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

TL;DR

This paper addresses the limitations of traditional models in describing charge noise from two-level fluctuators, proposing a spectator-qubit method to accurately capture noise spectra consistent with the fluctuation-dissipation theorem.

Contribution

It introduces a spectator-qubit approach to accurately model noise spectra from two-level fluctuators, overcoming the Markov approximation's limitations.

Findings

Noise exhibits a crossover from 1/f to 1/f^2 behavior.

Crossover frequency shows a T^3 temperature dependence.

Method provides a fluctuation-dissipation consistent noise spectrum.

Abstract

The analysis of charge noise based on the Bloch-Redfield treatment of an ensemble of dissipative two-level fluctuators generally results in a violation of the fluctuation-dissipation theorem. The standard Markov approximation (when applied to the two-level fluctuators coupled to a bath) can be identified as the main origin of this failure. The resulting decoherence rates only involve the bath response at the fluctuator frequency, and thus completely neglect the effects of frequency broadening. A systematic and computationally convenient way to overcome this issue is to employ the spectator-qubit method: by coupling an auxiliary qubit to the two-level fluctuator ensemble, an analytical approximation for $S({\omega})$ fully consistent with the fluctuation-dissipation theorem can be obtained. We discuss the resulting characteristics of the noise which exhibits distinct behavior over several frequency ranges, including a $1/f$ to $1/f^2$ crossover with a $T^3$ temperature dependence of the crossover frequency.