Exponential decay in a spin bath

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 superexponential 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, shape of the electron wave function, dimensionality, total nuclear spin $I$, and isotopic concentration for experimentally relevant heteronuclear-spin systems.