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Electron and nuclear spins of donor ensembles in isotopically pure siliconexperience a vacuum-like environment, giving them extraordinary coherence.However, in contrast to a real vacuum, electrons in silicon occupy quantumsuperpositions of valleys in momentum space. Addressable single-qubit andtwo-qubit operations in silicon require that qubits are placed near interfaces,modifying the valley degrees of freedom associated with these quantumsuperpositions and strongly influencing qubit relaxation and exchangeprocesses. Yet to date, spectroscopic measurements only indirectly probewavefunctions, preventing direct experimental access to valley population,donor position, and environment. Here we directly probe the probability densityof single quantum states of individual subsurface donors, in real space andreciprocal space, using scanning tunneling spectroscopy. We directly observequantum mechanical valley interference patterns associated with linearsuperpositions of valleys in the donor ground state. The valley population isfound to be within $5 \%$ of a bulk donor when $2.85\pm0.45$ nm from theinterface, indicating that valley perturbation-induced enhancement of spinrelaxation will be negligible for depths $>3$ nm. The observed valleyinterference will render two-qubit exchange gates sensitive to atomic-scalevariations in positions of subsurface donors. Moreover, these results will alsobe of interest to emerging schemes proposing to encode information directly invalley polarization.

Spatially Resolving Valley Quantum Interference of a Donor in Silicon