Valley-enhanced fast relaxation of gate-controlled donor qubits in silicon

TL;DR

This paper investigates how phonon-assisted relaxation times of gate-controlled donor qubits in silicon are significantly reduced due to valley effects, impacting quantum computing performance.

Contribution

It provides a theoretical analysis of relaxation mechanisms in flip-flop qubits, highlighting the role of valley structure in phonon interactions and quantifying relaxation times.

Findings

Relaxation time can be around 100 microseconds, much shorter than bulk silicon.

Valley structure enhances phonon interactions, boosting relaxation rates.

Relaxation times are affected by electron valley composition and interface proximity.

Abstract

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 phosphorous 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 $100 \, \mu\text{s}$, 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.