Quantum $1/f^\eta$ Noise Induced Relaxation in the Spin-Boson Model

TL;DR

This paper investigates the effects of quantum 1/f^η noise on the relaxation dynamics of the spin-boson model, providing a detailed phase diagram and empirical formulas for dephasing rates relevant to quantum computing.

Contribution

It extends the spin-boson model to include quantum 1/f^η noise with negative spectral exponents and uses numerically exact methods to analyze the dynamics and dephasing.

Findings

Identified pseudocoherent dynamics under quantum 1/f^η noise.

Derived empirical formula for dephasing rate at zero temperature.

Showed dependence of bath reorganization energy on infrared cutoff frequency.

Abstract

We extend the spin-boson model of open quantum systems to the regime of quantum $1/f^\eta$ noise characterized by negative exponents of its spectral distribution. Using the numerically exact time-evolving matrix product operator, we find the dynamic regime diagram, including pseudocoherent dynamics controlled by quantum $1/f^\eta$ noise. We determine the dephasing rate and find for it an empirical formula valid at zero temperature. The bath reorganization energy depends on the infrared bath cutoff frequency, revealing an increased sensitivity of the dephasing on the measurement time of an experiment. \ep{Our results apply to a qubit as an elementary building block of a quantum computer and pave the way towards a quantum treatment of low-frequency noise in more complex architectures.