Dissipation and resonance frequency shift of a resonator magnetically coupled to a semiclassical spin

TL;DR

This paper analytically investigates how a resonator's resonance frequency and dissipation are affected by coupling to a semiclassical spin, with implications for quantum device systems and general two-level systems.

Contribution

It provides an analytical framework for understanding the impact of spin relaxation on resonator properties, extending to general multi-level systems.

Findings

Resonance frequency shifts due to spin relaxation times.

Effective dissipation factor changes significantly with spin coupling.

Method applicable to electromagnetic and mechanical resonators.

Abstract

We calculate the change of the properties of a resonator, when coupled to a semiclassical spin by means of the magnetic field. Starting with the Lagrangian of the complete system, we provide an analytical expression for the linear response function for the motion of the resonator, thereby considering the influence of the resonator on the spin and vice versa. This analysis shows that the resonance frequency and effective dissipation factor can change significantly due to the relaxation times of the spin. We first derive this for a system consisting of a spin and mechanical resonator and thereafter apply the same calculations to an electromagnetic resonator. Moreover, the applicability of the method is generalized to a resonator coupled to general two and more level systems, providing a key to understand some of the problems of two level systems in quantum devices.