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ow-Frequency Flux Noise in dc SQUIDS*

M. E. Huber, Michael W. Cromar, Ronald H. Ono

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

tions of the device; in particular, variations in the critical current of small junctions can lead to significant lowfrequency noise [2]. In high-quality junctions, however, these fluctuations may be negligible. For the Stanford experiment, we require well-coupled ck SQUIDs with an energy sensitivity of 1 x lo-*’ J/Hz ai 5 mHz. Early in the development of these devices, we observed both excess low-frequency noise and resonances due to the input coil. (Our investigation of resonance phenomenon will be discussed elsewhere [3] and we focus on the excess low-frequency noise here.) To study the excess noise, we have fabricated devices with two geometries: a well-coupled SQUID with a washer geometry and a self-shielded SQUID with a stripline geometry [4, 51. Results of these experiments indicate that we are observing flux noise originating from within the SQUID. Process improvements have dramatically reduced this noise. We have also performed experiments to reduce the potential for flux motion in the SQUID; this work is still in progress.

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Excess low-frequency flux noise in dc SQUIDs

M. E. Huber, Michael W. Cromar, Ronald H. Ono

We have fabricated dc superconducting quantum interference devices (SQUIDs) incorporating Nb/Al-oxide/Nb Josephson junctions in both stripline and washer geometries. Low-frequency noise in excess of that predicted by the resistively-shunted junction model is present in both geometries and is demonstrated to be flux noise. This flux noise is not environmental. Improvements in fabrication processing over the past four years have reduced the level of this flux noise. SQUIDs are now fabricated with PdAu resistors, Nb wiring layers, and SiO/sub 2/ interlayer dielectric. In our best well-coupled SQUIDs, the white-noise energy sensitivity is 5/spl times/10/sup -31/ J/spl middot/s, with a 1/f knee below 0.1 Hz. We believe further reduction in the flux noise might be obtained with the use of on-chip flux shielding and/or trapping structures.

IEEE Transactions on Applied Superconductivity•Jun 1, 1997•5 citations

Investigation of Low-Frequency Excess Flux Noise in DC SQUIDs at mK Temperatures

D. Drung, J. Beyer, Jan-Hendrik Storm +2 more

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.

IEEE Transactions on Applied Superconductivity•Nov 10, 2010•25 citations

Magnetic flux noise in SQUIDs and qubits

Steven M. Anton

For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as $S_Phi(f) propto 1/f^alpha$, where $alpha lesssim 1$, 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 $Phisq propto R/W$ 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 $S_Phi(f) = A^2/(f/1~hbox{Hz})^alpha$, where $A$ is of the order of 1~$muPhi_0 , hbox{Hz}^{-1/2}$ and $0.6 leq alpha leq 1.2$; $Phi_{0}$ 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 $tau_phi$ of Ramsey and echo pulse sequences on $alpha$ for fixed $A$ show that $tau_phi$ decreases rapidly as $alpha$ is reduced. We find that $tau_phi$ is relatively insensitive to the noise bandwidth, $f_1 leq f leq f_2$, for all $alpha$ provided the ultraviolet cutoff frequency $f_2 > 1/tau_phi$. We calculate the ratio $tau_{phi,E} / tau_{phi,R}$ of the echo ($E$) and Ramsey ($R$) sequences, and the dependence of the decay function on $alpha$ and $f_2$. We investigate the case in which $S_Phi(f_0)$ is fixed at the ``pivot frequency'' $f_0 neq 1$~Hz while $alpha$ is varied, and find that the choice of $f_0$ can greatly influence the sensitivity of $tau_{phi,E}$ and $tau_{phi,R}$ 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.

•Jan 1, 2013•0 citations

Low-noise tunnel junction dc SQUID’s

Michael W. Cromar, P. Carelli

We present the results of an investigation of thin-film dc super conducting quantum interference device (SQUID’s) with very high energy resolution. The SQUID’s were fabricated using integrated-circuit techniques appropriate for superconducting devices. A weakly coupled SQUID with very low inductance (1 pH) had an intrinsic energy sensitivity 6×10−34 J/Hz = 0.9 h. A well-coupled SQUID (coupling constant α = 0.43) had an energy sensitivity referred to the input coil of 4.7×10−32 J/Hz = 71 h.

Applied Physics Letters•May 1, 1981•87 citations

Investigation and reduction of excess low-frequency noise in rf superconducting quantum interference devices

Michael Mück, Christoph Heiden, John L. Clarke

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.

Journal of Applied Physics•May 1, 1994•26 citations

A coupled DC SQUID with low 1/f noise

Heikki Seppä, M. Kiviranta, Alexandre Satrapinski +3 more

A low-noise coupled DC superconducting quantum interference device (SQUID) especially optimized for low frequency is discussed. Using large Josephson junctions and a low loop inductance the contribution of the critical current fluctuation to 1/f noise can be minimized. To minimize the inductance the Josephson junctions are placed in the center of the washer close to the SQUID loop. A scaled-up copper model of the SQUID and the signal coil is used to analyze the impedance of the SQUID loop affected by the signal coil. An equivalent circuit model describing the effective inductance of the SQUID loop as a function of the frequency is used to design appropriate damping of the resonances. The DC SQUID characteristics are smooth and the noise performance of the SQUID does not markedly suffer from resonances. The contribution of the 1/f noise at 1 Hz is found to be about 5*10/sup -7/ Phi /sub 0// square root Hz.>

IEEE Transactions on Applied Superconductivity•Mar 1, 1993•25 citations
tions of the device; in particular, variations in the critical current of small junctions can lead to significant lowfrequency noise [2]. In high-quality junctions, however, these fluctuations may be negligible. For the Stanford experiment, we require well-coupled ck SQUIDs with an energy sensitivity of 1 x lo-*’ J/Hz ai 5 mHz. Early in the development of these devices, we observed both excess low-frequency noise and resonances due to the input coil. (Our investigation of resonance phenomenon will be discussed elsewhere [3] and we focus on the excess low-frequency noise here.) To study the excess noise, we have fabricated devices with two geometries: a well-coupled SQUID with a washer geometry and a self-shielded SQUID with a stripline geometry [4, 51. Results of these experiments indicate that we are observing flux noise originating from within the SQUID. Process improvements have dramatically reduced this noise. We have also performed experiments to reduce the potential for flux motion in the SQUID; this work is still in progress.
We have fabricated dc superconducting quantum interference devices (SQUIDs) incorporating Nb/Al-oxide/Nb Josephson junctions in both stripline and washer geometries. Low-frequency noise in excess of that predicted by the resistively-shunted junction model is present in both geometries and is demonstrated to be flux noise. This flux noise is not environmental. Improvements in fabrication processing over the past four years have reduced the level of this flux noise. SQUIDs are now fabricated with PdAu resistors, Nb wiring layers, and SiO/sub 2/ interlayer dielectric. In our best well-coupled SQUIDs, the white-noise energy sensitivity is 5/spl times/10/sup -31/ J/spl middot/s, with a 1/f knee below 0.1 Hz. We believe further reduction in the flux noise might be obtained with the use of on-chip flux shielding and/or trapping structures.
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/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.
We present the results of an investigation of thin-film dc super conducting quantum interference device (SQUID’s) with very high energy resolution. The SQUID’s were fabricated using integrated-circuit techniques appropriate for superconducting devices. A weakly coupled SQUID with very low inductance (1 pH) had an intrinsic energy sensitivity 6×10−34 J/Hz = 0.9 h. A well-coupled SQUID (coupling constant α = 0.43) had an energy sensitivity referred to the input coil of 4.7×10−32 J/Hz = 71 h.
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.
A low-noise coupled DC superconducting quantum interference device (SQUID) especially optimized for low frequency is discussed. Using large Josephson junctions and a low loop inductance the contribution of the critical current fluctuation to 1/f noise can be minimized. To minimize the inductance the Josephson junctions are placed in the center of the washer close to the SQUID loop. A scaled-up copper model of the SQUID and the signal coil is used to analyze the impedance of the SQUID loop affected by the signal coil. An equivalent circuit model describing the effective inductance of the SQUID loop as a function of the frequency is used to design appropriate damping of the resonances. The DC SQUID characteristics are smooth and the noise performance of the SQUID does not markedly suffer from resonances. The contribution of the 1/f noise at 1 Hz is found to be about 5*10/sup -7/ Phi /sub 0// square root Hz.>