentally.
