Dependence of SQUID Intrinsic Flux Noise on Stewart–McCumber Parameter $\beta_{c}$ of Josephson Junction

It is known that three superconducting quantum interference device (SQUID) parameters, namely, the intrinsic flux noise δΦ
_s
, the flux-to-voltage transfer coefficient ∂V/∂Φ, and the dynamic resistance R
_d
, increase with increasing the Stewart- McCumber parameter β
_c
of Josephson junction. It is very difficult to obtain the low values of δΦ
_s
for a strongly damped SQUID due to its small ∂V/∂Φ. In this paper, we employ a two-stage scheme (TSS) to measure δΦ
_s
directly. Here, we use single chip readout electronics and a weakly damped SQUID with a β
_c
of flux noise of the readout-SQUID system is about 4.8 μΦ
₀
/√Hz 1.2, both acting as a readout-SQUID system (a preamplifier). The with a corner frequency of about 10 Hz. The front-end SQUID is coupled to the readout SQUID via the input coil with a mutual inductance of M
_i
. In our experiment, the flux gain for a readout SQUID, i.e., G
_Φ
= M
_i
× (∂I/∂Φ)
_front-end
is adjusted to be 20. Using the TSS, we measured δΦ
_s
with different β
_c
changing from 0.3 to 13.5 and found δΦ
_s
increasing from 1.0 to 5.0 μΦ
₀
/√Hz. We also discussed the relations between L
_s
, β
_c
, and δΦ
_s
quantitatively. Finally, we proposed designing a suitable β
_c
to match the preamplifier in a direct readout scheme to simplify a SQUID measurement system.