Electrical manipulation of semiconductor spin qubits within the g-matrix formalism

TL;DR

This paper introduces a g-matrix formalism for modeling electrical control of spin qubits, enabling efficient prediction of Rabi and Larmor frequencies based on wave functions, with applications demonstrated on silicon hole qubits.

Contribution

The paper develops a generalized g-matrix approach that simplifies the analysis of spin qubit control and symmetry effects, applicable to various electron and hole qubits.

Findings

g-matrix formalism accurately predicts qubit frequencies

Rabi frequency depends complexly on magnetic field orientation and gate voltages

Switching bias points optimizes qubit control and coherence

Abstract

We discuss the modeling of the electrical manipulation of spin qubits in the linear-response regime where the Rabi frequency is proportional to the magnetic field and to the radio-frequency electric field excitation. We show that the Rabi frequency can be obtained from a generalized g-tensor magnetic resonance formula featuring a g-matrix and its derivative g' with respect to the electric field (or gate voltage) as inputs. These matrices can be easily calculated from the wave functions of the qubit at zero magnetic field. The g-matrix formalism therefore provides the complete dependence of the Larmor and Rabi frequencies on the orientation of the magnetic field at very low computational cost. It also provides a compact model for the control of the qubit, and a simple framework for the analysis of the effects of symmetries on the anisotropy of the Larmor and Rabi frequencies. The g-matrix formalism applies to a wide variety of electron and hole qubits, and we focus on a hole qubit in a silicon-on-insulator nanowire as an illustration. We show that the Rabi frequency of this qubit shows a complex dependence on the orientation of the magnetic field, and on the gate voltages that control the symmetry of the hole wave functions. We point out that the qubit may be advantageously switched between two bias points, one where it can be manipulated efficiently, and one where it is largely decoupled from the gate field but presumably longer lived. We also discuss the role of residual strains in such devices in relation to recent experiments.