The origin of magnetic flux noise in superconducting quantum interference devices with a power spectrum scaling as 1/f (f is frequency) has been a puzzle for over 20 years. This noise limits the decoherence time of superconducting qubits. A consensus has emerged that the noise arises from fluctuating spins of localized electrons with an areal density of 5x10(17) m(-2). We show that, in the presence of potential disorder at the metal-insulator interface, some of the metal-induced gap states become localized and produce local moments. A modest level of disorder yields the observed areal density.
Abstract : Qubit dephasing is governed by low-frequency noise in the bias parameters that control the energy separation between the qubit states. It has been shown that dephasing in phase and flux qubits is dominated by an excess low frequency magnetic flux noise with a 1/f power spectrum and magnitude at 1 Hz of order 1 microPhi0/sqrt(Hz). Recent experiments by McDermott et al. provide clear evidence for the existence of unpaired magnetic states on the surfaces of superconducting thin film devices; it is now believed that fluctuations of these surface spin states are the source of the ubiquitous 1/f flux noise. However, the microscopic mechanism that drives fluctuations of these spins is not understood; moreover, there is no clear path to reducing the flux noise magnitude. This program is devoted to a systematic investigation of magnetic surface defects in SQUIDs and phase qubits. Measurements of surface spin susceptibility and susceptibility noise will yield valuable clues about the microscopic nature of the magnetic fluctuators, and shed light on interactions between defects. The role of qubit loop geometry on flux noise magnitude and dephasing will be explored in detail. The experiments will guide theoretical efforts to develop improved models for flux noise.
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.
Flux noise in superconducting quantum interference devices (SQUIDs) is produced by spins on the surface of metals. We have modeled these with Monte Carlo simulations of 2D and 3D Ising spin glasses that produce magnetization noise SMconsistent with flux noise. The frequency dependence of the magnetization noise goes as 1/fαwhere the exponent a varies slightly with temperature. In 3D the noise power spectrum in the order parameter q goes as 1/ f1.4at Tc. The low frequency noise in both q and the magnetization is a maximum at Tc.
Recent experiments implicate spins on the surface of metals as the source of flux noise in superconducting quantum interference devices and indicate that these spins are able to relax without conserving total magnetization. We present a model of 1/f flux noise in which electron spins on the surface of metals can relax via hyperfine interactions. Our results indicate that flux noise would be significantly reduced in superconducting materials where the most abundant isotopes do not have nuclear moments, such as zinc and lead.