Noise Analysis of Single Junction Superfluid ⁴He SQUID

We have studied the low temperature (T< 600 mK) thermal noise limit for a single junction, superfluid ⁴He SQUID, extending previous analysis to regions with negligible normal fluid.[1,2] The device we consider is a superfluid loop, interrupted by a single Josephson junction, in parallel with a diaphragm to drive and sense the superfluid transport. We have identified three dissipation mechanisms that will produce thermal noise and limit the sensitivity to changes in quantum phase across the junction at these temperatures: 3-phonon losses in the sensing loop[3], thermo-viscous losses at the junction[4], and mechanical loss in the diaphragm. Assuming a 20 cm diam. sensing loop of 2 cm diam. tubing, and a critical current of 10^-9 kg/s, we find a sensitivity to rotation at 10 mK to be 8^.10^-15 rad/s/Hz^1/2 for a diaphragm quality factor (Q_d) of 10⁴, and 5^.10^-17 rad/s/Hz^1/2 for Q_d=10⁹. This corresponds to a sensitivity to extraodinarly small proper time differences due to Sagnac effects of: 6^.10^-33 s/Hz^1/2 for Q_d=10⁴, and 3^.10^-35 s/Hz^1/2 for Q_d=10⁹. This work suggests that realizing a Josephson junction structure which can operate at these low temperatures, T/T_λ~1/200, with materials such as 2D nanoporous membranes[5], will open the possibility for allow laboratory sensing of general relativistic effects such as frame dragging, and probing the fundamental limits of time with precision measurements of phase noise in superfluids, in addition to practical uses such as precision sensing of the Earth's motion.