[Paper Review] Tunable hole spin-photon interaction based on g-matrix modulation

V. P. Michal, J. C. Abadillo-Uriel+4 more|arXiv (Cornell University)|Apr 1, 2022

Quantum and electron transport phenomena4 citations

TL;DR

This paper proposes a tunable hole spin-photon interaction in a semiconductor quantum dot coupled to a superconducting microwave resonator, leveraging electrically controlled g-matrix modulation via strong spin-orbit coupling. By tuning gate voltages and magnetic field orientation, the interaction switches between fully transverse and fully longitudinal coupling, with maximal strength in a reciprocal manner, enabling robust spin-photon entanglement and parametric coupling with enhanced coherence, achieving coupling rates up to ~10 MHz in realistic devices.

ABSTRACT

We consider a spin circuit-QED device where a superconducting microwave resonator is capacitively coupled to a single hole confined in a semiconductor quantum dot. Thanks to the strong spin-orbit coupling intrinsic to valence-band states, the gyromagnetic g-matrix of the hole can be modulated electrically. This modulation couples the photons in the resonator to the hole spin. We show that the applied gate voltages and the magnetic-field orientation enable a versatile control of the spin-photon interaction, whose character can be switched from fully transverse to fully longitudinal. The longitudinal coupling is actually maximal when the transverse one vanishes and vice-versa. This "reciprocal sweetness" results from geometrical properties of the g-matrix and protects the spin against dephasing or relaxation. We estimate coupling rates reaching ~ 10 MHz in realistic settings and discuss potential circuit-QED applications harnessing either the transverse or the longitudinal spin-photon interaction. Furthermore, we demonstrate that the g-matrix curvature can be used to achieve parametric longitudinal coupling with enhanced coherence.

Motivation & Objective

• To enable all-electrical, gate-voltage-tunable spin-photon interactions in a hole spin qubit system without external driving or micro-magnets.
• To exploit the geometric properties of the non-scalar g-matrix in hole quantum dots to achieve switchable transverse and longitudinal coupling.
• To demonstrate that parametric longitudinal coupling with high coherence can be achieved through g-matrix curvature modulation.
• To estimate realistic coupling strengths and identify viable circuit-QED applications such as quantum state transfer and CZ gates.

Proposed method

• Model a hole spin qubit in a [110]-oriented Si nanowire quantum dot with a front gate and back gate to control the confining potential.
• Use a 6-band k⋅p model with finite-difference discretization to compute the hole wavefunction and g-matrix under varying gate voltages and magnetic field orientations.
• Calculate the g-matrix derivatives to determine transverse and longitudinal spin-photon coupling susceptibilities β⊥ and β∥.
• Compute the curvature parameter γ∥ to assess parametric longitudinal coupling strength.
• Solve Poisson's equation with finite-volume methods to model electrostatic potential and gate-induced electric fields.
• Map coupling strengths as functions of magnetic field direction and back gate voltage to identify optimal operation points.

Experimental results

Research questions

• RQ1 Can the spin-photon interaction in a hole spin qubit be tuned from purely transverse to purely longitudinal coupling using only gate voltages and magnetic field orientation?
• RQ2 How do the geometric properties of the non-scalar g-matrix enable reciprocal tuning between transverse and longitudinal coupling?
• RQ3 What is the maximum achievable coupling rate between a hole spin and a microwave photon in a realistic device?
• RQ4 Can parametric longitudinal coupling with enhanced coherence be realized through g-matrix curvature modulation?
• RQ5 How do device geometry and gate overlap affect the strength and tunability of spin-photon coupling?

Key findings

• The spin-photon coupling can be fully switched between transverse and longitudinal character by tuning gate voltages and magnetic field orientation, with maximal coupling in a reciprocal manner.
• At a back gate voltage of V_BG ≈ -68 mV, the hole wavefunction spans the full channel width, leading to vanishing β∥ and β⊥ susceptibilities due to symmetry reversal.
• Maximum longitudinal coupling (γ∥^max) and transverse susceptibility (β⊥^max) are achieved at V_BG ≈ -77 mV, with coupling rates reaching ~10 MHz in realistic simulations.
• The curvature parameter γ∥^max is enhanced by reducing gate-channel overlap, with a factor of two improvement in γ∥ for S_y = 10 nm vs. 20 nm.
• Voltage drops in oxide layers reduce β susceptibilities by up to 40%, but non-linearities compensate, preserving strong γ∥ coupling.
• The system supports parametric longitudinal coupling with long coherence, enabling applications in fast quantum non-demolition measurements and multi-qubit entangling gates.