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Japanese Journal of Applied Physics

Characteristics of Flux Noise in Long Superconducting Quantum Interference Device Array

T. Morooka, Hiroaki Myoren, S. Takada, Kazuo Chinone

Published Nov 10, 2003• 3 citations
Publisher

Abstract

The flux noise in a long superconducting quantum interference device (SQUID) array consisting of at least 100 dc-SQUID elements connected in series was characterized analytically, and then compared with measurements. In the analysis, noise sources in the array were shunt resistors for Josephson junctions, a damping resistor for a SQUID loop, the dynamic resistance of the SQUID array, and the noise of electronics at room temperature. The flux noise of the array was calculated analytically as a function of the number of dc-SQUID elements. The results reveal that the flux noise is significantly influenced by the dynamic resistance of the array, although the influence by the dynamic resistance for a single SQUID is negligibly small. The dynamic resistance becomes dominant for the flux noise when the number of SQUID elements in the array exceeds 100. These results agree well with the measured flux noise for a long SQUID array constructed using a Nb/AlO x /Nb fabrication process.

DOI
10.1143/jjap.42.6848

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The flux noise in a long superconducting quantum interference device (SQUID) array consisting of at least 100 dc-SQUID elements connected in series was characterized analytically, and then compared with measurements. In the analysis, noise sources in the array were shunt resistors for Josephson junctions, a damping resistor for a SQUID loop, the dynamic resistance of the SQUID array, and the noise of electronics at room temperature. The flux noise of the array was calculated analytically as a function of the number of dc-SQUID elements. The results reveal that the flux noise is significantly influenced by the dynamic resistance of the array, although the influence by the dynamic resistance for a single SQUID is negligibly small. The dynamic resistance becomes dominant for the flux noise when the number of SQUID elements in the array exceeds 100. These results agree well with the measured flux noise for a long SQUID array constructed using a Nb/AlO x /Nb fabrication process.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.
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.
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
Abstract Noise in superconducting quantum interference devices (dc SQUIDs) with different design, based on Nb/AlO x /Nb technology, has been systematically measured at temperature T = 4.2 K. We demonstrate that for all our devices the power spectral density of the white noise (above a frequency of about 1 kHz) is determined by the shunt resistors, reaching about 5 times Planck’s constant. The low-frequency noise level was measured for washer- and multi-loop-type SQUIDs with systematically varied effective area, SQUID loop perimeter, and inductance. We show that at 1 Hz the noise spectral density is approximately 40 times higher than the white noise level and its scaling with washer width and effective area is negligible. These results are incompatible with several models of the flicker noise source. Possible origins of this noise are discussed.
We have fabricated Y1Ba2Cu3O7−x step-edge junction dc superconducting quantum interference devices (SQUIDs) and characterized their noise performance. The current-voltage characteristics of our SQUIDs are of resistively shunted junction type with critical current densities jc of about 104 A/cm2 and maximum flux to voltage transfer functions δV/δΦ of 20 μV/Φ0 at 77 K. We compare model predictions for 1/f noise in dc SQUIDs with experimental data and show that the frequency dependent noise in our devices results from critical current fluctuations of the Josephson junctions. A bias current reversing technique is effective in suppressing this noise contribution. A flux noise Φn of 80 μΦ0/Hz1/2 at 1 Hz and 77 K was measured on a dc SQUID with an inductance Ls of 60 pH.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.