Dephasing in the central spin problem with long-range Ising spin-bath coupling

TL;DR

This paper rigorously proves the Gaussian approximation for qubit dephasing in the central spin model with a disordered Ising spin bath, clarifying when this approximation holds or breaks down.

Contribution

It provides the first formal proof of the Gaussian dephasing approximation for a disordered Ising bath with various couplings, including conditions where it fails.

Findings

Gaussian approximation holds for long-range couplings

Breaks down for short-range (exponentially decaying) couplings

Offers a framework for understanding decoherence in quantum systems

Abstract

The study of coherence dynamics in open quantum systems, specifically addressing various physical realizations of quantum systems and environments, is a long-standing and central pillar of quantum science and technology. As such, a large body of work establishes a firm theoretical understanding of these processes. Nevertheless, a fundamental aspect of decoherence dynamics, namely the central limit theorem of qubit dephasing in the central spin model, which leads to a Gaussian approximation, lacks formal proof in realistically relevant scenarios. Here we prove this approximation for a bath depicted by an Ising spin system, in the presence of disorder and several (most relevant) functional forms of qubit-bath coupling. Importantly, we show that in certain cases, namely for short-range (exponentially decaying) coupling, this approximation breaks. These results provide a theoretical framework for studying decoherence dynamics in various systems and lead to insights into dephasing behavior with implications for applications in quantum information, quantum computing, and other quantum technologies.