Phonon-mediated decay of singlet-triplet qubits in double quantum dots

We study theoretically the phonon-induced relaxation (T-1) and decoherence times (T-2) of singlet-triplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via two-phonon processes. This mechanism requires neither hyperfine nor spin-orbit interaction and yields T-2 << T-1, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find T-2 similar or equal to 2T(1) and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature T, whereas the rates due to two-phonon processes reveal a transition from T-2 to higher powers as T is decreased. Remarkably, both T-1 and T-2 exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of T-1 and T-2 on system properties such as the detuning, the spin-orbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.