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Applied Physics Letters

Reduction of 1/f noise in high-T c dc superconducting quantum interference devices cooled in an ambient magnetic field

E. Dantsker, Saburo Tanaka, P.-Å. Nilsson, R. Kleiner, John L. Clarke

Published Dec 23, 1996• 102 citations
Publisher

Abstract

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.

DOI
10.1063/1.117831

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Applied Physics Letters•Jan 5, 1998•41 citations
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 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.
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.
High-transition temperature dc superconducting quantum interference devices (SQUIDs) have been fabricated with arrays of slots or holes patterned in the 186×204 μm2 washers. In two designs, with seven slots or 248 holes, the linewidth of the remaining YBa2Cu3O7−x film was 4 μm. These devices exhibited virtually no increase in their low-frequency noise when they were cooled in static magnetic fields up to a certain threshold, above 100 μT in the best case. Furthermore, the mutual inductance between these devices and a seven-turn, spiral coil was at least 85% of that for a solid SQUID with the same outer dimensions.
For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as SPhi(f)propto1/falphaS_Phi(f) propto 1/f^alphaSP​hi(f)propto1/falpha, where alphalesssim1alpha lesssim 1alphalesssim1, 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 alphaalphaalpha 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/f1/f1/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 PhisqPhisqPhisq from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, PhisqPhisqPhisq is proportional to langleBbf(rbf)2ranglelangleBbf(rbf)^2ranglelangleBbf(rbf)2rangle, where Bbf(rbf)Bbf(rbf)Bbf(rbf) is the magnetic field generated by a circulating current around the loop and rbfrbfrbf 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 PhisqPhisqPhisq 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/WPhisq propto R/WPhisqproptoR/W in the limit where the loop radius RRR is much greater than the linewidth WWW. We further show that the previously neglected contribution of edge spins to PhisqPhisqPhisq 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)alphaS_Phi(f) = A^2/(f/1~hbox{Hz})^alphaSP​hi(f)=A2/(f/1 hboxHz)alpha, where AAA is of the order of 1~muPhi0,hboxHz−1/2muPhi_0 , hbox{Hz}^{-1/2}muPhi0​,hboxHz−1/2 and 0.6leqalphaleq1.20.6 leq alpha leq 1.20.6leqalphaleq1.2; Phi0Phi_{0}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 tauphitau_phitaup​hi of Ramsey and echo pulse sequences on alphaalphaalpha for fixed AAA show that tauphitau_phitaup​hi decreases rapidly as alphaalphaalpha is reduced. We find that tauphitau_phitaup​hi is relatively insensitive to the noise bandwidth, f1leqfleqf2f_1 leq f leq f_2f1​leqfleqf2​, for all alphaalphaalpha provided the ultraviolet cutoff frequency f2>1/tauphif_2 > 1/tau_phif2​>1/taup​hi. We calculate the ratio tauphi,E/tauphi,Rtau_{phi,E} / tau_{phi,R}tauphi,E​/tauphi,R​ of the echo (EEE) and Ramsey (RRR) sequences, and the dependence of the decay function on alphaalphaalpha and f2f_2f2​. We investigate the case in which SPhi(f0)S_Phi(f_0)SP​hi(f0​) is fixed at the ``pivot frequency'' f0neq1f_0 neq 1f0​neq1~Hz while alphaalphaalpha is varied, and find that the choice of f0f_0f0​ can greatly influence the sensitivity of tauphi,Etau_{phi,E}tauphi,E​ and tauphi,Rtau_{phi,R}tauphi,R​ to the value of alphaalphaalpha.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.
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 dc-superconducting quantum interference device (SQUID) is a low-noise converter from magnetic flux to voltage which can have, in principle, an energy sensitivity near the quantum limit of ℏ/2. A critical parameter for the ideal performance is the device inductance, which must be kept as small as possible. Minimizing the SQUID inductance, however, is a major concern for a practical device; this requirement implies a small SQUID ring and hence magnetic coupling with an external signal is more difficult to achieve. Here we present an original scheme (called multiwasher) to circumvent this problem, and its implementation in an all-refractory thin-film device. Our scheme not only provides good magnetic coupling with a large input coil (0.5 μH) and very low SQUID inductance, but also shielding from outside uniform fields, such as those generated by ambient disturbances. The measured coupled spectral energy sensitivity in the white region at about 1 kHz is 28ℏ at 4.2 K and 5.5ℏ in a pumped helium bath at 0.9 K. The flux noise spectral density at 0.1 Hz and 0.9 K is Φn=1×10−6 Φ0/Hz.