Statistical characterization of valley coupling in Si/SiGe quantum dots via $g$-factor measurements near a valley vortex

TL;DR

This paper introduces a new method using $g$-factor measurements to characterize valley coupling and phase in Si/SiGe quantum dots, improving the understanding of valley effects crucial for spin qubit reliability.

Contribution

The paper proposes a novel approach to measure valley phase and coupling in quantum wells using $g$-factor loops, enhancing qubit characterization techniques.

Findings

Realistic valley energy distributions overestimate valley coupling.

Knowledge of valley phase improves valley coupling estimates.

Method can be implemented with current experimental setups.

Abstract

The presence of low-energy valley excitations in Si/SiGe heterostructures often causes spin qubits to fail. It is therefore important to develop robust protocols for characterizing the valley coupling. Here, we show that realistically sized samplings of valley energy distributions tend to dramatically overestimate the average valley coupling. But we find that knowledge of the valley phase, in addition to the valley splitting, can significantly improve our estimates. Motivated by this understanding, we propose a novel method to probe the valley phase landscape across the quantum well using simple $g$-factor measurements. An important calibration step in this procedure is to measure $g$ in a loop enclosing a valley vortex, where the valley phase winds by $\pm 2\pi$ around a zero of the valley splitting. This proposal establishes an important new tool for probing spin qubits, and it can be implemented in current experiments.