Landau-Zener-Stuckelberg-Majorana Interferometry of a Single Hole

We perform Landau-Zener-Stuckelberg-Majorana (LZSM) spectroscopy on a system with strong spin-orbit interaction (SOI), realized as a single hole confined in a gated double quantum dot. Analogous to electron systems, at a magnetic field B = 0 and high modulation frequencies, we observe photon-assisted- tunneling between dots, which smoothly evolves into the typical LZSM funnel-shaped i-nterference pattern as the frequency is decreased. In contrast to electrons, the SOI enables an additional, efficient spin-flip int-erdot tunneling channel, introducing a distinct interference pattern at finite B. Magnetotransport spectra at low-frequency LZSM driving show the two channels to be equally coherent. High-frequenc-y LZSM driving reveals complex photon-assisted- tunneling pathways, both spin conserving and spin flip, which form closed loops at critical magnetic fields. In one such loop, an arbitrary hole spin state is inverted, opening the way toward its all-electric-al manipulation.