Superconducting Quantum Interference Devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/f^{\alpha}$ with $\alpha<1$ whose origin is believed to be due to spin impurities. Here we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing $\sim 5$ % of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing e.g. the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, flux noise power is exactly equal to zero when the spins are polarized along the flux vector direction, forming what we call a poloidal state. Flux noise is non-zero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or inter-surface correlation provides a method to reduce flux noise in superconducting devices.Superconducting Quantum Interference Devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/f^{\alpha}$ with $\alpha<1$ whose origin is believed to be due to spin impurities. Here we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing $\sim 5$% of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing e.g. the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, flux noise power is exactly equal to zero when the spins are polarized along the flux vector direction, forming what we call a poloidal state. Flux noise is non-zero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or inter-surface correlation provides a method to reduce flux noise in superconducting devices.

Jan 15, 20150 citations

Flux-vector model of spin noise in superconducting circuits: Electron versus nuclear spins and role of phase transition

S. LaForest, Rogério de Sousa

Superconducting quantum interference devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/{f}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<1$ whose origin is believed to be due to spin impurities. Here, we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux-noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing $\ensuremath{\sim}5%$ of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing, e.g., the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, the flux-noise power is exactly equal to zero when the spins are polarized along the flux-vector direction, forming what we call a poloidal state. Flux noise is nonzero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or intersurface correlation provides a method to reduce flux noise in superconducting devices.Superconducting quantum interference devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/{f}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<1$ whose origin is believed to be due to spin impurities. Here, we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux-noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing $\ensuremath{\sim}5%$ of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing, e.g., the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, the flux-noise power is exactly equal to zero when the spins are polarized along the flux-vector direction, forming what we call a poloidal state. Flux noise is nonzero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or intersurface correlation provides a method to reduce flux noise in superconducting devices.

arXiv:1501.03776Physical Review BAug 3, 201518 citations

Investigation of 1/f flux noise in SQUIDs and Superconducting Qubits

Antonio Puglielli, S. Sendelbach, Taylor Klaus +1 more

Bulletin of the American Physical SocietyMar 19, 20130 citations

Modeling Flux Noise in SQUIDs due to Hyperfine Interactions

Jiansheng Wu, Clare C. Yu

Recent experiments implicate spins on the surface of metals as the source of flux noise in superconducting quantum interference devices and indicate that these spins are able to relax without conserving total magnetization. We present a model of 1/f flux noise in which electron spins on the surface of metals can relax via hyperfine interactions. Our results indicate that flux noise would be significantly reduced in superconducting materials where the most abundant isotopes do not have nuclear moments, such as zinc and lead.Recent experiments implicate spins on the surface of metals as the source of flux noise in superconducting quantum interference devices and indicate that these spins are able to relax without conserving total magnetization. We present a model of 1/f flux noise in which electron spins on the surface of metals can relax via hyperfine interactions. Our results indicate that flux noise would be significantly reduced in superconducting materials where the most abundant isotopes do not have nuclear moments, such as zinc and lead.

arXiv:1111.2056Physical Review LettersJun 11, 201214 citations

1/f Flux Noise in SQUIDs and Josephson Junction Qubits

David Cardamone, Clare C. Yu

Bulletin of the American Physical SocietyMar 18, 20090 citations

Superconducting Quantum Interference Devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density

1/f^{\alpha}

with

\alpha<1

whose origin is believed to be due to spin impurities. Here we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing

\sim 5

% of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing e.g. the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, flux noise power is exactly equal to zero when the spins are polarized along the flux vector direction, forming what we call a poloidal state. Flux noise is non-zero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or inter-surface correlation provides a method to reduce flux noise in superconducting devices.