It is shown theoretically that by the use of two radio-frequency fields of the same resonance frequency but with the different phases and directions the degeneracy of the energy spectrum of a spin system with I = 3/2 is removed. This leads to four non-degenerate spin states which can be used as a platform for quantum computing. The feasibility of quantum computing based on a pure (without DC magnetic fields) nuclear quadrupole resonance technique is investigated in detail. Various quantum logic gates can be constructed by using different excitation techniques allowing different manipulations with the spin system states. Three realizations of quantum logic gates are considered: the application of an additional magnetic field with the resonance frequency, the amplitude modulation of one of the applied RF fields by the resonance frequency field, and the level-crossing method. It is shown that the probabilities of the resonance transitions depend on the method of excitation and on the direction of the excitation field. Feasibility of quantum computing is demonstrated with the examples of constructing a controlled-NOT logic gate using the resonance excitation technique and SWAP and NOT2 logic gates using the level-crossing method.
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
13C 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
13C 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.
In an electron-spin two-level system a bichromatic radiation field, consisting of a transverse microwave field and a radio frequency field oriented parallel to the static magnetic field, can induce multiple photon transitions of the type ${\ensuremath{\sigma}}_{\text{mw}}^{+}+k{\ensuremath{\pi}}_{\text{rf}}$, with the photons ${\ensuremath{\sigma}}_{\text{mw}}^{+}$ and ${\ensuremath{\pi}}_{\text{rf}}$ absorbed from the microwave and radio frequency fields, and
k being an integer. The two-level spin system may become transparent under such a bichromatic radiation field. This phenomenon directly depends on the presence of the $\ensuremath{\pi}$ photons of the longitudinal radio frequency field. An analytical description of the multiple photon processes and the resulting transparency effects, based on a toggling-frame approach, is given. The effective field amplitudes of the multiple photon transitions are found to have a Bessel-function-like dependence on the radio frequency amplitude. The behavior of the magnetization vector during a bichromatic pulse is illustrated by using classical equations of motion. The theoretically predicted effects are verified experimentally. As an example for an application of the investigated type of electromagnetically induced transparency, a one-pulse echo experiment is described, where the free evolution period is created artificially.