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

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 center coupled to a first-shell $^{13}$C nuclear spin in diamond at a level anti-crossing point that occurs in the $m_{s}=pm1$ manifold when the energy level splitting between the $m_{s}$ = $+1$ and $-1$ spin states due to the static magnetic field is $approx$ 127 MHz, which is roughly equal to the spectral splitting due to the $^{13}$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 $z$-component of the RF field. 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 much smaller than the transition frequency become complex when the driving field strength is comparable 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.