  We present a quantum solution to the electron spin decoherence by a nuclear
pair-correlation method for the electron-nuclear spin dynamics under a strong
magnetic field and a temperature high for the nuclear spins but low for the
electron. The theory incorporates the hyperfine interaction, the intrinsic
(both direct and indirect) nuclear interactions, and the extrinsic nuclear
coupling mediated by the hyperfine interaction with the single electron in
question. The last is shown to be important in free-induction decay (FID) of
the single electron spin coherence. The spin echo eliminates the
hyperfine-mediated decoherence but only reduces the decoherence by the
intrinsic nuclear interactions. Thus, the decoherence times for single spin FID
and ensemble spin echo are significantly different. The decoherence is
explained in terms of quantum entanglement, which involves more than the
spectral diffusion.

Mesoscale and Nanoscale Physics