Spin Resonance in Perspective of Floquet Theory and Brillouin-Wigner Perturbation Method

TL;DR

This paper presents a novel theoretical approach combining Floquet theory and Brillouin-Wigner perturbation to analyze spin resonance, providing explicit solutions for Rabi frequency and Bloch-Siegert shift.

Contribution

The work introduces a new framework that simplifies the analysis of spin resonance by transforming the Hamiltonian and constructing an effective Hamiltonian via perturbation theory.

Findings

Resonance condition determined by an upper triangular element of the Hamiltonian.

Explicit first and second order solutions for Rabi frequency and Bloch-Siegert shift.

Framework simplifies calculations and offers clear physical insights.

Abstract

We studied the two-level spin resonance in a new perspective. Using the Floquet theory, the periodic interaction Hamiltonians were transfromed into a time-independent interaction. Using the Brillouin-Wigner perturbation method, a degenerated subspace is constructed, where the effective Hamiltonian is given in a perturbation expansion. In this framework, we found that the upper triangular element $\langle \alpha | H^1 | \beta \rangle$, determines whether the resonance happens. The generalized Rabi frequency and the Bloch-Siegert shift were solved straightforwardly as the first order and the second order solution, proving the benefit of the developed method.