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 T2 T1, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find T22T1 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 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.

The recent proposals of experiments with single Andreev bound states make relevant a detailed analysis of these states in multi-terminal superconducting nanostructures. We evaluate the energy splitting of degenerate Andreev bound states, that overlap in a superconducting lead, and find that the splitting is reduced in comparison with their energy by a small factor RGQ, RGQ being the dimensionless resistance of the overlap region in the normal state. This permits quantum manipulation of the quasiparticles in these states. We provide a simple scheme of such manipulation.

We study the nuclear spin relaxation in a ballistic nanowire with hyperfine and Rashba spin-orbit interactions (SOI) and in the presence of magnetic field and electron interactions. The relaxation rate shows pronounced peaks as a function of magnetic field and chemical potential due to van Hove singularities in the Rashba bands. As a result, the regimes of weak and strong SOIs can be distinguished by the number of peaks in the rate. The relaxation rate increases with increasing magnetic field if both Rashba subbands are occupied, whereas it decreases if only the lowest one is occupied.

In our original paper, we investigated the phonon-mediated decay of singlet-triplet qubits in double quantum dots (DQDs) in the biased and unbiased regime, where we inadvertently omitted relevant references regarding the dephasing mechanism which does not require hyperfine or spin-orbit interaction. Here, we wish to correct this omission and note that this mechanism corresponds to a two-phonon Raman process and has been studied before for impurity atoms [1][2][3][4], particularly in the presence of singlet states [2][3][4]. The same mechanism is used in Ref.[5] to analyze the dephasing of singlet-triplet qubits in unbiased DQDs. We note that the conclusions of our original paper and Ref.[5] substantially differ from each other. While Ref.[5] finds dominant dephasing times due to this Raman process, we find that this process for dephasing is negligible in the unbiased regime for realistic DQD parameter values (see Appendix H in our original paper).

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.