The electronic structure of vertically stacked self-assembled quantum disks is studied within the effective mass approximation. The energy spectrum is calculated in the adiabatic approximation and using an exact diagonalization technique. The influence of the strain, dot separation, and the magnetic field on the formation of coupled quantum dot levels is discussed.

We demonstrate that, even when employing above band gap excitation, photons emitted from semiconductor quantum dots can have linewidths that approach their transform-limited values. This is accomplished by using quantum dots embedded within bottom-up photonic nanowires, an approach which mitigates several potential mechanisms that can result in linewidth broadening: (i) Only a single quantum dot is present in each device, (ii) dot nucleation proceeds without the formation of a wetting layer, and (iii) the sidewalls of the photonic nanowire are comprised not of etched facets, but of epitaxially grown crystal planes. Using these structures we achieve linewidths of $2\times$ the transform limit for above band gap excitation. We also demonstrate a highly nonlinear dependence of the linewidth on both excitation power and temperature which can be described by an independent boson model that considers both deformation and piezoelectric exciton-phonon coupling. We find that for sufficiently low excitation powers and temperatures, the observed excess broadening is not dominated by phonon dephasing, a surprising result considering the high phonon occupation that occurs with above band gap excitation.

A theory of electronic properties of a spin-singlet quantum Hall droplet at filling factor $\nu =2\mathrm{}$ in a parabolic quantum dot is developed. The excitation spectrum and the stability of the droplet due to the transfer of electrons into the second Landau level at low magnetic fields and due to spin flip at the edge at higher magnetic fields are determined using Hartree-Fock, exact diagonalization, and spin-density functional methods. We show that above a critical number of electrons $N_c$ the unpolarized $\nu =2\mathrm{}$ quantum Hall droplet ceases to be a ground state in favor of spin-polarized phases. We determine the characteristic pattern in the addition and current-amplitude Coulomb blockade spectra associated with the stable $\nu =2\mathrm{}$ droplet. We show that the spin transition of the droplet at a critical number of electrons is accompanied by the reversal of the current-amplitude modulation at the $\nu =2\mathrm{}$ line, as observed in recent experiments.

We present an experimental study of the coherence properties of a single heavy-hole spin qubit formed in one quantum dot of a gated GaAs/AlGaAs double quantum dot device. We use a modified spin-readout latching technique in which the second quantum dot serves both as an auxiliary element for a fast spin-dependent readout within a 200 ns time window and as a register for storing the spin-state information. To manipulate the single-spin qubit, we apply sequences of microwave bursts of various amplitudes and durations to make Rabi, Ramsey, Hahn-echo, and CPMG measurements. As a result of the qubit manipulation protocols combined with the latching spin readout, we determine and discuss the achieved qubit coherence times: $T_1$, $T_{Rabi}$, $T_2^{*}$, and $T_2^{CPMG}$ vs. microwave excitation amplitude, detuning, and additional relevant parameters.

We present a microscopic theory of the optical properties of self-assembled quantum dots doped with a single magnetic manganese (Mn) impurity and containing a controlled number of electrons. The single-particle electron and heavy-hole electronic shells are described by two-dimensional harmonic oscillators. The electron-electron, electron-hole Coulomb as well as the short-range electron spin-Mn spin and hole spin-Mn spin contact exchange interactions are included. The electronic states of the photoexcited electron-hole-Mn complex and of the final electron-Mn complex are expanded in a finite number of configurations and the full interacting Hamiltonian is diagonalized numerically. The emission spectrum is predicted as a function of photon energy for a given number of electrons and different number of confined electronic quantum dot shells. We show how emission spectra allow to identify the number of electronic shells, the number of electrons populating these shells and, most importantly, their spin. We show that electrons not interacting directly with the spin of Mn ion do so via electron-electron interactions. This indirect interaction is a strong effect even when Mn impurity is away from the quantum dot center.