Limitations of the -tensor formalism of semiconductor spin qubits
Phys. Rev. B 112, 045428 – Published 28 July, 2025
DOI: https://doi.org/10.1103/gq3h-76mx
Abstract
The -tensor formalism is a powerful method for describing the electrical driving of semiconductor spin qubits. However, up to now, this technique has only been applied to the simplest qubit dynamics, resonant monochromatic driving by a single gate. Here, we study the description of (i) monochromatic driving using two driving gates and bichromatic driving via (ii) one or (iii) two gates. Assuming a general Hamiltonian with qubit states well separated from excited orbital states, we find that when (i) two driving gates are used for monochromatic driving or (ii) a single one for bichromatic, the -tensor formalism successfully captures the leading-order dynamics. We express the Rabi frequency and the Bloch-Siegert shift using the -tensor and its first and second derivatives with respect to the gate voltage. However, when (iii) bichromatic driving is realized using two distinct driving gates, we see a breakdown of -tensor formalism: The Rabi frequency cannot be expressed using the -tensor and its derivatives. We find that beyond the -tensor and its derivatives, three additional parameters are needed to capture the dynamics. We demonstrate our general results by assuming an electron (hole) confined in a circular quantum dot, subjected to Rashba spin-orbit interaction.
