# The possibility of direct observation of the Bloch-Siegert shift in coherent dynamics of multiphoton Raman transitions

## TL;DR

This paper demonstrates the direct observation of the Bloch-Siegert shift in the coherent dynamics of multiphoton Raman transitions in a qubit, highlighting the significance of counter-rotating effects in the ultrastrong driving regime.

## Contribution

It provides experimental and theoretical evidence of the Bloch-Siegert oscillation in a qubit system, revealing new insights into driven quantum dynamics beyond the rotating wave approximation.

## Key findings

- Rabi oscillations vanish under certain parameters due to destructive interference.
- Bloch-Siegert oscillations can be directly observed in time-resolved dynamics.
- Fourier spectra show triplet-to-doublet transformation with characteristic splitting.

## Abstract

We study Rabi oscillations of the second-order Raman transition realized on dressed states of a qubit excited by an amplitude-modulated microwave field. The co-rotating component of the ultrastrong low-frequency modulation field excites virtual multiple photon processes between the dressed states and forms the Rabi frequency in the so-called rotating wave approximation (RWA). The counter-rotating modulation component also gives a significant contribution to the Rabi frequency owing to the Bloch--Siegert effect. It is shown that for properly chosen parameters of the modulation field and qubit, the Rabi oscillations in the RWA vanish due to destructive interference of multiple photon processes. In this case the Rabi oscillation results exclusively from the Bloch--Siegert effect and is directly observed in the time-resolved coherent dynamics as the Bloch--Siegert oscillation. Correspondingly, in Fourier spectra of the coherent response, triplets are transformed into doublets with the splitting between the lines equal to twice the Bloch--Siegert shift. We demonstrate these features by calculations of the qubit's evolution in the conditions of experiments with a NV center in diamond, where Raman transitions were observed. The direct observation of the Bloch--Siegert oscillation offers new possibilities for studying driven quantum systems in the ultastrong regime.