Multiphoton Raman transitions and Rabi oscillations in driven spin systems

TL;DR

This paper develops a theoretical framework to analyze multiphoton Raman transitions and Rabi oscillations in driven spin systems, revealing effects like the Bloch-Siegert shift and dependencies on initial phase, with implications for quantum control.

Contribution

The study introduces closed-form expressions for Rabi frequencies beyond the rotating wave approximation, accounting for antiresonant interactions and phase dependencies in driven spin systems.

Findings

Rabi frequency decreases with transition order

Bloch-Siegert shift becomes dominant at higher orders

Experimental data for NV centers are well explained by the model

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.