Noisy Spins and the Richardson-Gaudin Model

TL;DR

This paper models a system of spins in a noisy environment using an exactly solvable Richardson-Gaudin model, revealing how inhomogeneous frequencies affect decoherence and correlations.

Contribution

It introduces an exact solution to the quantum master equation for spins with inhomogeneous precession frequencies coupled to a common bath, using a non-Hermitian integrable model.

Findings

Exact spectrum of the master equation derived

Decay rates influenced by frequency inhomogeneity

Long-lived correlations due to common noise

Abstract

We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit, and hence determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.