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Register a new userValley interference and spin exchange at the atomic scale in silicon
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Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.
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The presence of valley states is a significant obstacle to realizing quantum information technologies in Silicon quantum dots, as leakage into alternate valley states can introduce errors into the computation. We use a perturbative analytical approach to study the dynamics of exchange-coupled quantum dots with valley degrees of freedom. We show that if the valley splitting is large and electrons are not properly initialized to valley eigenstates, then time evolution of the system will lead to spin-valley entanglement. Spin-valley entanglement will also occur if the valley splitting is small and electrons are not initialized to the same valley state. Additionally, we show that for small valley splitting, spin-valley entanglement does not affect measurement probabilities of two-qubit systems; however, systems with more qubits will be affected. This means that two-qubit gate fidelities measured in two-qubit systems may miss the effects of valley degrees of freedom. Our work shows how the existence of valleys may adversely affect multiqubit fidelities even when the system temperature is very low.
Storing and accessing information in atomic-scale magnets requires magnetic imaging techniques with single-atom resolution. Here, we show simultaneous detection of the spin-polarization and exchange force, with or without the flow of current, with a new method, which combines scanning tunneling microscopy and non-contact atomic force microscopy. To demonstrate the application of this new method, we characterize the prototypical nano-skyrmion lattice formed on a monolayer of Fe/Ir(111). We resolve the square magnetic lattice by employing magnetic exchange force microscopy, demonstrating its applicability to non-collinear magnetic structures, for the first time. Utilizing distance-dependent force and current spectroscopy, we quantify the exchange forces in comparison to the spin-polarization. For strongly spin-polarized tips, we distinguish different signs of the exchange force which we suggest arises from a change in exchange mechanisms between the probe and a skyrmion. This new approach may enable both non-perturbative readout combined with writing by current-driven reversal of atomic-scale magnets.
Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunctions, preventing direct experimental access to valley population, donor position, and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunneling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within $5 %$ of a bulk donor when $2.85pm0.45$ nm from the interface, indicating that valley perturbation-induced enhancement of spin relaxation will be negligible for depths $>3$ nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest to emerging schemes proposing to encode information directly in valley polarization.
Although silicon is a promising material for quantum computation, the degeneracy of the conduction band minima (valleys) must be lifted with a splitting sufficient to ensure formation of well-defined and long-lived spin qubits. Here we demonstrate that valley separation can be accurately tuned via electrostatic gate control in a metal-oxide-semiconductor quantum dot, providing splittings spanning 0.3 - 0.8 meV. The splitting varies linearly with applied electric field, with a ratio in agreement with atomistic tight-binding predictions. We demonstrate single-shot spin readout and measure the spin relaxation for different valley configurations and dot occupancies, finding one-electron lifetimes exceeding 2 seconds. Spin relaxation occurs via phonon emission due to spin-orbit coupling between the valley states, a process not previously anticipated for silicon quantum dots. An analytical theory describes the magnetic field dependence of the relaxation rate, including the presence of a dramatic rate enhancement (or hot-spot) when Zeeman and valley splittings coincide.
A single spin in a Josephson junction can reverse the flow of the supercurrent. At mesoscopic length scales, such $pi$-junctions are employed in various instances from finding the pairing symmetry to quantum computing. In Yu-Shiba-Rusinov (YSR) states, the atomic scale counterpart of a single spin in a superconducting tunnel junction, the supercurrent reversal so far has remained elusive. Using scanning tunneling microscopy (STM), we demonstrate such a 0 to $pi$ transition of a Josephson junction through a YSR state as we continuously change the impurity-superconductor coupling. We detect the sign change in the critical current by exploiting a second transport channel as reference in analogy to a superconducting quantum interference device (SQUID), which provides the STM with the required phase sensitivity. The measured change in the Josephson current is a signature of the quantum phase transition and allows its characterization with unprecedented resolution.
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