White paper: 1-10 Hz matter-wave interferometer to test the spin entanglement witness for quantum gravity
Abstract
In this white paper, we highlight the importance of the 1–10 mHz frequency range for laboratory tests of the quantum nature of gravity using the quantum gravity-induced entanglement of masses (QGEM) protocol. QGEM requires matter-wave interferometers with masses m ∼ 10⁻¹⁵–10⁻¹⁴ kg, brought within separations d ∼ 30–50 μm, while maintaining spatial superpositions of 1–20 μm and coherence for τ ∼ 0.1–1 s. These requirements make low-frequency environmental noise a central experimental challenge and place QGEM in a regime closely related to the low-frequency goals of the Einstein Telescope (ET) and the Cosmic Explorer (CE). In particular, QGEM is sensitive to relative acceleration noise (RAN) and to gravity-gradient noise (GGN) generated by seismic and other environmental mass-density fluctuations. For representative parameters m = 10⁻¹⁴ kg, Δx = 10 μm, and τ = 1 s, the differential acceleration-noise amplitude spectral density must be suppressed well below the 10⁻¹⁵ m s⁻²/√Hz level to keep acceleration-induced dephasing below the relevant experimental scale. Achieving this level of low-frequency noise suppression is therefore a key requirement for QGEM and closely parallels the seismic and gravity-gradient noise challenges that ET and CE address.
