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IEEE Transactions on Applied Superconductivity

Role of Geometry on the Color of Flux Noise in dc SQUIDs

F. C. Wellstood, C. Urbina, John L. Clarke

Published Dec 23, 2010• 8 citations
Publisher

Abstract

We examine the behavior of low frequency flux noise measured in ten Nb-NbOx-Pbln dc SQUIDs in the temperature range 1 K to 20 mK. As previously reported, the flux noise power spectrum SΦ(f) typically scales with frequency as A/fα. Remark ably, the excess noise power A at 1 Hz increases as the temperature is decreased below about 0.7 K, saturating to a value around (10 μΦα)2/Hz below about 0.2 K. Here we report on the dependence of both the magnitude A and the slope a on the size and linewidth of the SQUID loops. In particular, at the lowest temperatures we find that a declines to values as low as 0.5 in the smallest devices, while a is in the range 0.9-1 for the largest devices.

DOI
10.1109/tasc.2010.2093092

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IEEE Transactions on Applied Superconductivity•Dec 9, 2016•4 citations
We examine the behavior of low frequency flux noise measured in ten Nb-NbOx-Pbln dc SQUIDs in the temperature range 1 K to 20 mK. As previously reported, the flux noise power spectrum SΦ(f) typically scales with frequency as A/fα. Remark ably, the excess noise power A at 1 Hz increases as the temperature is decreased below about 0.7 K, saturating to a value around (10 μΦα)2/Hz below about 0.2 K. Here we report on the dependence of both the magnitude A and the slope a on the size and linewidth of the SQUID loops. In particular, at the lowest temperatures we find that a declines to values as low as 0.5 in the smallest devices, while a is in the range 0.9-1 for the largest devices.
The excess low-frequency flux noise in dc superconducting quantum interference devices (SQUIDs) operated at ultra-low temperatures was studied. A large number of single SQUIDs as well as SQUID arrays from 16 wafers fabricated over a period of six years were characterized at 4.2 K and1/fon the SQUID design or fabrication parameters. In contrast, below 4.2 K the low-frequency noise changed moderately or increased strongly depending on whether the bottom Nb or the insulation layer were fabricated in our newer sputter system instead of the older one. The corresponding excess noise levels ε1/fat1/f∝ f-αwith α typically around 0.6 for good devices. For devices with strong low-frequency excess noise, α increases up to about 0.9. The best energy resolution ε achieved so far with a 50 pH test SQUID operated at 16 mK is 0.62 h at 100 kHz, increasing to 1.64 h at 1 kHz and 14 h at 10 Hz.
The spectral density S(Φ)(f) = A(2)/(f/1 Hz)(α) of magnetic flux noise in ten dc superconducting quantum interference devices (SQUIDs) with systematically varied geometries shows that α increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean-square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID. These results are incompatible with a model based on the random reversal of independent, surface spins.
At temperatures below about 1 K, a series of dc superconducting quantum interference devices (SQUID’s) exhibited an apparent flux noise with a spectral density scaling as 1/f α, where 0.58<α<0.80. Typically, the magnitude of the noise increased as the temperature was lowered below 1 K, tending to flatten out at low temperatures with a value of 7±3 μΦ0Hz−1/2 at 1 Hz that was nearly independent of the parameters and materials of the SQUID’s. Although a large number of hypothetical sources of the noise have been eliminated, the origin remains unidentified.
We have measured the low-frequency noise in the critical current Ic of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted Nb–NbOx–PbIn Josephson junctions in the temperature range T=0.09–4.2K. Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies f, there is a component of the power spectrum of the critical current fluctuations given approximately by SIc(f)=CIc2T2∕Af, where A is the area of both junctions, and C≈(3.9±0.4)×10−23m2∕K2. For quantum bits based on Josephson junctions, the scaling of SIc(f) with T2 implies that the dephasing time limited by critical current l∕f noise should scale as 1∕T for temperatures down to at least 0.09K.
Abstract Noise in superconducting quantum interference devices (dc SQUIDs) with different design, based on Nb/AlO x /Nb technology, has been systematically measured at temperature T = 4.2 K. We demonstrate that for all our devices the power spectral density of the white noise (above a frequency of about 1 kHz) is determined by the shunt resistors, reaching about 5 times Planck’s constant. The low-frequency noise level was measured for washer- and multi-loop-type SQUIDs with systematically varied effective area, SQUID loop perimeter, and inductance. We show that at 1 Hz the noise spectral density is approximately 40 times higher than the white noise level and its scaling with washer width and effective area is negligible. These results are incompatible with several models of the flicker noise source. Possible origins of this noise are discussed.
The quality factors and noise performances of superconducting resonators play an important role in microwave SQUID multiplexer (MW-MUX). Since we develop microwave SQUID multiplexer for transition edge sensor arrays, the operation temperature is around 100 mK where the effects of two level system (TLS) can be significant. In this paper, we have investigated the electrode-material or wafer dependence of noise performance of MW-MUX by characterizing four types of resonators. Although the temperature dependence of resonance frequency and the power dependence of Qu show clear difference among the materials, frequency noises which contribute the readout noise of MW-MUX are similar. Theoretical model predicts that not TLS but other loss dominates Qu in the power region suitable for the low-noise operation of our MW-MUX. Further, the estimated flux noise calculated from the measured frequency noise and the conversion √ coefficient from frequency to flux were 1-5 (μΦ0/√Hz) @ 1 Hz, 0.2-0.8 (μΦ0/√Hz) @ 3 kHz. These results indicate the noise of our MW-MUX has small material dependence and the compatible low noise operation to typical dc SQUIDs would be possible. Therefore, the MW-MUX with our materials would not suffer from the low frequency noise due to TLS.