Subharmonic transitions and Bloch-Siegert shift in electrically driven spin resonance

TL;DR

This paper provides a theoretical analysis of subharmonic multi-photon transitions in electrically driven spin resonance, revealing a negative Bloch-Siegert shift in EDSR and deriving analytical expressions for resonance and Rabi frequencies.

Contribution

It introduces a novel theoretical framework for understanding subharmonic transitions and Bloch-Siegert shifts in EDSR using Floquet theory and Schrieffer-Wolff perturbation.

Findings

Demonstration of two-photon Rabi oscillations.

Analytical calculation of resonance and Rabi frequencies.

Discovery of a negative drive-strength dependent Bloch-Siegert shift in EDSR.

Abstract

We theoretically study coherent subharmonic (multi-photon) transitions of a harmonically driven spin. We consider two cases: magnetic resonance (MR) with a misaligned, i.e., non-transversal driving field, and electrically driven spin resonance (EDSR) of an electron confined in a one-dimensional, parabolic quantum dot, subject to Rashba spin-orbit interaction. In the EDSR case, we focus on the limit where the orbital level spacing of the quantum dot is the greatest energy scale. Then, we apply time-dependent Schrieffer-Wolff erturbation theory to derive a time-dependent effective two-level Hamiltonian, allowing to describe both MR and EDSR using the Floquet theory of periodically driven two-level systems. In particular, we characterise the fundamental (single-photon) and the half-harmonic (two-photon) spin transitions. We demonstrate the appearance of two-photon Rabi oscillations, and analytically calculate the fundamental and half-harmonic resonance frequencies and the corresponding Rabi frequencies. For EDSR, we find that both the fundamental and the half-harmonic resonance frequency changes upon increasing the strength of the driving electric field, which is an effect analogous to the Bloch-Siegert shift known from MR. Remarkably, the drive-strength dependent correction to the fundamental EDSR resonance frequency has an anomalous, negative sign, in contrast to the corresponding Bloch-Siegert shift in MR which is always positive. Our analytical results are supported by numerical simulations, as well as by qualitative interpretations for simple limiting cases.