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.
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.
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 SΦ(f ) of the low-frequency 1/f noise of high transition temperature dc superconducting quantum interference devices (SQUIDs) with narrow linewidths was independent of B0, the magnetic field in which they were cooled, up to a threshold value, about 33 μT in the best case. Above this threshold, which is associated with the entry of flux vortices into the film, the noise increased rapidly. By contrast, for large square washer SQUIDs, SΦ(f ) scaled linearly with B0. Estimates indicate that the 1/f flux noise produced by the pickup loop of a directly coupled magnetometer is negligible.
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.
For many types of superconducting qubits, magnetic flux noise is a source of pure dephasing. Measurements on a representative dc superconducting quantum interference device (SQUID) over a range of temperatures show that ${S}_{\ensuremath{\Phi}}(f)={A}^{2}/{(f/1\phantom{\rule{0.28em}{0ex}}\text{Hz})}^{\ensuremath{\alpha}}$, where ${S}_{\ensuremath{\Phi}}$ is the flux noise spectral density,
A is of the order of 1 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}\phantom{\rule{0.28em}{0ex}}{\text{Hz}}^{\ensuremath{-}1/2}$, $0.61\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}0.95$, and ${\ensuremath{\Phi}}_{0}$ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, calculations of the dependence of the pure dephasing time ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ of Ramsey and echo pulse sequences on $\ensuremath{\alpha}$ for fixed
A show that ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ decreases rapidly as $\ensuremath{\alpha}$ is reduced. We find that ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ is relatively insensitive to the noise bandwidth, ${f}_{1}\ensuremath{\leqslant}f\ensuremath{\leqslant}{f}_{2}$, for all $\ensuremath{\alpha}$ provided the ultraviolet cutoff frequency ${f}_{2}>1/{\ensuremath{\tau}}_{\ensuremath{\varphi}}$. We calculate the ratio ${\ensuremath{\tau}}_{\ensuremath{\varphi},E}/{\ensuremath{\tau}}_{\ensuremath{\varphi},R}$ of the echo (
E) and Ramsey (
R) sequences and the dependence of the decay function on $\ensuremath{\alpha}$ and
f2. We investigate the case in which ${S}_{\ensuremath{\Phi}}({f}_{0})$ is fixed at the ``pivot frequency'' ${f}_{0}\ensuremath{\ne}1$ Hz while $\ensuremath{\alpha}$ is varied and find that the choice of
f0 can greatly influence the sensitivity of ${\ensuremath{\tau}}_{\ensuremath{\varphi},E}$ and ${\ensuremath{\tau}}_{\ensuremath{\varphi},R}$ to the value of $\ensuremath{\alpha}$. Finally, we present calculated values of ${\ensuremath{\tau}}_{\ensuremath{\varphi}}$ in a qubit corresponding to the values of
A and $\ensuremath{\alpha}$ measured in our SQUID.
We have performed a study of the low-frequency noise in high-temperature radio frequency (rf) superconducting quantum interference devices (SQUIDs) cooled in static magnetic fields. At 77 K, the noise of different thin-film YB2C3O7−x washer rf SQUIDs was measured in static magnetic fields up to 55 μT. The SQUID inductances ranged from 150 to 300 pH. The measured low-frequency flux noise of the SQUIDs SΦ1/2 at 1 Hz was between 70 and 350 μΦ0/√Hz, and in terms of magnetic field noise SB1/2 between 120 and 1100 fT/√Hz. The low-frequency noise of all devices at 1 Hz showed no significant increase for all applied static fields.