Effective out-of-plane g-factor in strained-Ge/SiGe quantum dots

Recently, lithographic quantum dots in strained-Ge/SiGe have become a promising candidate for quantum computation, with a remarkably quick progression from demonstration of a quantum dot to qubit logic demonstrations. Here we present a measurement of the out-of-plane $g$-factor for single-hole quantum dots in this material. As this is a single-hole measurement, this is the first experimental result that avoids the strong orbital effects present in the out-of-plane configuration. In addition to verifying the expected $g$-factor anisotropy between in-plane and out-of-plane magnetic ($B$)-fields, variations in the $g$-factor dependent on the occupation of the quantum dot are observed. These results are in good agreement with calculations of the $g$-factor using the heavy- and light-hole spaces of the Luttinger Hamiltonian, especially the first two holes, showing a strong spin-orbit coupling and suggesting dramatic $g$-factor tunability through both the $B$-field and the charge state.