Non-Perturbative Bounds on Hyperfine-Induced Electron Spin Coherence Times

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 non-perturbative 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 ~ .001 - 2 Tesla 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.