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

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. arXiv:1807.09185v2 [quant-ph]

Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation

“…We have checked that this conclusion still holds when solving the model in a converged basis set, as well as for more realistic device layouts such as those investigated in Ref 29…”

“…This is supported by a symmetry analysis: When E 0 = 0, the system has three mirror planes perpendicular to x, y, z, which, as shown in Ref. 29, implies that the Rabi frequency is zero to first order in B and E ac .…”

“…34 As discussed in Ref. 29, the diamagnetic Hamiltonian H d is not relevant for the calculation of the Larmor and Rabi frequencies of the qubit (to first order in the magnetic field) and will be dropped out in the following. The paramagnetic Hamiltonian H p has no action in the minimal basis set B.…”

“…(25) g x , g y and g z can be identified as the principal g-factors along the magnetic axes x, y and z. 29 Also,…”

“…However, as shown in the next section, the Rabi frequency decreases at large E 0 , in particular because the dipole matrix element 2 −|y|1− dies out once the |1− and |2− states get spatially separated by the static electric field. 29 An expression for the Rabi frequency accurate for arbitrary electric fields can be derived when λ 1± 2∓ and λ 2∓…”