Extreme Harmonic Generation in Electrically Driven Spin Resonance*

InAs nanowire double quantum dots offer a rich platform for studying single spin physics in a material with large spin-orbit (SO) coupling. The large SO coupling allows all electrical control of the electron spin through electric dipole spin resonance (EDSR).\footnote{V. N. Golovach, M. Borhani, and D. Loss, Phys. Rev. B \textbf{74}, 165319 (2006).} Here an oscillating electric field of frequency $f$ displaces the electron wave function, while a magnetic field with strength $B$ is applied. Spin rotations occur when the resonance condition $hf = g \mu_{\rm B} B$ is met. Here $g$ is the electron $g$-factor, $h$ is Planck's constant, and $\mu_{\rm B}$ is the Bohr magneton. We find that near zero interdot detuning efficient spin rotations also occur when $hf = n g \mu_{\rm B} B$, with $n$ being an integer as large as 8 in our system.\footnote{J. Stehlik, M. D. Schroer, M. Z. Maialle, M. H. Degani, and J. R. Petta, Phys. Rev. Lett. \textbf{112}, 227601 (2014).} The harmonics feature a striking odd/even dependence. While the odd harmonics show an enhancement of the leakage current, the even harmonics show a reduction. In contrast, we do not observe any measurable harmonics at large detuning. We link the presence of harmonics with additional anti-crossings present in the level diagram. This implies that harmonics are the result of Landau-Zener transitions occurring at multiple anti-crossings. Recent theoretical work supports this conclusion.\footnote{J. Danon and M. S. Rudner, arXiv:1407.2097.}