Lorentz Force Detuning in Heterodyne Gravitational Wave Experiments

TL;DR

This paper provides a theoretical analysis of Lorentz Force Detuning effects in heterodyne gravitational wave experiments, highlighting the need to adapt coupling parameters for optimal detection across different mechanical and gravitational wave frequencies.

Contribution

It extends previous models by deriving an additional back-action term from electromagnetic fields, revealing complex dependencies crucial for future experiment design.

Findings

Lorentz Force Detuning affects signal power dependence on coupling.

Optimal coupling varies with mechanical mode and GW frequency.

Designs must adapt coupling parameters across parameter space.

Abstract

Heterodyne cavity experiments for gravitational wave (GW) detection experience a rising interest since recent studies showed that they allow to probe the ultra high frequency regime above $10\,\text{kHz}$. In this paper, we present a concise theoretical study of the experiment based on ideas from the former MAGO collaboration which already started experiments in turn of the millenium. It extends the former results via deriving an additional term originating from a back-action of the electromagnetic field on the cavity walls, also known as Lorentz Force Detuning. We argue that this term leads to a complex dependence of the signal power $P_{\text{sig}}$ on the coupling coefficient between the mechanical shell modes and the electromagnetic eigenmodes of the cavity. It turns out that one has to adapt the coupling over the whole parameter space since the optimal value depends on the mechanical mode $\omega_l$ and the GW frequency $\omega_g$. This result is particularly relevant for the design of future experiments.