Direct Identification of Dilute Surface Spins on ${\mathrm{Al}}_2{\mathrm{O}}_3$: Origin of Flux Noise in Quantum Circuits

An on-chip electron spin resonance technique is applied to reveal the nature and origin of surface spins on ${\mathrm{Al}}_2{\mathrm{O}}_3$. We measure a spin density of $2.2\times 10^{17}\text{spins}/{\mathrm{m}}^2$, attributed to physisorbed atomic hydrogen and $S=1/2$ electron spin states on the surface. This is direct evidence for the nature of spins responsible for flux noise in quantum circuits, which has been an issue of interest for several decades. Our findings open up a new approach to the identification and controlled reduction of paramagnetic sources of noise and decoherence in superconducting quantum devices.

Figure 1

Spin energy spectrum and characteristics. (a) Spectrum observed (red) at 10 mK with a fit (black). An excellent fit is obtained for a Lorentzian central peak (peak 2) and Gaussian satellite peaks (peaks 1 and 3). The broad spin background is fit to a wide Gaussian onset followed by a constant contribution to the dissipation over almost 100 mT. The shown quantity $Q_b^{-1}=Q^{-1}(B)-Q^{-1}(B=0)$ is the magnetic-field-associated losses, obtained from the quality factor $Q$. See Supplemental Material [27] for details. (b) Extracted peak positions for a large number of resonators with different frequencies jointly fitted to the energy level transitions of our model. Inset shows the same data where a constant slope of $g=2.0$ has been subtracted. (c) Temperature dependence of the extracted peak areas fitted to the expected temperature dependence. Solid black line is for a doublet ($S=1/2$) spin ensemble while the black dashed line corresponds to the best fit to a triplet ($S=1$). Error bars are 95% confidence bounds to spectral fits such as the fit presented in (a).

Figure 2

Probing the surface chemistry. (a) The influence of a series of surface treatments (see text) on the measured spectrum. Curves have been offset for clarity. (b) Post fabrication annealing a sample to $300°\mathrm{C}$ removes the peaks associated with H via ${\mathrm{H}}_2$ generation. The H does not return at ambient conditions. An oxygen plasma and immersion into water returns the H peaks with the same intensity, while the central peak remains largely unaffected throughout, even in the presence of the additional broad peak after immersion in water [27]. Traces have been offset for clarity. (c) The result of exposing a sample to a H-ion plasma and subsequent relaxation back to the original spin density. The central peak is unaffected while the hydrogen spin density increased just after plasma exposure by 70%, returning to equilibrium conditions after 50 hours. Solid black lines are fits to extract spin density [27]. $T=300\mathrm{mK}$.