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arXiv:1709.06208 · Physical review. B./Physical review. B

Hydrogen as a source of flux noise in SQUIDs

Zhe Wang, Hui Wang, Clare C. Yu, Ruqian Wu

Published Jul 9, 2018• 17 citations
arXivHTMLPDF

Abstract

Superconducting qubits are hampered by flux noise produced by surface spins from a variety of microscopic sources. Recent experiments indicated that hydrogen (H) atoms may be one of those sources. Using density functional theory calculations, we report that H atoms either embedded in, or adsorbed on, an $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}(0001)$ surface have sizable spin moments ranging from 0.81 to $0.87{\ensuremath{\mu}}_{B}$ with energy barriers for spin reorientation as low as $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. Furthermore, H adatoms on the surface attract gas molecules such as ${\mathrm{O}}_{2}$, producing new spin sources. We propose coating the surface with graphene to eliminate H-induced surface spins and to protect the surface from other adsorbates.

DOI
10.1103/physrevb.98.020403

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Superconducting qubits are hampered by flux noise produced by surface spins from a variety of microscopic sources. Recent experiments indicated that hydrogen (H) atoms may be one of those sources. Using density functional theory calculations, we report that H atoms either embedded in, or adsorbed on, an \ensuremathα\ensuremath-Al2O3(0001)\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}(0001)\ensuremathα\ensuremath-Al2​O3​(0001) surface have sizable spin moments ranging from 0.81 to 0.87\ensuremathμB0.87{\ensuremath{\mu}}_{B}0.87\ensuremathμB​ with energy barriers for spin reorientation as low as \ensuremath∼10mK\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{mK}\ensuremath∼10mK. Furthermore, H adatoms on the surface attract gas molecules such as O2{\mathrm{O}}_{2}O2​, producing new spin sources. We propose coating the surface with graphene to eliminate H-induced surface spins and to protect the surface from other adsorbates.
Superconducting qubits are hampered by flux noise produced by surface spins from a number of sources. Recent experiments indicated that hydrogen (H) atoms may be one of the sources. Using density functional theory calculations, we report that H atoms either embedded in or adsorbed on an {\alpha}-Al2O3(0001) surface have sizeable spin moments ranging from 0.81 to 0.87 {\mu}B with extremely shallow energy barriers for spin reorientation as low as ~10 mK. Furthermore, H adatoms on the surface attract gas molecules such as O2 and produce new spin sources. We propose using a protective graphene coating on an {\alpha}-Al2O3(0001) surface to eliminate H-induced surface spins and to screen other adsorbates from the environment.
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, O 2, NO, and NO 2 that adsorb on the surfaces of Mg-based and Pb-based SQUIDs, respectively, producing large local magnetic moments ranging from 0.7–1.6 μ B, 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.
A major obstacle to using superconducting quantum interference devices (SQUIDs) as qubits is flux noise. We propose that the heretofore mysterious spins producing flux noise could be O_{2} molecules adsorbed on the surface. Using density functional theory calculations, we find that an O_{2} molecule adsorbed on an α-alumina surface has a magnetic moment of ~1.8 μ_{B}. The spin is oriented perpendicular to the axis of the O-O bond, the barrier to spin rotations is about 10 mK. Monte Carlo simulations of ferromagnetically coupled, anisotropic XY spins on a square lattice find 1/f magnetization noise, consistent with flux noise in Al SQUIDs.
Superconducting quantum devices, from qubits and magnetometers to dark matter detectors, are influenced by magnetic flux noise originating from paramagnetic surface defects and impurities. These spin systems can feature complex dynamics, including a Berezinskii-Kosterlitz-Thouless transition, that depend on the lattice, interactions, external fields, and disorder. However, the disorder included in typical models is not materials-specific, diminishing the ability to accurately capture measured flux noise phenomena. We present a first principles-based simulation of a spin lattice consisting of paramagnetic O2_22​ molecules on an Al2_22​O3_33​ surface, a likely flux noise source in superconducting qubits, to elucidate opportunities to mitigate flux noise. We simulate an ensemble of surface adsorbates with disordered orientations and calculate the orientation-dependent exchange couplings using density functional theory. Thus, our spin simulation has no free parameters or assumed functional form of the disorder, and captures correlation in the defect landscape that would appear in real systems. We calculate a range of exchange interactions between electron pairs, with the smallest values, 0.016 meV and -0.023 meV, being in the range required to act as a two-level system and couple to GHz resonators. We calculate the flux noise frequency, temperature, and applied external magnetic field dependence, as well as the susceptibility-flux noise cross-correlation. Calculated trends agree with experiment, demonstrating that a surface harboring paramagnetic adsorbates arranged with materials-specific disorder and interactions captures the various properties of magnetic flux noise observed in superconducting circuits. In addition, we find that an external electric field can tune the spin-spin interaction strength and reduce magnetic flux noise.
Magnetic flux noise is a dominant source of dephasing and energy relaxation in superconducting qubits. The noise power spectral density varies with frequency as 1/fα, with α1, and spans 13 orders of magnitude. Recent work indicates that the noise is from unpaired magnetic defects on the surfaces of the superconducting devices. Here, we demonstrate that adsorbed molecular O2 is the dominant contributor to magnetism in superconducting thin films. We show that this magnetism can be reduced by appropriate surface treatment or improvement in the sample vacuum environment. We observe a suppression of static spin susceptibility by more than an order of magnitude and a suppression of 1/f magnetic flux noise power spectral density of up to a factor of 5. These advances open the door to the realization of superconducting qubits with improved quantum coherence.
Superconducting Quantum Interference Devices (SQUIDs) are currently being used as flux qubits and read-out detectors in a variety of solid-state quantum computer architectures. The main limitation of SQUID qubits is that they have a coherence time of the order of 10 us, due to the presence of intrinsic flux noise that is not yet fully understood. The origin of flux noise is currently believed to be related to spin impurities present in the materials and interfaces that form the device. Here we present a novel numerical method that enables calculations of the flux produced by spin impurities even when they are located quite close to the SQUID wire. We show that the SQUID will be particularly sensitive to spins located at its wire edges, generating flux shifts of up to 4 nano flux quanta, much higher than previous calculations based on the software package FastHenry. This shows that spin impurities in a particular region along the wire's surface play a much more important role in producing flux noise than other spin impurities located elsewhere in the device.