Exponential decay in a spin bath

TL;DR

This paper demonstrates that under specific conditions, electron spin coherence decays exponentially due to interactions with a nuclear spin bath, providing explicit formulas for decoherence times relevant for quantum information applications.

Contribution

It introduces the concept of purely exponential decay in spin baths under narrowed initial conditions and derives explicit decoherence time expressions considering various physical parameters.

Findings

Exponential decay occurs in specific bath conditions with strong magnetic fields.

Derived explicit formulas for decoherence time T_2.

Decay behavior differs from typical super-exponential or power-law forms.

Abstract

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.