Spin qubits are typically operated in the lowest orbital of a quantum dot to minimize interference from nearby states. In valence-band hole systems, strong spin-orbit coupling links spin and orbital degrees of freedom, strongly influencing the hole
g-factor, a key parameter for qubit control. We investigate the out-of-plane
g-factor in Ge quantum dots using excitation (single-particle) and addition (many-body) spectra. Excitation spectra allow us to distinguish the pure Zeeman
g-factor from orbital contributions to the magnetic field splitting of states despite the strong spin-orbit coupling. This distinction clarifies discrepancies between
g-factors extracted with the two methods, for different orbital states and different hole numbers. Furthermore, we find gate-tunability of
g-factors at the level of 15%, highlighting its relevance for all-electric qubit manipulation.
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\ensuremath{\pi}$ in
t2g4 spin-orbit coupled three-orbital Hubbard models at electronic density
n=4. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at
n=3.5 in a one-dimensional Hubbard model with a degenerate
t2g sector, when in the presence of spin-orbit coupling. At intermediate Hubbard
U and spin-orbit $\ensuremath{\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q=\ensuremath{\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\ifmmode\pm\else\textpm\fi{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\ifmmode\pm\else\textpm\fi{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\ensuremath{\lambda}$ vs
U phase diagram, at a fixed and robust Hund coupling. Interestingly, this new ``block excitonic phase'' is present even at large values of $\ensuremath{\lambda}$, unlike the
n=4 excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with
d3.5 valence and robust spin-orbit coupling.
We studied the optical steady-state generation of spin in the III-V semiconductor quantum dots, where an external laser field couples to the quantum dot only via the electric dipole interband transition and generation of spin in the conduction band is due to the optical transition from the spin-split valence band. In the weak field regime, the optical spin generation is second order in the Rabi frequency. At the intense laser fields, the spin-orbit interaction is of no importance and the optical spin generation is absent. Therefore, there should be a region featured by intermediate Rabi frequencies where the optical spin generation reaches its maximum. We demonstrated this upper limit using a simple model of the III-V quantum dot. The maximum corresponds to the optical interaction energy equal to the spin-orbit interaction energy in the valence band. The work addressed here sets the upper limit for steady-state optical spin generation in the III-V semiconductor quantum dots and completes the physical picture of this process for all optical field strengths.