Low temperature 1/f noise in microwave dielectric constant of amorphous dielectrics in Josephson qubits

TL;DR

This paper provides an analytical solution for low temperature 1/f noise in the dielectric constant of amorphous films with TLSs, explaining experimental observations in Josephson qubits.

Contribution

It introduces a detailed analytical model including TLS interactions that explains the temperature dependence of 1/f noise in amorphous dielectrics used in Josephson qubits.

Findings

The noise amplitude increases as temperature decreases below 0.1K.

Long time correlations arise from logarithmic broadening of TLS resonances.

The model aligns with recent experimental data on Josephson junction qubits.

Abstract

The accurate analytical solution for the low temperature $1/f$ noise in a microwave dielectric constant of amorphous films containing tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The results are consistent with the recent experimental investigations of $1/f$ noise in Josephson junction qubits including the power law increase of the noise amplitude with decreasing temperature at low temperatures $T<0.1$K. The long time correlations needed for $1/f$ noise are provided by the logarithmic broadening of TLS absorption resonances with time due to their interaction with neighboring TLSs. The noise behavior at higher temperatures $T>0.1$K and its possible sensitivity to quasi-particle excitations are discussed.