Controlling spin-orbit interactions in silicon quantum dots using magnetic field direction

Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction which degrade the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum dot system. We probe the derivative of the Stark shift, $g$-factor and $g$-factor difference for two single-electron quantum dot qubits as a function of external magnetic field and find that they are dominated by spin-orbit interactions originating from the vector potential, consistent with recent theoretical predictions. Conversely, by populating the double dot with two electrons we probe the mixing of singlet and spin-polarized triplet states during electron tunneling, which we conclude is dominated by momentum-term spin-orbit interactions that varies from 1.85 MHz up to 27.5 MHz depending on the magnetic field orientation. Finally, we exploit the tunability of the derivative of the Stark shift of one of the dots to reduce its sensitivity to electric noise and observe an 80 % increase in $T_2^*$. We conclude that the tuning of the spin-orbit interaction will be crucial for scalable quantum computing in silicon and that the optimal setting will depend on the exact mode of qubit operations used

High-fidelity adiabatic inversion of a 31P^{31}\mathrm{P} electron spin qubit in natural silicon

The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit gate fidelities for an electron spin qubit bound to a $^{31}$P atom in natural silicon, by applying adiabatic inversion instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of adiabatic inversion techniques for spin control in fluctuating environments.Comment: 4 pages, 2 figure

Bell's inequality violation with spins in silicon

Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states. For this reason the Bell signal has been tagged as a single-number benchmark for the performance of quantum computing devices. Here we demonstrate deterministic, on-demand generation of two-qubit entangled states of the electron and the nuclear spin of a single phosphorus atom embedded in a silicon nanoelectronic device. By sequentially reading the electron and the nucleus, we show that these entangled states violate the Bell/CHSH inequality with a Bell signal of 2.50(10). An even higher value of 2.70(9) is obtained by mapping the parity of the two-qubit state onto the nuclear spin, which allows for high-fidelity quantum non-demolition measurement (QND) of the parity. Furthermore, we complement the Bell inequality entanglement witness with full two-qubit state tomography exploiting QND measurement, which reveals that our prepared states match the target maximally entangled Bell states with $>$96\% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom, and show that this system is able to maintain its simultaneously high initialization, manipulation and measurement fidelities past the single-qubit regime.Comment: 10 pages, 3 figures, 1 table, 4 extended data figure

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best investigated models of linked selection is the recurrent full sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity, and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way towards providing a more flexible framework to describe genomic patterns of diversity than is currently available.Comment: 44 pages. 5 figure

A complex pattern of post‐divergence expansion, contraction, introgression and asynchronous responses to Pleistocene climate changes in two Dipelta sister species from western China

The well-known vicariance and dispersal models dominate in understanding the allopatric pattern for related species and presume the simultaneous occurrence of speciation and biogeographic events. However, the formation of allopatry may postdate the species divergence. We examined this hypothesis using DNA sequence data from 3 chloroplast fragments and 5 nuclear loci of Dipelta floribunda and D. yunnanensis, two shrub species with the circum Sichuan Basin distribution, combining the climatic niche modeling approach. The best-fit model supported by the approximate Bayesian computation (ABC) analysis indicated that, D. floribunda and D. yunnanensis diverged during the mid-Pleistocene period, consistent with the largest glacial period in the Qinghai-Tibet Plateau (QTP). The historically inter-specific gene flow was identified but seemed to have ceased after the last interglacial period (LIG), when the range of D. floribunda moved northward from the south of the Sichuan Basin. Further, populations of D. floribunda had expanded obviously in the north of the Sichuan Basin after the last glacial maximum (LGM). Relatively, the range of D. yunnanensis expanded before the LGM, reduced during the post-LGM especially in the north of the Sichuan Basin, reflecting the asynchronous responses of related species to the contemporary climate changes. Our results suggested that complex topography should be considered in understanding the distributional patterns even for closely related species and their demographic responses

Electrically controlling single spin qubits in a continuous microwave field

Large-scale quantum computers must be built upon quantum bits that are both highly coherent and locally controllable. We demonstrate the quantum control of the electron and the nuclear spin of a single 31P atom in silicon, using a continuous microwave magnetic field together with nanoscale electrostatic gates. The qubits are tuned into resonance with the microwave field by a local change in electric field, which induces a Stark shift of the qubit energies. This method, known as A-gate control, preserves the excellent coherence times and gate fidelities of isolated spins, and can be extended to arbitrarily many qubits without requiring multiple microwave sources.Comment: Main paper: 13 pages, 4 figures. Supplementary information: 25 pages, 13 figure