Abstract
We consider, in the framework of the central spin $s=1/2$ model, driven dynamics of two electrons in a double quantum dot subject to hyperfine interaction with nuclear spins and spin-orbit coupling. The nuclear subsystem dynamically evolves in response to Landau-Zener singlet-triplet transitions of the electronic subsystem controlled by external gate voltages. Without noise and spin-orbit coupling, subsequent Landau-Zener transitions die out after about ${10}^{4}$ sweeps, the system self-quenches, and nuclear spins reach one of the numerous glassy dark states. We present an analytical model that captures this phenomenon. We also account for the multi-nuclear-specie content of the dots and numerically determine the evolution of around ${10}^{7}$ nuclear spins in up to $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ Landau-Zener transitions. Without spin-orbit coupling, self-quenching is robust and sets in for arbitrary ratios of the nuclear spin precession times and the waiting time between Landau-Zener sweeps as well as under moderate noise. In the presence of spin-orbit coupling of a moderate magnitude, and when the waiting time is in resonance with the precession time of one of the nuclear species, the dynamical evolution of nuclear polarization results in stroboscopic screening of spin-orbit coupling. However, small deviations from the resonance or strong spin-orbit coupling destroy this screening. We suggest that the success of the feedback loop technique for building nuclear gradients is based on the effect of spin-orbit coupling.
Highlights
Electrical operation of electron spins in semiconductor double quantum dots (DQD) is one of the central avenues of semiconductor spintronics [1] and quantum computing [2,3,4,5]
We have studied the evolution of the nuclear spin dynamics during up to 2 × 105 LZ sweeps for 107 spins and used various pseudorandom initial configurations of nuclear spins
As applied to a double quantum dot of a GaAs type, where electron and nuclear spins are coupled via hyperfine interaction, pumping nuclear magnetization across a S-T+ avoided crossing through successive Landau-Zener sweeps ceases after about 104 sweeps
Summary
Electrical operation of electron spins in semiconductor double quantum dots (DQD) is one of the central avenues of semiconductor spintronics [1] and quantum computing [2,3,4,5]. Most widely explored singlet-triplet DQD qubits [7] are based on GaAs [8,9] and InAs [10,11,12] Both in GaAs and InAs, there are three species of nuclei possessing nonvanishing angular momenta, and the coupling between electron and nuclear spins (mostly through contact interaction) strongly influences electron-spin dynamics. This coupling has a destructive effect causing electron-spin relaxation, and many theoretical studies have focused on the challenging problem of determining the relaxation rate of an electron spin interacting with about N ≈ 106 nuclear spins [13,14,15,16,17,18,19,20]. The problem of an electron spin interacting with a bath of nuclear spins is known as the central spin problem
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