Universal scaling of hyperfine-induced electron spin echo decay

The decoherence of a localized electron spin in a lattice of nuclear spins is an important problem for potential solid-state implementations of a quantum computer. We demonstrate that even at high fields, virtual electron spin-flip processes due solely to the hyperfine interaction can lead to complex nuclear spin dynamics. These dynamics, in turn, can lead to single electron spin phase fluctuation and decoherence. We show here that remarkably, a spin echo pulse sequence can almost completely reverse these nuclear dynamics except for a small visibility loss, thereby suppressing contribution of the hyperfine interaction to T₂ processes. For small systems, we present numerical evidence which demonstrates a universal scaling of the magnitude of visibility loss that depends only on the inhomogeneous linewidth of the system and the magnetic field.