Thermal noise in a high Q cryogenic resonator

Abstract

In order to evaluate the feasibility of a mixed mechanical and electrical multimode matching network for a resonant gravitational wave detector, current noise measurements were performed on a high quality factor LC resonator, based on a superconducting coil, by using a dc SQUID weakly coupled to the coil. We present a method to identify different noise sources in the system by their dependence on the temperature or on the resonator quality factor. Measurements performed at quality factors up to 10 6 in the temperature range 1.2-4.2 K, show that the total measured noise is only contributed by the resonator thermal noise.

Thermal noise in a high Q ultracryogenic resonator

“…Different behaviors are instead observed by changing the capacitor. In particular, the capacitors used by Bonaldi et al 3 lead to a quality factor nearly independent of temperature, as was reported. Given these results, in the near future we plan to use homemade vacuum-gap capacitors, which should both improve the quality factor, because of reduced dielectric losses, 17 and give further indication on the origin of the temperature dependent dissipation.…”

“…Regarding the quality factor of the resonator, we have observed a rather unexpected dependance on temperature. Figure 4 shows the measured dissipation expressed by 1 / Q as function of the inverse of temperature 1 / T. The evident increase of 1 / Q at low temperature points to some kind of dissipation which grows roughly as 1 / T. In order to understand the origin of this unexpected behavior, which has not been pointed out in a previous work, 3 we have performed further quality factor measurements with a different resona- tor setup. For this purpose the resonator has been housed in the same experimental probe described by Bonaldi et al, 3 which allows quicker tests with less liquid helium consumption in the temperature range 1.3-4.2 K. We have found that the temperature dependent dissipation is still present, and does not change significantly by using different coils with the same inductance or placing in parallel to the resonator an additional ϳ200 pF formvar capacitance to simulate an increased coil stray capacitance.…”

“…1. Since the model has already been discussed, 3 we recall here only the main features. The LC resonator is modeled by lumped inductance and capacitance L and C. A lumped resistor r accounts for the resonator dissipation and for the thermal voltage noise source V th with power spectral density 4k B Tr.…”

“…Both dissipation and noise have been well characterized at liquid helium temperature ͑1.2-4.2 K͒. 3 Practical applications of such resonators include the characterization of the dynamic input impedance or the back action noise of superconducting quantum interference device ͑SQUID͒ amplifiers [4][5][6] and low noise field effect transistor ͑FET͒ amplifiers. 7 Recently it has been recognized that tuning a high Q electrical resonant mode to the mechanical modes of a resonant gravitational wave detector, 8,9 which typically operates at about 1 kHz, leads to a significant increase of the detector bandwidth and sensitivity, provided that two requirements are fulfilled: the quality factor of the tuned electrical mode must be at least of the same order as that of the mechanical modes ͑Ӎ10 6 ͒, and its noise must be dominated by thermal noise.…”

Directly Deflecting Particle Dark Matter

“…2 shows the projected reach of the planned DM Radio experiment, which is optimized to detect small magnetic fields and is expected to consist of a meter 3 detector with T LC ¼ 10 mK and Q ¼ 10 6 , assuming that it is modified to include a meter 3 upstream PHYSICAL REVIEW LETTERS 124, 011801 (2020) 011801-4 deflector. The construction of thermal-noise-limited resonant LC circuits operating at kHz frequencies with quality factors of Q ≃ 10 6 has already been firmly established by the existing gravity-wave experiment, AURIGA [39][40][41]. Therefore, we also consider a future dedicated experimental configuration optimized for measuring the electric field signal, as shown by the lines labeled "E field (I-III)" in Fig.…”