Field-Dependent Qubit Flux Noise Simulated from Materials-Specific Disordered Exchange Interactions Between Paramagnetic Adsorbates

Abstract

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 O$_2$ molecules on an Al$_2$O$_3$ 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.

Figures (5)

• Figure 1: (a) Oxygen molecule on the (0001) Al$_2$O$_3$ surface, inset: top-down view showing the six possible O$_2$ binding orientations. (b) Monte Carlo generated arrangement of an O$_2$ molecule monolayer at 0.01 K, where the O$_2$ dimers are represented by red cylinders with exaggerated length compared to the lattice spacing. (c) Distribution of O$_2$-O$_2$ spin exchange couplings from the arrangement depicted in (b), showing mostly weakly negative (ferromagnetic) interactions. (d) Monte Carlo generated lattice of O$_2$ spins, represented by light blue arrows, at 0.01 K on the O$_2$ molecular surface configuration shown in (b).
• Figure 2: (a) Spin-spin correlation functions for several temperatures show the algebraic decay characteristic of BKT phases below the transition temperature. (b) By fitting the correlation functions to the expected algebraic scaling, $(|r - r'|/l)^{-\eta}$, as a function of temperature, we can extract the transition temperature, which corresponds to the case with $\eta = 1/4$; the data here give a transition temperature of 121 mK.
• Figure 3: (a) The magnetic flux noise spectrum computed for a sapphire surface covered with paramagnetic O$_2$ spins with 100%, 75%, and 50% occupancy, at 0.01 K in zero applied magnetic and electric fields, as well as with 100% occupancy in an applied E-field. (b) Simulated magnetic flux noise at 160 MHz vs. temperature compared to measurements in the literature. Experimental series are each scaled to have consistent low-temperature noise magnitude, so the temperature dependency can be highlighted. (c) Cross-correlation between magnetization and magnetic susceptibility ($S_{M\chi"} / S_M S_{\chi"}$) vs. temperature for our simulations averaged over frequencies between 1.5 and 2.5 MHz (blue dots) compared to measurements by Sendelbach et al. at 1 Hzsendelbach2009complex (orange dots).
• Figure 4: Simulated magnetic flux noise at 100 MHz and 0.1 K vs. applied magnetic field. Experimental results at 4.3 MHz are included for comparison and are scaled so that the experimental zero field flux noise aligns with the simulated zero field flux noise.
• Figure 5: (a) Side and top-down views of the charge density difference between antiferromagnetic (AFM) and ferromagnetic (FM) spin configurations on a particular nearest neighbor O$_2$ orientation on a (0001) sapphire surface (isosurface: 0.0025 e$/\text{\AA}^3$). Yellow (blue) denotes charge accumulation (depletion) of the AFM spin configuration compared to the FM configuration. (b) Spin-spin correlation functions for several temperatures, with an applied electric field of 10$^7$ V/cm, show the algebraic decay characteristic of BKT phases below the transition temperature. (c) For the expected algebraic scaling, $(|r - r'|/l)^{-\eta}$, $\eta = 1/4$ at the transition temperature. We plot $\eta$ and find the transition temperature to be 276 mK.