Low frequency critical current noise and two level system defects in Josephson junctions

The critical current in a Josephson junction is known to exhibit a 1/f low frequency noise. Implemented as a superconducting qubit, this low frequency noise can lead to decoherence. While the 1/f noise has been known to arise from an ensemble of two level systems connected to the tunnel barrier, the precise microscopic nature of these TLSs remain a mystery. In this thesis we will present measurements of the 1/f low frequency noise in the critical current and tunneling resistance of Al-AlOx-Al Josephson junctions. Measurements in a wide range of resistively shunted and unshunted junctions confirm the equality of critical current and tunneling resistance noise. That is the critical current fluctuation corresponds to fluctuations of the tunneling resistance. In not too small Al-AlOx-Al junctions we have found that the fractional power spectral density scales linearly with temperature. We confirmed that the 1/f power spectrum is the result of a large number of two level systems modulating the tunneling resistance. At small junction areas and low temperatures, the number of thermally active TLSs is insufficient to integrate out a featureless 1/f spectral shape. By analyzing the spectral variance in small junction areas, we have been able to deduce the TLS defect density, n ~ 2.53 per micrometer squared per Kelvin spread in the TLS energy per factor e in the TLS lifetimes. This density is consistent with the density of tunneling TLSs found in glassy insulators, as well as the density deduced from coherent TLSs interacting at qubit frequencies. The deduced TLS density combined with the magnitude of the 1/f power spectral density in large area junctions, gives an average TLS effective area, A ~ 0.3 nanometer squared. In ultra small tunnel junctions, we have studied the time-domain dynamics of isolated TLSs. We have found a TLS whose dynamics is described by the quantum tunneling between the two localized wells, and a one-phonon absorption/emission switching rate. From the quantum limiting rate and the WKB approximation, we estimated that the TLS has a mass and tunneling distance product consistent with an atomic mass tunneling through crystal lattice distances. At higher temperatures TLSs have been found that obey a simple thermal activation dynamics. By analyzing the TLS response to an external electric field, we have deduced that the TLS electric dipole is in the order of, P ~ 1 electron-Angstrom, consistent with the TLS having the charge of one electron tunneling through a disorder potential of distances, d ~ 1 Angstrom