Low-frequency Flux Noise Research Articles

Possible Origin of Low-Frequency Magnetic Flux Noise in Superconducting Devices

The magnetic flux noise caused by surface spin fluctuations in superconducting quantum interference devices (SQUIDs) limits their development. In this work, we report that different adsorbents such as H, O2, NO, and NO2 that adsorb on the surfaces of Mg-based and Pb-based SQUIDs, respectively, producing large local magnetic moments ranging from 0.7-1.6 μB, with energy barriers for thermal spin fluctuation as low as 10-30 mK. Moreover, we observe that the presence of H atoms on the surface of MgO can cause the coadsorption of other molecules, which generates additional spin sources. Monte Carlo simulations of the weakly coupled spin on a two-dimensional square lattice produce a low-frequency flux noise spectrum. We suggest eliminating the surface magnetism by coating the surface with monolayer indium phosphide or protecting the surface from other molecules by nonmagnetic preoccupants with a larger adsorption energy. The work provides important physical insights and feasible strategies for reducing magnetic noise sources in superconducting circuits.

Long-time stable and high-performance YBa2Cu3O7 nanoSQUIDs with more interfaces

We report on the fabrication and characterization of nanopatterned superconducting quantum interference devices (SQUIDs) based on grain boundary Josephson junctions in epitaxially grown multilayer YBa2Cu3O7 (YBCO)/SiTrO3 (STO) thin films. Nanopatterning is performed by Ga+ focused ion beam milling. The evolution of the electric transport and noise properties of the YBCO nanoSQUIDs over a time span of more than one year are recorded and analyzed. We find that the multilayer YBCO/STO nanoSQUIDs show stable and high performance over time. The critical current decreases within ∼40 days by 30%–50% and then remains almost constant without obvious decline trend for nanoSQUIDs with STO layer as the interface even more than 380 days, which demonstrates the superiority of STO as the capping layer. Moreover, we find that the multilayer nanoSQUIDs have about an order of magnitude smaller low-frequency excess flux noise (compared to similar single layer devices) with root-mean-square spectral density ∼5–6 µΦ0/Hz1/2 at 1 Hz. For one device, we show that the low-frequency excess noise does not degrade within three months.

Fast, High-Fidelity Conditional-Phase Gate Exploiting Leakage Interference in Weakly Anharmonic Superconducting Qubits.

Conditional-phase (cz) gates in transmons can be realized by flux pulsing computational states towards resonance with noncomputational ones. We present a 40ns cz gate based on a bipolar flux pulse suppressing leakage (0.1%) by interference and approaching the speed limit set by exchange coupling. This pulse harnesses a built-in echo to enhance fidelity (99.1%) and is robust to long-timescale distortion in the flux-control line, ensuring repeatability. Numerical simulations matching experiment show that fidelity is limited by high-frequency dephasing and leakage by short-timescale distortion.

Tunable Superconducting Qubits with Flux-Independent Coherence

We have studied the impact of low-frequency magnetic flux noise upon superconducting transmon qubits with various levels of tunability. We find that qubits with weaker tunability exhibit dephasing that is less sensitive to flux noise. This insight was used to fabricate qubits where dephasing due to flux noise was suppressed below other dephasing sources, leading to flux-independent dephasing times T2* ~ 15 us over a tunable range of ~340 MHz. Such tunable qubits have the potential to create high-fidelity, fault-tolerant qubit gates and fundamentally improve scalability for a quantum processor.

Dielectric Loss in Superconducting NbN (200) CPW Resonator Developed on Si Substrate

In current superconducting qubit circuit development, coherence time is limited by low-frequency flux noise introduced from localized two-level systems (TLSs) in the fabricated superconducting circuit, including superconducting materials, the interface between thin films, and the substrate. As a part of the effect to tackle this issue from a substrate standpoint, we succeed in fabricating NbN (200) oriented coplanar waveguide resonator (CPWR) on a thin titanium nitride (TiN) (200) buffered Si (100) substrate. The internal loss is close to 3 × 10 -5 near <;n photon > ~1, improved from ~2 × 10 -4 in NbN (200) CPWR fabricated on MgO (100). For NbN (200) resonators grown on Si (100), the internal loss shows microwave energy independent. To further clarity if this energy independence is due to the change of substrate material, we also fabricated TiN (200) CPWR on Si (100). In contrast to NbN (200) CPWR, the loss of TiN (200) resonator shows a strong microwave dependent, an indication of TLSs originated from the interface and the surface. We suggest TLSs in NbN (200) CPWR are dominated from different mechanism other than arising from the interface and surface.

Towards noise engineering: Recent insights in low-frequency excess flux noise of superconducting quantum devices

The comprehensive analysis of low-frequency excess flux noise both in terms of magnetic flux noise SΦ,1/f and energy sensitivity ϵ1∕f of 84 superconducting quantum devices studied at temperatures below 1 K reveals a universal behavior. When analyzing data in terms of ϵ1∕f, we find that noise spectra of independent devices cross each other all at certain crossing frequencies fc. Besides this main result of our paper, we further show that superconducting quantum interference device (SQUID) arrays systematically feature higher noise exponents than single SQUIDs and give evidence for a material and device type dependence of low-frequency excess flux noise. The latter results facilitate to engineer the shape of magnetic flux noise spectra and thus to experimentally modify key properties such as coherence or measurement times of superconducting quantum devices.

Cosmological flux noise and measured noise power spectra in SQUIDs

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.

Flux Noise Probed with Real Time Qubit Tomography in a Josephson Phase Qubit

We measure the dependence of qubit phase coherence and flux noise on inductor loop geometry. While wider inductor traces change neither the flux noise power spectrum nor the qubit dephasing time, increased inductance leads to a simultaneous increase in both. Using our new tomographic protocol for measuring low frequency flux noise, we make a direct comparison between the flux noise spectrum and qubit phase decay, finding agreement within 10% of theory.

Noise correlations in a flux qubit with tunable tunnel coupling

We have measured flux-noise correlations in a tunable superconducting flux qubit. The device consists of two loops that independently control the qubit's energy splitting and tunnel coupling. Low frequency flux noise in the loops causes fluctuations of the qubit frequency and leads to dephasing. Since the noises in the two loops couple to different terms of the qubit Hamiltonian, a measurement of the dephasing rate at different bias points provides a way to extract both the amplitude and the sign of the noise correlations. We find that the flux fluctuations in the two loops are anti-correlated, consistent with a model where the flux noise is generated by randomly oriented unpaired spins on the metal surface.

Role of Geometry on the Color of Flux Noise in dc SQUIDs

We examine the behavior of low frequency flux noise measured in ten Nb-NbOx-Pbln dc SQUIDs in the temperature range 1 K to 20 mK. As previously reported, the flux noise power spectrum SΦ(f) typically scales with frequency as A/fα. Remark ably, the excess noise power A at 1 Hz increases as the temperature is decreased below about 0.7 K, saturating to a value around (10 μΦα)2/Hz below about 0.2 K. Here we report on the dependence of both the magnitude A and the slope a on the size and linewidth of the SQUID loops. In particular, at the lowest temperatures we find that a declines to values as low as 0.5 in the smallest devices, while a is in the range 0.9-1 for the largest devices.

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

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 and <;320 mK. Considering the large spread in the low-frequency noise at 4.2 K, there was no observable dependence of the low-frequency energy resolution ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/f</sub> on 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 ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/f</sub> at <;320 mK and f=10 Hz are typically 40 h and 300 h, respectively (h is Planck's constant). The excess noise scales as ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/f</sub> ∝ f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</sup> with 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.

Spinlike Susceptibility of Metallic and Insulating Thin Films at Low Temperature

Susceptibility measurements of patterned thin films at sub-K temperatures were carried out using a scanning SQUID microscope that can resolve signals corresponding to a few hundred Bohr magnetons. Several metallic and insulating thin films, even oxide-free Au films, show a paramagnetic response with a temperature dependence that indicates unpaired spins as the origin. The observed response exhibits a measurable out-of-phase component, which implies that these spins will create 1/f-like magnetic noise. The measured spin density is consistent with recent explanations of low frequency flux noise in SQUIDs and superconducting qubits in terms of spin fluctuations, and suggests that such unexpected spins may be even more ubiquitous than already indicated by earlier measurements. Our measurements set several constraints on the nature of these spins.

Geometrical dependence of the low-frequency noise in superconducting flux qubits

A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson-junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hypothesis that local impurities in the vicinity of the qubit wiring are a key source of low-frequency flux noise in superconducting devices.

Decoherence in rf SQUID qubits

We report measurements of coherence times of an rf SQUID qubit using pulsed microwaves and rapid flux pulses. The modified rf SQUID, described by an double-well potential, has independent, in situ, controls for the tilt and barrier height of the potential. The decay of coherent oscillations is dominated by the lifetime of the excited state and low frequency flux noise and is consistent with independent measurement of these quantities obtained by microwave spectroscopy, resonant tunneling between fluxoid wells and decay of the excited state. The oscillation’s waveform is compared to analytical results obtained for finite decay rates and detuning and averaged over low frequency flux noise.

Microscopic Origin of Low-Frequency Flux Noise in Josephson Circuits

We analyze the data and discuss their implications for the microscopic origin of the low-frequency flux noise in superconducting circuits. We argue that this noise is produced by spins at superconductor insulator boundary whose dynamics is due to RKKY interaction. We show that this mechanism explains size independence of the noise, different frequency dependences of the spectra reported in large and small SQUIDs, and gives the correct intensity for realistic parameters.

Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise

We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with a significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.

Tunable coupling scheme for flux qubits at the optimal point

We discuss a practical design for tunably coupling a pair of flux qubits via the quantum inductance of a third high-frequency qubit. The design is particularly well suited for realizing a recently proposed microwave-induced parametric coupling scheme. This is attractive because the qubits can always remain at their optimal points. Furthermore, we will show that the resulting coupling also has an optimal point where it is insensitive to low-frequency flux noise. This is an important feature for the coherence of coupled qubits. The presented scheme is an experimentally realistic way of carrying out two-qubit gates and should be easily extended to multiqubit systems.

Microscopic analysis of low-frequency flux noise in YBa2Cu3O7 direct current superconducting quantum interference devices

We use low-temperature scanning electron microscopy combined with superconducting quantum interference device (SQUID) detection of magnetic flux to image vortices and to investigate low-frequency flux noise in YBa2Cu3O7 thin film SQUIDs. The low-frequency flux noise shows a nonlinear increase with magnetic cooling field up to 60μT. This effect is explained by the surface potential barrier at the SQUID hole. By correlating flux noise data with the spatial distribution of vortices, we obtain information on spatial fluctuations of vortices on a microscopic scale, e.g., an average vortex hopping length of ∼10nm.

Low-frequency flux noise in current-carrying high critical temperature superconducting films

The low-frequency flux noise of a narrow current-carrying superconducting film is measured in order to examine the flux noise induced by shielding current in directly coupled high critical temperature superconducting quantum interference devices. Reversible flux noise is found to appear during the application of current above a threshold level, but to disappear when the current is removed. However, as the current is increased beyond a second threshold, where the strip enters a flux creep∕flow state, a flux noise occurs that remains after the current is removed. The threshold current for the onset of the reversible flux noise strongly depends on the edge-shape processing applied to the strip. The sources of the reversible and remaining flux noises are discussed on the basis of existing models of vortex penetration and pinning in a superconducting thin film.

Original superconducting quantum interference device (SQUID) design and measurement technique for flux noise source localization in SQUID systems

We present an original method for studying the low frequency flux noise due to vortices in superconducting quantum interference device (SQUID) systems. We use two SQUIDs connected to the same washer in order to study the correlation of their outputs. A dedicated electronic system has been built so as to operate both SQUIDs at the same time. It was thus possible to distinguish fluctuations due to vortices located in the film far from the SQUID from fluctuations originating from vortices located close to the SQUID itself. In this article, the experimental setup is described and some preliminary noise measurements are presented.