The authors have studied low-frequency resistance fluctuations in shadow-evaporated Al/AlOx/Al tunnel junctions. Between 300 and 5?K the spectral density follows a 1/f law. Below 5?K, individual defects distort the 1/f shape of the spectrum. The spectral density decreases linearly with temperature between 150 and 1?K and saturates below 0.8?K. At 4.2?K, it is about two orders of magnitude lower than expected from a recent survey [D. J. Van Harlingen et al., Phys. Rev. B 70, 064510 (2004)]. Due to saturation below 0.8?K the estimated qubit dephasing times at 100?mK are only about two times longer than calculated by Van Harlingen et al.
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