Breaking the rotating wave approximation for a strongly driven dressed single-electron spin

Abstract

We investigate the dynamics of a strongly driven microwave-dressed donor-bound electron spin qubit in silicon. A resonant oscillating magnetic field ${B}_{1}$ is used to dress the electron spin and create a new quantum system with a level splitting proportional to ${B}_{1}$. The dressed two-level system can then be driven by modulating the detuning $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}$ between the microwave source frequency ${\ensuremath{\nu}}_{\mathrm{MW}}$ and the electron spin transition frequency ${\ensuremath{\nu}}_{e}$ at the frequency of the level splitting. The resulting dressed qubit Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{R\ensuremath{\rho}}$ is defined by the modulation amplitude, which can be made comparable to the level splitting using frequency modulation on the microwave source. This allows us to investigate the regime where the rotating wave approximation breaks down without requiring microwave power levels that would be incompatible with a cryogenic environment. We observe clear deviations from normal Rabi oscillations and can numerically simulate the time evolution of the states in excellent agreement with the experimental data.