Delocalized Oxygen as the Origin of Two-Level Defects in Josephson Junctions

Timothy C. DuBois, Manolo C. Per, Salvy P. Russo, and Jared H. Cole

Phys. Rev. Lett. 110, 077002 – Published 12 February 2013; Erratum Phys. Rev. Lett. 113, 029901 (2014)

Abstract

One of the key problems facing superconducting qubits and other Josephson junction devices is the decohering effects of bistable material defects. Although a variety of phenomenological models exist, the true microscopic origin of these defects remains elusive. For the first time we show that these defects may arise from delocalization of the atomic position of the oxygen in the oxide forming the Josephson junction barrier. Using a microscopic model, we compute experimentally observable parameters for phase qubits. Such defects are charge neutral but have nonzero response to both applied electric field and strain. This may explain the observed long coherence time of two-level defects in the presence of charge noise, while still coupling to the junction electric field and substrate phonons.

Received 7 September 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.077002

Erratum

Erratum: Delocalized Oxygen as the Origin of Two-Level Defects in Josephson Junctions [Phys. Rev. Lett. 110, 077002 (2013)]

Timothy C. DuBois, Manolo C. Per, Salvy P. Russo, and Jared H. Cole

Phys. Rev. Lett. 113, 029901 (2014)

Authors & Affiliations

Timothy C. DuBois¹, Manolo C. Per^1,2, Salvy P. Russo¹, and Jared H. Cole¹

¹Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
²Virtual Nanoscience Laboratory, CSIRO Materials Science and Engineering, Parkville, Victoria 3052, Australia

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Vol. 110, Iss. 7 — 15 February 2013

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Images

Figure 1
(a) Depiction of a JJ with two aluminium slabs surrounding an amorphous ${AlO}_{1.25}$ barrier (aluminium: gray, oxygen: red). (b) The projected radial distribution function $G (r)$ using oxygen as a reference. (c) The total energy per atom of this structure as a function of oxide density. Fluctuations in the fine structure of (b) and (c) are due to finite box restrictions of the model. (d) An illustration of the 2D oxygen delocalization model. Aluminium atoms in gray, with the delocalized oxygen atom probability density shown for an example ground state distribution.Reuse & Permissions
Figure 2
(a) Map of the $E_{01}$ energy splittings of the delocalized oxygen 2D model. The $| X |$ and $| Y |$ axes represent aluminium pair positions with $| Z | = 2.5788 Å$ . (b) The difference between the absolute dipole moment (in $x$ and $y$ directions) over the same range. We see either $| ℘_{x} |$ (red, upper and lower domains) or $| ℘_{y} |$ (green, left and right domains) dominated behavior in all regions except $| X |$ , $| Y | ≲ 3.5 Å$ (where the oxygen is tightly confined). (c)–(f) The first excited state wave function of the oxygen atom and the acting potential of four configurations indicated on (a). For comparison with existing qubit experiments we plot contour lines corresponding $E_{01} / h = 0.5 - 10 GHz$ (red to yellow, outer to inner) overlayed on (a) and (b). The same resonant frequencies are discussed in Fig. 3; hence, (c)–(f) all represent configurations of $E_{01} / h = 8 GHz$ ; whereas points i-vi are the locations selected for the strain study in Fig. 4.Reuse & Permissions
Figure 3
Coupling strength to a fictitious phase-qubit $S_{\max }$ as a function of $| X |$ in the domains where $| ℘_{x} |$ is dominant [see Eq. (2)] for a set of constant $E_{01}$ splitting frequencies. For comparison with experimental results, $E_{01}$ and $S_{\max }$ are expressed in frequency units.Reuse & Permissions
Figure 4
(a) Depiction of a number of deformations which were applied to the aluminium atoms in the $x − y$ plane (see text). Only one of the modes responded with over a few Hz of movement (highlighted), which is indicative of an optical phonon mode, generating frequency splittings of $O$ (100 MHz) for picometer deformations. A deformation range of 100 pm was applied to the points i-vi from Fig. 2 yielding responses that are both hyperbolic and symmetric (b). Over the range 20–100 pm the response is linear with a strain gradient, shown in (c) for both the tetra and hemitetra domains in the $℘_{x}$ direction.Reuse & Permissions

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