Nonlinear dynamics of a two-level system of a single spin driven beyond the rotating-wave approximation

Abstract

Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single nitrogen-vacancy (NV) center in diamond coupled to a first-shell $^{13}\mathrm{C}$ nuclear spin at a level anticrossing point. This near degeneracy occurs in the ${m}_{s}=\ifmmode\pm\else\textpm\fi{}1$ manifold of the electron spin when the energy level splitting between the ${m}_{s}=\ensuremath{-}1$ and $+1$ states due to the static magnetic field is $\ensuremath{\approx}127$ MHz and thus equal to the splitting due to the $^{13}\mathrm{C}$ hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the component of the radio-frequency (RF) field along the NV symmetry axis. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is small compared to the transition frequency evolve into complex patterns when the driving field amplitude is comparable to or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.