# Low-temperature 1/f noise in microwave dielectric constant of amorphous dielectrics in Josephson qubits Academic Article

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### abstract

• The analytical solution for the low-temperature $1/f$ noise in the microwave dielectric constant of amorphous films at frequency ${\ensuremath{\nu}}_{0}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ due to tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The $1/f$ frequency dependence is caused by TLS spectral diffusion characterized by the width growing logarithmically with time. Temperature and field dependencies are predicted for the noise spectral density in typical glasses with universal TLSs. The satisfactory interpretation of the recent experiment by J. Burnett et al. [Nat. Commun. 5, 4119 (2014)] in Pt-capped Nb superconducting resonators is attained by assuming a smaller density of TLSs compared to ordinary glasses, which is consistent with the very high internal quality factor in those samples.

### publication date

• January 1, 2015