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

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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 T₁ and T₂ coherence times for the electron spin are provided. It is shown that for magnetic fields B greater than some critical field Bc (Bc.001 - 2 Tesla for the systems studied here), the z-polarization of the electron spin cannot relax, and hence T₁ is infinite. However, even at high fields dephasing can still occur. We provide a lower bound on the T₂ coherence time that explicitly takes into account the effects of a spin echo pulse sequence.