Nonperturbative bounds on electron spin coherence times induced by hyperfine interactions

Abstract

We address the decoherence of a localized electron spin in an external magnetic field due to the hyperfine interaction with a lattice of nuclear spins. Using a completely nonperturbative method, rigorous bounds on the ${T}_{1}$ and ${T}_{2}$ coherence times for the electron spin are provided. It is shown that for magnetic fields $B$ greater than some critical field ${B}_{c}$ (${B}_{c}\ensuremath{\approx}0.001\text{--}2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ for the systems studied here), the $z$ polarization of the electron spin cannot relax, and hence ${T}_{1}$ is infinite. However, even at high fields dephasing can still occur. We provide a lower bound on the ${T}_{2}$ coherence time that explicitly takes into account the effects of a spin-echo pulse sequence.