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

We study theoretically the phonon-induced relaxation (T1) and decoherence times (T2) 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 T2T1, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find T2 2T1 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 T2 to higher powers as T is decreased. Remarkably, both T1 and T2 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 T1 and T2 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.