Phonon-Induced Decay of the Electron Spin in Quantum Dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit (SO) interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time T₂ is as large as the spin relaxation time T₁, under realistic conditions. For the Dresselhaus and Rashba SO couplings, we find that, in leading order, the effective B field can have only fluctuations transverse to the applied B field. As a result, T₂=2T₁ for arbitrarily large Zeeman splittings, in contrast to the naively expected case T₂T₁. We show that the spin decay is drastically suppressed for certain B-field directions and ratios of SO coupling constants. Finally, for the spin-phonon coupling, we show that T₂=2T₁ for all SO mechanisms in leading order in the electron-phonon interaction.