The dynamics of a qubit in a spin-boson environment: a comparison between analytical and numerical method

TL;DR

This paper compares analytical and numerical methods for studying qubit dynamics in a spin-boson environment, revealing their agreement and effects of temperature and coupling on decoherence.

Contribution

It introduces a perturbation method based on a unitary transformation and compares it with the numerically exact QUAPI technique for qubit decoherence analysis.

Findings

Analytical method agrees well with QUAPI across many parameters.

Temperature and TLF-bath coupling significantly affect qubit decoherence.

Non-adiabatic effects are efficiently captured by the unitary transformation.

Abstract

The dynamics of a qubit under the decoherence of a two level fluctuator (TLF) in addition to its coupling to a bosonic bath is investigated theoretically. Two different methods are applied and compared for this problem. One is a perturbation method based on a unitary transformation. With the merit of our unitary transformation, non-adiabatic effect can be taken into account efficiently. And the other one is the numerically exact method, namely the quasi-adiabatic path-integral (QUAPI) propagator technique. We find that the analytical method works well for a wide parameter range and show good agreement with QUAPI. On the other hand, The enhancement and the reduction of quantum decoherence of the qubit is checked with varying bath temperature $T$ and TLF-bath coupling.