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 2.85 ± 0.45 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.
Fabrication of devices1,2 , spin readout 1 , and quantum control of spins 3,4 in silicon has been accomplished at the single-donor level. However, addressable control and coupling within qubit arrays requires local gates and control interfaces, whose atomic-scale potentials strongly influence electronic valley degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16] . While these unconventional orbital degrees of freedom play no role in conventional silicon microelectronics, they invariably arise in quantized states in indirect gap materials, and are pervasive in quantum electronics. In silicon, valley physics determines qubit relaxation rates 13,17,18 and are predicted to strongly influence two qubit gates Here, individual states of subsurface donors were measured using cryogenic scanning tunneling spectroscopy. Quantum mechanical valley interference patterns were observed in real space, associated with linear quantum superpositions of wavevectors in the six conduction band valleys of silicon. Enabled by high-accuracy empirical determination of donor depth and electric field, we perform a parameter-free comparison with atomistic theory establishing that the z-valley population is ∼ 38 ± 2% for a 2.85 ± 0.45 nm deep donor, perturbed by only ∼ 5% compared with ∼ 33.3% for a donor in bulk silicon. Consequently, donors more than 3 nm deep should not experience a significant valley-repopulation induced increase in spin-lattice relaxation. Moreover, the nearly bulklike valley interference observed will render two-qubit excha...
