Quantum Sensing of Gravitational Frame-Dragging and Time Dilation with a Superfluid ⁴He Gyrometer

We propose an Earth-based, laboratory-scale experiment capable of measuring the Earth’s general-relativistic frame-dragging at the 0.2% level in one second using the macroscopic quantum properties of a novel superfluid ⁴He single Josephson junction gyrometer. We derive the frame-dragging and related geodetic and Thomas precession effects in such a gyrometer, emphasizing that all three effects, in addition to the Sagnac effect, can be thought of as frame-dragging effects in a reference frame co-moving with the gyrometer. Using a novel thermal noise analysis for such a superfluid ⁴He gyrometer operating at mK temperatures, we estimate that a thermal noise spectral density of 5 x10^-17 rads/s/Hz^1/2 should be achievable. In a one-second measurement, this gives a rotational sensitivity of 1 revolution in 4 Byrs, or 0.2% of the Earth’s frame-dragging precession rate. We show that this extreme sensitivity corresponds to a measurement of proper time differences as small as 10^-35 s.