Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time T 1 affected as the electron is shuttled between the donor and the interface? We focus on the example of the 'flip-flop qubit' (Tosi et al arXiv:1509.08538v1), defined as a combination of the nuclear and electronic states of a phosphorus donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe orbital relaxation, flip-flop relaxation, and electron spin relaxation. We estimate that the flip-flop qubit relaxation time can be of the order of 100 μs, 8 orders of magnitude shorter than the value for an on-donor electron in bulk silicon, and a few orders of magnitude shorter (longer) than the predicted inhomogeneous dephasing time (gate times). All three relaxation processes are boosted by (i) the nontrivial valley structure of the electron-phonon interaction, and (ii) the different valley compositions of the involved electronic states.Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time T 1 affected as the electron is shuttled between the donor and the interface? We focus on the example of the 'flip-flop qubit' (Tosi et al arXiv:1509.08538v1), defined as a combination of the nuclear and electronic states of a phosphorus donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe orbital relaxation, flip-flop relaxation, and electron spin relaxation. We estimate that the flip-flop qubit relaxation time can be of the order of 100 μs, 8 orders of magnitude shorter than the value for an on-donor electron in bulk silicon, and a few orders of magnitude shorter (longer) than the predicted inhomogeneous dephasing time (gate times). All three relaxation processes are boosted by (i) the nontrivial valley structure of the electron-phonon interaction, and (ii) the different valley compositions of the involved electronic states.

arXiv:1602.03691NanotechnologyJun 23, 201620 citations

Kinetics of electron-phonon scattering in silicon resolved by Rydberg transitions of donors

Nils Dessmann, Aidan G. McConnell, Sergey G. Pavlov +6 more

Rydberg states of atoms in vacuum are now well recognized as a resource for quantum technologies. Donors in semiconductors also display analogous states, which have been proposed for similar applications. While they benefit from permanent locations in their host crystals, electron-lattice coupling leads to much shorter excited-state lifetimes than for neutral atoms in vacuum. Here we provide a quantitative description of donor-phonon kinetics, creating a basis for engineering donor systems in realistic material stacks for quantum devices. Our theory incorporates both form factors for the Rydberg states, which given their large extents in real space provide strong selectivity in momentum space, and tabulated deformation potentials for all six phonon branches throughout the Brillouin zone. By confronting this framework with carefully controlled time-resolved free electron laser measurements, we show that the widely quoted position of the silicon conduction band minimum, $k_0$ , is inconsistent with observed donor relaxation rates and that quantitative agreement is obtained for a value further from the X-point than commonly assumed. This stringent experiment-theory comparison establishes donor relaxation as a precision metrology for conduction band parameters and scattering processes in silicon, with consequences spanning from quantum devices to classical electronics.Rydberg states of atoms in vacuum are now well recognized as a resource for quantum technologies. Donors in semiconductors also display analogous states, which have been proposed for similar applications. While they benefit from permanent locations in their host crystals, electron-lattice coupling leads to much shorter excited-state lifetimes than for neutral atoms in vacuum. Here we provide a quantitative description of donor-phonon kinetics, creating a basis for engineering donor systems in realistic material stacks for quantum devices. Our theory incorporates both form factors for the Rydberg states, which given their large extents in real space provide strong selectivity in momentum space, and tabulated deformation potentials for all six phonon branches throughout the Brillouin zone. By confronting this framework with carefully controlled time-resolved free electron laser measurements, we show that the widely quoted position of the silicon conduction band minimum, $k_0$, is inconsistent with observed donor relaxation rates and that quantitative agreement is obtained for a value further from the X-point than commonly assumed. This stringent experiment-theory comparison establishes donor relaxation as a precision metrology for conduction band parameters and scattering processes in silicon, with consequences spanning from quantum devices to classical electronics.

quant-pharXiv:2606.28893Jun 30, 2026

Demonstration and benchmarking of electron and nuclear 2-qubit logic gates with implanted donors in silicon

Andrea Morello

Bulletin of the American Physical SocietyMar 4, 20200 citations

k_0

, is inconsistent with observed donor relaxation rates and that quantitative agreement is obtained for a value further from the X-point than commonly assumed. This stringent experiment-theory comparison establishes donor relaxation as a precision metrology for conduction band parameters and scattering processes in silicon, with consequences spanning from quantum devices to classical electronics.