The impact of hole $g$-factor anisotropy on spin-photon entanglement generation with InGaAs quantum dots

Self-assembled InGaAs/GaAs quantum dots (QDs) are of particular importance for the deterministic generation of spin-photon entanglement. One promising scheme relies on the Larmor precession of a spin in a transverse magnetic field, which is governed by the in-plane $g$-factors of the electron and valence band heavy-hole. We probe the origin of heavy-hole $g$-factor anisotropy with respect to the in-plane magnetic field direction and uncover how it impacts the entanglement generated between the spin and the photon polarization. First, using polarization-resolved photoluminescence measurements on a single QD, we determine that the impact of valence-band mixing dominates over effects due to a confinement-renormalized cubic Luttinger $q$ parameter. From this, we construct a comprehensive hole $g$-tensor model. We then use this model to simulate the concurrence and fidelity of spin-photon entanglement generation with anisotropic hole $g$-factors, which can be tuned via magnetic field angle and excitation polarization. The results demonstrate that post-growth control of the hole $g$-factor can be used to improve spin-photon cluster state generation.