Detecting gravitational waves with spin systems

TL;DR

The paper tackles the challenge of detecting high-frequency gravitational waves by proposing spin-based sensing with nuclear magnetic resonance. It derives the GW-spin couplings from the Dirac equation in curved spacetime, identifying three effects—the Gertsenshtein effect, a metric-induced spin interaction, and the gravitational spin Hall effect—and shows how these can be transduced into measurable magnetic signals. By using nuclear spins such as $^{129}$Xe with long coherence times and CASPEr-like polarization, the GW signal can be amplified via the induced effective fields, projecting sensitivities of $\\sqrt{S_h}\\approx 10^{-20} \,\\mathrm{Hz}^{-1/2}$ around $f \\sim 100\ \mathrm{MHz}$. The proposed four-sensor gradiometer arrangement in a magnetically shielded chamber, spanning 1 kHz to 0.4 GHz, offers a viable path to access unexplored GW bands and complements existing detectors, while highlighting a close relation to CASPEr geometries for baseline benchmarking.

Abstract

The observation of gravitational waves has opened a new window into the Universe through gravitational-wave astronomy. However, high-frequency gravitational waves remain undetected. In this work, we propose that spin systems can be employed to detect gravitational waves in this unexplored frequency regime. We derive the spin's response to gravitational waves and identify three distinct effects: the well-known Gertsenshtein effect, a metric-induced interaction, and the gravitational spin Hall effect. We focus on nuclear spins and utilize nuclear magnetic resonance to enhance the gravitational response, leveraging the advantages of long coherence time, high polarization, and a small gyromagnetic ratio. The proposed experimental scheme is capable of probing gravitational waves in the kilohertz to gigahertz range, with projected sensitivities reaching $\sqrt{S_h}\approx10^{-20}~\mathrm{Hz}^{-1/2}$.

Figures (3)

• Figure 1: The solid lines show the conditions when the amplitude of the induced magnetic field by the Gertsenshtein effect is equal to that from $B^i_{\rm metric}$, the gravitational effect on spin. The signal from the equivalent field $B^i_{\rm metric}$ can be more significant with a lower external $B_0$ and a smaller gyromagnetic factor. The dashed lines are the dependence relations between the external magnetic field and the corresponding Larmor frequency of electron and ($^3{\rm He}$) nucleus.
• Figure 2: Spatial distributions for $B_{\rm metric}^i$ (upper panels) and magnetic field caused by Gertsenshtein effect (lower panels) with natural normalization. The length is given in units of $L$. In panel (c), we illustrate the GW detection scheme using an array of four sensors $S_1 - S_4$.
• Figure 3: Projected GW sensitivity for spin systems (blue). For comparison, other proposed sensitivity curves from superconducting levitated detectors Carney:2024zzk, DM-Radio DMRadio:2022jfv, magnetized Weber bar Domcke:2024mfu, and extrapolated LIGO sensitivity to higher frequencies Aggarwal:2025noe are shown in green, red, and orange colors, respectively.