Dark graviton sensing with magnetically levitated superconductors

Abstract

Levitated sensors have emerged as a new frontier to detect ultra-light dark matter such as axion-like particles and dark photons. In this work we study how a magnetically levitated superconductor responds to a spin-2 dark matter field, the dark graviton, in the dHz to kHz frequency range. To do so, we compute the forces that the dark graviton exerts on the superconductor, separately for matter and light couplings. The matter coupling produces a strain-like tidal acceleration between the superconductor and the readout pick-up loop in a way that is akin to a slow, continuous, massive gravitational wave. The light coupling instead induces an effective current that sources an oscillating magnetic field, thus driving the superdiamagnetic response of the superconductor. We find that, even with significant experimental improvements, the sensitivity reach for the matter coupling is not competitive with existing interferometers or fifth-force experiments. On the other hand, magnetically levitated superconductors could be among the most sensitive laboratory probes of the dark-graviton coupling to electromagnetism, especially at low frequencies, provided technical and readout noise can be kept under control.

Figures (2)

• Figure 1: Angular currents $j_i$ of \ref{['eq:littlej']} as a function of the angles $\theta$ and $\phi$ (arbitrary units, shared colour scale across panels), assuming equipartition among the five dark graviton polarisations. In a realistic case of a superposition of many waves each will have its own polarisation structure and orientation.
• Figure 2: Projected sensitivities to the dark graviton coupling to matter $\alpha_\mathfrak{m}$ (left panel) and light $\alpha_\mathfrak{l}$ (right panel) as a function of frequency $f$. The dotted lines refer to the "baseline" set-up, the dashed lines are for the "improved" set-up and the solid lines are for the "future" set-up (see main text). Dark purple lines refer to the resonant regime, dark orange lines to the broadband case and dark green are for a $1\,\mathrm{yr}$ resonant scan. Existing fifth-force constraints Murata:2014nraCembranos:2017vgi are shown in the shaded grey region; the recent LVK limits obtained with the LPSD method are also shown in a fainter grey LIGOScientific:2025ttj -- notice that these limits apply differently to matter coupling (solid grey) and light coupling (dotted grey), see main text.