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We report on pump-power-dependent emission features of a nonthermalized and interacting dynamical condensate of exciton polaritons. The system based on a planar AlAs/AlGaAs microcavity sample with twelve GaAs quantum wells in the active region is investigated comprehensively by measuring the energy-momentum dispersion characteristics, the spatial coherence, and the photon statistics under resonant, fs-pulsed optical excitation at high momentum. We observe a significant polariton-population-dependent modification of the emission signatures above the quantum degeneracy. The nonequilibrium polariton condensate is confirmed by its polaritonic energy-momentum dispersion as well as excitation-power-dependent coherence properties and its photon statistics, being different from that of an ideal coherent state. The polaritonic condensate is characterized by a spatial coherence length of up to 4 \ensuremath{\mu}m and a super-Poissonian photon statistic of the emitted light well above threshold. Results obtained in second-order photon autocorrelation measurements in momentum-space resolved spectroscopy indicate polariton repulsive interaction throughout the condensate and a spatial coherence length being shorter than the condensate extension of 20--30 \ensuremath{\mu}m.

Photoluminescence of excitons (X) and biexcitons (XX) from single neutral $\mathrm{CdSe}∕\mathrm{ZnSe}∕\mathrm{ZnMnSe}$ quantum dots (QDs) with various magnitudes of $sp\text{\ensuremath{-}}d$ exchange interaction has been investigated in magnetic fields $B$ up to $10\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ at $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The magnitude of the $sp\text{\ensuremath{-}}d$ interaction is varied by changing the penetration of the exciton wave function ${\ensuremath{\psi}}_{X}$ into the diluted magnetic semiconductor (DMS) barrier, $\ensuremath{\eta}$, by variation of the nonmagnetic $\mathrm{ZnSe}$ barrier layer thickness about a value of $1.75\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The small penetration of ${\ensuremath{\psi}}_{X}$ into the DMS barrier allowed a decrease of the X and XX emission line broadening caused by magnetic fluctuations and resolution of the fine structure of X states in a single QD. In contrast to bulk DMSs, the exciton line broadening when $B$ is normal to the QD plane was found to be a nonmonotonic function of magnetic field: at high $B$ it is suppressed due to Mn ion spin alignment, whereas at low $B$ it is decreased due to the mixing of ${J}_{z}=+1$ and $\ensuremath{-}1\phantom{\rule{0.3em}{0ex}}\mathrm{X}$ states in low-symmetry QDs by the electron-hole $(e\text{\ensuremath{-}}h)$ exchange interaction. In addition, magnetic fluctuations result in (i) emission depolarization and enhanced splitting of exciton emission lines compared to the $e\text{\ensuremath{-}}h$ exchange interaction at $B=0$ and (ii) strong enhancement of spin relaxation between ``bright'' $J=1$ exciton states in magnetic fields normal to the QD plane already at $\ensuremath{\eta}\ensuremath{\sim}1%$. The spin relaxation from bright to ``dark'' exciton states is negligible up to $\ensuremath{\eta}\ensuremath{\sim}4%$. Auger recombination of excitons with excitation of Mn ions markedly decreases the quantum efficiency of exciton emission at $B=0$ already at $\ensuremath{\eta}\ensuremath{\sim}4%$.

Magnetoluminescence of $\mathrm{Cd}\mathrm{Mn}\mathrm{Se}\text{\ensuremath{-}}\mathrm{Zn}\mathrm{Se}$ disk-shaped quantum dots in a magnetic field up to $11\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ is measured in the Faraday and Voigt geometries at liquid He temperatures and various levels of laser excitation. Within the range of $B=0--11\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ the intensity of the quantum dot photoluminescence increases strongly (up to two orders of magnitude) in the Faraday geometry and only slightly ($\ensuremath{\sim}1.5$ times) in the Voigt geometry. To explain the observed dependence on magnetic field direction the selection rules for the Auger recombination of excitons with excitation of Mn-ion are revised. The magnetic field dependence of the quantum yield of quantum dot exciton emission and its anisotropy are shown to appear due to the dependence of Auger recombination of uncharged excitons with excitation of Mn-ion on the spin of both exciton and Mn-ion. The anisotropy is provided by a quick spin relaxation of photoexcited excitons into the ground state which spin structure depends on the direction of the magnetic field.

Statistical fluctuations of the magnetization on a nanometer scale have been investigated with the use of magneto-optical spectroscopy of quasi-zero-dimensional excitonic magnetic polarons (EMP) in individual pancake-shaped CdSe/ZnMnSe quantum dots (QD's). The EMP emission line demonstrates a qualitatively different behavior in magnetic field B normal and parallel to the QD plane. In the first case, the alignment of the Mn spins in high magnetic fields results in a giant Zeeman shift and linewidth narrowing of almost one order of magnitude to values characteristic of nonmagnetic QD's. No similar effects are observed in the second case where the emission line demonstrates a weak blue shift and small linewidth variation. It is shown that the difference originates from the anisotropy of the hole exchange field in the QD's and can be described using the fundamental fluctuation-dissipation theorem and taking into account the anisotropy of the hole g factor. Both the longitudinal and transverse fluctuations of the magnetization are determined from the analysis of EMP emission lines recorded in the two directions of magnetic field B. We demonstrate that in high magnetic fields the longitudinal fluctuations decrease exponentially whereas the transverse ones decrease as $1/B.$

Very large changes in the population distributions of microcavity polaritons are reported under conditions of simultaneous resonant and nonresonant excitation. The strong relaxation bottleneck, which results in weak emission from the lower polariton branch for resonant excitation alone, is fully suppressed if additional nonresonant excitation is employed. By comparison with theory, the massive enhancement of the polariton relaxation is shown to arise from scattering of polaritons by free carriers, present in quantum wells due to residual doping, which are then heated by the nonresonant excitation.