We theoretically study the interaction of a heavy hole with nuclear spins in a quasi-twodimensional III-V semiconductor quantum dot and the resulting dephasing of heavy-hole spin states. It has frequently been stated in the literature that heavy holes have a negligible interaction with nuclear spins. We show that this is not the case. In contrast, the interaction can be rather strong and will be the dominant source of decoherence in some cases. We also show that for unstrained quantum dots the form of the interaction is Ising-like, resulting in unique and interesting decoherence properties, which might provide a crucial advantage to using dot-confined hole spins for quantum information processing, as compared to electron spins.

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

We analytically calculate the nuclear-spin interactions of a single electron confined to a carbon nanotube or graphene quantum dot. While the conduction-band states in graphene are p-type, the accordant states in a carbon nanotube are sp-hybridized due to curvature. This leads to an interesting interplay between isotropic and anisotropic hyperfine interactions. By using only analytical methods, we are able to show how the interaction strength depends on important physical parameters, such as curvature and isotope abundances. We show that for the investigated carbon structures, the 13 C hyperfine coupling strength is less than 1 µeV, and that the associated electronspin decoherence time can be expected to be several tens of microseconds or longer, depending on the abundance of spin-carrying 13 C nuclei. Furthermore, we find that the hyperfine-induced Knight shift is highly anisotropic, both in graphene and in nanotubes of arbitrary chirality.

Consolidation of motor skills after training can occur in a time- or sleep-dependent fashion. Recent studies revealed time-dependent consolidation as a common feature of visuomotor tasks. We have previously shown that anodal transcranial direct current stimulation (tDCS) in combination with repeated motor training benefits consolidation by the induction of offline skill gains in a complex visuomotor task, preventing the regular occurrence of skill loss between days. Here, we asked 2 questions: What is the time course of consolidation between days for this task and do exogenously induced offline gains develop as a function of time or overnight sleep? We found that both the development of offline skill loss in sham-stimulated subjects and offline skill gains induced by anodal tDCS critically depend on the passage of time after training, but not on overnight sleep. These findings support the view that tDCS interacts directly with the physiological consolidation process. However, in a control experiment, anodal tDCS applied after the training did not induce skill gains, implying that coapplication of tDCS and training is required to induce offline skill gains, pointing to the initiation of consolidation already during training.

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi-contact hyperfine interaction. Our perturbative treatment is valid for special ͑narrowed͒ bath initial conditions and when the Zeeman energy of the electron b exceeds the total hyperfine coupling constant A: b Ͼ A. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find an unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give subleading corrections to the decoherence rate, and show that, in general, the decoherence rate has a nonmonotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly interacting system with non-Markovian ͑history-dependent͒ dynamics.