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We propose a microscopic model of critical current noise inJosephson-junctions based on individual trapping-centers in the tunnel barrierhybridized with electrons in the superconducting leads. We calculate the noiseexactly in the limit of no on-site Coulomb repulsion. Our result reveals anoise spectrum that is dramatically different from the usual Lorentzian assumedin simple models. We show that the noise is dominated by sharp subgapresonances associated to the formation of pairs of Andreev bound states, thusproviding a possible explanation for the spurious two-level systems(microresonators) observed in Josephson junction qubits [R.W. Simmonds et al.,Phys. Rev. Lett. 93, 077003 (2004)]. Another implication of our model is thateach trapping-center will contribute a sharp dielectric resonance only in thesuperconducting phase, providing an effective way to validate our resultsexperimentally. We derive an effective Hamiltonian for a qubit interacting withAndreev bound states, establishing a direct connection between phenomenologicalmodels and the microscopic parameters of a Fermionic bath.

Microscopic model of critical current noise in Josephson-junction qubits: Subgap resonances and Andreev bound states