Multiphoton Raman transitions and Rabi oscillations in driven spin systems

Abstract

In the framework of the non-secular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions have been obtained beyond the rotating wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second-and third-order Raman transitions observed for nitrogen-vacancy center in diamond [Z. Shu, et al., arXiv:1804. 10492] are well described in the frame of our approach. Our results provide new possibilities for coherent control of quantum systems.

Experimental protection of quantum coherence by using a phase-tunable image drive

“…The use of strong continuous microwave excitation has been proposed as a way to protect qubits 16 , 17 although the quantum gates would need proper redesigning. In related studies, complex pulse design using an arbitrary waveform generator, proved essential in studying Floquet Raman transitions 18 , 19 and quantum metric of a two-level system 20 in nitrogen vacancy (NV) centers. It is worth noting that in the case of concatenated DD, the frequency of the second order ( ) excitation has to match the Rabi frequency of the first excitation ( ); also, the two excitations are linearly polarized and perpendicular to each other (the method extends to higher orders in n ).…”

Bloch–Siegert oscillations in the Rabi model with an amplitude-modulated driving field

“… . This resonance is well observed and has the largest Rabi frequency among others multiphoton Rabi resonances[32]. The Hamiltonian 2 H contains an infinite sum of oscillating harmonics with the frequencies which are integer multiples of the frequency the terms of the sum with these n give the largest contribution and correspond to the RWA.…”

“…Their contribution can be taken into account using the Bogoliubov averaging method [34] for constructing time-independent effective Hamiltonian in the framework of the non-secular perturbation theory. The averaging procedure up to the second order in cos / A  (see [32]) gives the following effective Hamiltonian: (1) (…”

Harmonic dual dressing of spin one-half systems

“…Within the context of atomic trapping by rf dressed adiabatic potentials, synthetic/rectified fields are created by commensurable bichromatic or multiple driving in [32]. An effective Hamiltonian describing the action of a bichromatic drive for a two-level system is introduced by [33]. In [34] for the two-level space of a dual well occupation, a Floquet engineering approach based on the bichromatic commensurable driving of the optical lattice tunnelling generates an effective static field.…”