Observation of the Two-Photon Landau-Zener-Stückelberg-Majorana Effect

Harnessing second-order processes enables new control schemes in quantum dynamics. We show that the Landau-Zener-Stückelberg-Majorana (LZSM) transition can be generalized to a virtual-state process in a three-level system, employing a phase modulated drive whereby two photons excite the system from the first to the third level while avoiding the second one. We implement experimentally this process in a transmon, achieving 98% population transfer. We predict and observe the doubling of LZSM velocity. Furthermore, we demonstrate robustness to amplitude and frequency offsets, made possible by the nearly exact cancellation of the two-photon ac Stark shift due to the presence of the fourth state.