We study theoretically phonon-induced spin dynamics of two electrons confined in a self-assembled double quantum dot. We calculate the transition rates and time evolution of occupations for the spin-triplet and spin-singlet states. We characterize the relative importance of various relaxation channels, including two-phonon processes, as a function of the electric and magnetic fields. The simulations are based on a model combining the eight-band [Formula: see text] method and configuration-interaction approach. We show that the electron g-factor mismatch between the Zeeman doublets localized on different dots opens a relatively fast triplet-singlet phonon-assisted relaxation channel. We also demonstrate, that the relaxation near the triplet-singlet anticrossing is slowed down up to several orders of magnitude due to vanishing of some relaxation channels.
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 ${T}_{2}\ensuremath{\ll}{T}_{1}$, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find ${T}_{2}\ensuremath{\simeq}2{T}_{1}$ 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
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.
We show that singlet-triplet superpositions of two-electron spin states in a double quantum dot undergo a phonon-induced pure dephasing which relies only on the tunnel coupling between the dots and on the Pauli-exclusion principle. As such, this dephasing process is independent of spin-orbit coupling or hyperfine interactions. The physical mechanism behind the dephasing is elastic phonon scattering, which persists to much lower temperatures than real phonon-induced transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs gate-defined double quantum dot yield microsecond dephasing times at sub-Kelvin temperatures, which is consistent with experimental observations.
Phonon-induced dephasing of two-electron spin states in two vertically stacked self-assembled GaAs/InGaAs quantum dots is studied.A pure dephasing process due to elastic phonon scattering is found to dominate at low temperatures.This process is independent of the spin-orbit coupling and does not require the presence of a magnetic field.It relies on interdot tunneling and the Pauli principle, which make the double quantum dot gate for spin based quantum computing possible, and therefore cannot be avoided.
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.
We characterize numerically and analytically the signatures of the spin-orbit interaction in a two-electron GaAs double quantum dot in the presence of an external magnetic field. In particular, we obtain the return probability of the singlet state by simulating Landau-Zener voltage detuning sweeps which traverse the singlet-triplet ($S\ensuremath{-}{T}_{+}$) resonance. Our results indicate that non-spin-conserving interdot tunneling processes arising from the spin-orbit interaction have well defined signatures. These allow direct access to the spin-orbit interaction scales and are characterized by a frequency shift and Fourier amplitude modulation of the Rabi flopping dynamics of the singlet-triplet qubits $S\ensuremath{-}{T}_{0}$ and $S\ensuremath{-}{T}_{+}$. By applying the Bloch-Feshbach projection formalism, we demonstrate analytically that the aforementioned effects originate from the interplay between spin-orbit interaction and processes driven by the hyperfine interaction between the electron spins and those of the GaAs nuclei.