Sensitivity limitation of a superconducting quantum interferometer sensor-based gravity gradiometer

Differential displacement due to a gravitational force gradient, acting on two superconducting test masses which are elastically suspended from the instrument frame, is sensed by a superconducting quantum interference device (SQUID), coupled to the masses by a current flowing in the sensing circuits. The SQUID transducer absorbs energy from the masses, and, hence, it reacts with a random force (fluctuation-dissipation principle). This force increases if the coupling current grows. Additionally, the transducer outputs an amplification noise that is independent of the coupling. This output noise is equivalent to a force, applied to the masses, which decreases with stronger coupling, Hence, the strength of the total equivalent gravity gradient noise has a minimum with respect to the coupling. The minimum is found to be about 1.5ε_Aω₀ ²/(ml²), where ε_A means the equivalent energy sensitivity, in the white noise limit, of the SQUID junctions; ω₀ is the natural frequency of the mass suspension; m is the test mass, and l is the base length,