A 3D investigation of delocalised oxygen two-level defects in Josephson junctions

Environmental two-level systems (TLS) have been identified as significant decoherence sources in Josephson junction (JJ) based circuits. For such quantum devices to be functional, the removal or control of the TLS is a necessity. Understanding the microscopic origins of the 'strongly coupled' TLS type is one current path of investigation to that end. The delocalized oxygen model suggests the atomic position of an oxygen atom is spatially delocalized in the oxide forming the JJ barrier. In this report we extend this model from its previous 2+1D construction to a complete 3D description using a Wick-rotated time-dependent Schrodinger equation to solve for time-independent solutions in three dimensions. We compute experimentally observable parameters for phase qubits and compare the results to the 2+1D framework. We devise a Voronoi classification scheme to investigate oxygen atoms delocalizing within strained and non-strained crystalline lattices, as well as realistic atomic positions a JJ amorphous tunnel barrier constructed in previous density functional studies.