Nonperturbative bounds on electron spin coherence times induced by hyperfine interactions

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 T₁ and T₂ coherence times for the electron spin are provided. It is shown that for magnetic fields B greater than some critical field B₂ (B₂0. 001--20. 3em{0ex}T 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.