Quantum Sensing of Gravitational Frame-Dragging with a Superfluid $^4$He Gyrometer

TL;DR

This paper proposes a superfluid helium gyrometer experiment to detect Earth's gravitational frame-dragging effect with unprecedented sensitivity, leveraging quantum properties and low-temperature technology.

Contribution

It introduces a novel superfluid helium Josephson junction gyrometer design for measuring relativistic frame-dragging effects at laboratory scale.

Findings

Expected noise spectral density of 5×10⁻¹⁷ rad/s/√Hz at 10 mK

Ability to resolve frame-dragging rate to 0.2% within one second

Measurement of proper time differences as small as 10⁻³⁵ seconds

Abstract

We propose a laboratory-scale experiment to locally measure the general relativistic frame-dragging effect on Earth using the macroscopic quantum properties of a novel superfluid $^4$He single Josephson junction gyrometer. We derive the frame-dragging and related geodetic and Thomas effects in the superfluid gyrometer and present a procedure for their experimental measurement. We compute the expected thermal noise floor and find that very high sensitivity can be expected at millikelvin temperatures, where near-future Josephson junctions using nanoporous 2D materials are expected to operate. Assuming utilization of the lowest mechanical loss materials, we find a noise spectral density of $5\times 10^{-17}$ rads/s/$\sqrt{\mathrm{Hz}}$ at 10 mK, which is sufficient to resolve the frame-dragging rate to 0.2% within one second of measurement, giving a rotational sensitivity of 1 revolution in 4 Byrs. This extreme sensitivity to rotation corresponds to a measurement of proper time differences as small as $10^{-35}$ s.