Positive- and negative-frequency noise from an ensemble of two-level fluctuators

Depolarization of superconducting qubits with intrinsic protection, such as heavy fluxonium or the 0-π qubit, is dominated by excitation rather than relaxation processes. To extract the corresponding excitation rates, it is thus crucial to carefully consider the negative-frequency components of the noise spectral density. We are particularly interested in noise sources with the ubiquitous 1/f spectrum at positive frequencies. Existing models based on an ensemble of two-level fluctuators predict a symmetric noise spectral density valid in the high-temperature limit. We extend the analysis beyond this limit, and derive results explicitly obeying the fluctuation–dissipation theorem. We discuss deviations from pure 1/f behavior and compare with recent experimental observations.