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.
For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as
SPhi(f)propto1/falpha, where
alphalesssim1, has been known to limit the low-frequency performance of dc superconducting quantum interference devices (SQUIDs). In recent years, experiments indicate that this same noise persists to frequencies up to 1~GHz and is a dominant source of dephasing in flux-sensitive superconducting quantum bits (qubits). Thus, the reduction of flux noise presents a major hurdle towards the successful realization of scalable quantum computers that are based on flux-based qubits. In this thesis, we present experimental measurements, theoretical analyses, and numerical simulations that support a more detailed understanding of both the microscopic and macroscopic properties of flux noise.Our experimental work begins with flux noise measurements of a large number of SQUIDs in the temperature range from 0.1~K to 4~K. We report on measurements of ten SQUIDs with systematically varied geometries and show that
alpha 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 washer. We show that these results are incompatible with a model based on the random reversal of independent, spins that are located at the surface of the SQUID washer.In the course of our flux noise measurements, we became aware of a spurious contribution to low-frequency critical current noise in Josephson junctions---normally attributed to charge trapping in the barrier---arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. By computing cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions, we show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because
1/f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.Next, we introduce a numerical method of calculating the mean square flux noise
Phisq from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity,
Phisq is proportional to
langleBbf(rbf)2rangle, where
Bbf(rbf) is the magnetic field generated by a circulating current around the loop and
rbf varies over the loop surface. By discretizing the loop nonuniformly, we efficiently and accurately compute the current distribution and resulting magnetic field, which may vary rapidly across the loop. We use this method to compute
Phisq in a number of scenarios in which we systematically vary physical parameters of the loop. We compare our simulations to an earlier analytic result predicting that
PhisqproptoR/W in the limit where the loop radius
R is much greater than the linewidth
W. We further show that the previously neglected contribution of edge spins to
Phisq is significant---even dominant---in narrow-linewidth loops.To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density
SPhi(f)=A2/(f/1 hboxHz)alpha, where
A is of the order of 1~
muPhi0,hboxHz−1/2 and
0.6leqalphaleq1.2;
Phi0 is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time
tauphi of Ramsey and echo pulse sequences on
alpha for fixed
A show that
tauphi decreases rapidly as
alpha is reduced. We find that
tauphi is relatively insensitive to the noise bandwidth,
f1leqfleqf2, for all
alpha provided the ultraviolet cutoff frequency
f2>1/tauphi. We calculate the ratio
tauphi,E/tauphi,R of the echo (
E) and Ramsey (
R) sequences, and the dependence of the decay function on
alpha and
f2. We investigate the case in which
SPhi(f0) is fixed at the ``pivot frequency''
f0neq1~Hz while
alpha is varied, and find that the choice of
f0 can greatly influence the sensitivity of
tauphi,E and
tauphi,R to the value of
alpha.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.
The subject of electronic noise in high- superconducting Josephson devices and in their applications is considered. Several types of grain boundary junctions, prepared in different ways by four separate international laboratories, are fully characterized in terms of their electrical and noise properties at a range of temperatures, frequencies, magnetic fields and in the presence of microwaves. Similar characterization is carried out for multijunction Josephson flux-flow arrays, and bi-epitaxial SQUIDs. The theory of Likharev and Semenov for thermal noise in low- junctions is adopted as a reference against which excess noise can be identified in high- junctions. It is combined with theoretical models of excess noise based on fluctuations of critical current and resistance to provide accurate fitting of the observed noise curves. It is shown that the normalized levels of critical current and normal resistance fluctuations for all of the junction types examined are remarkably close (typically around and at 100 Hz) and are nearly independent of temperature in the range T = 30 - 80 K. The frequency dependence is close to the universal 1/f law with some deviations due to trapping of charge carriers at discrete states in the tunnelling barrier. Measurements of voltage noise levels and critical current fluctuations in multijunction flux-flow amplifiers, reported for the first time, are consistent with levels in single junctions of the same type. Excess noise is studied as a function of external magnetic field, in a way that has not been previously described. A new interpretation of the magnetic field-dependent noise data indicates that absolute levels of critical current fluctuations are nearly independent of applied magnetic field. This observation does not appear to have been reported elsewhere. It has important implications for the operation of grain boundary Josephson devices in real applications. Voltage noise in the presence of microwave irradiation, at operating points between Shapiro steps, is consistent with a modified form of the Likharev - Semenov equation which takes into account the known level of critical current fluctuations as measured in field-free conditions. The implications of these results for further improvements in device performance are discussed, and directions for further work are suggested.
A detailed study has been made of the low-frequency excess noise of rf superconducting quantum interference devices (SQUIDs), fabricated from thin niobium films and operated at 4.2 K, with rf bias frequencies of 0.15, 1.7, and 3 GHz. When the SQUIDs were operated in an open-loop configuration in the absence of low-frequency flux modulation, the demodulated rf voltage exhibited a substantial level 1/f noise, which was essentially independent of the rf bias frequency. As the rf bias frequency was increased, the crossover frequency at which the 1/f noise power was equal to the white noise power moved to higher frequencies, because of the reduction in white noise. On the other hand, when the SQUID was flux modulated at 50 kHz and operated in a flux locked loop, no 1/f noise was observed at frequencies above 0.5 Hz. A detailed description of how the combination of rf bias and flux modulation removes 1/f noise due to critical current fluctuations is given. Thus, the results demonstrate that the 1/f noise observed in these SQUIDs is generated by critical current fluctuations, rather than by the hopping of flux vortices in the niobium films.
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 understanding of the origin of 1/f magnetic flux noise commonly observed in superconducting devices such as SQUIDs and qubits is still a major unsolved puzzle. Here we discuss the possibility that a significant part of the observed low-frequency flux noise measured in these devices is ultimately seeded by cosmological fluctuations. We consider a theory where a primordial flux noise field left over in unchanged form from an early inflationary or quantum gravity epoch of the universe intrinsically influences the phase difference in SQUIDs and qubits. The perturbation seeds generated by this field can explain in a quantitatively correct way the form and amplitude of measured low-frequency flux noise spectra in SQUID devices if one takes as a source of fluctuations the primordial power spectrum of curvature fluctuations as measured by the Planck collaboration. Our theoretical predictions are in excellent agreement with recent low-frequency flux noise measurements of various experimental groups. Magnetic flux noise, so far mainly considered as a nuisance for electronic devices, may thus contain valuable information about fluctuation spectra in the very early universe.