We show that pristine MoS$_2$ single layer (SL) exhibits two bandgaps $E_{gparallel}=1.9$ eV and $E_{gperp}=3.2$ eV for the optical in-plane and out-of-plane susceptibilities $chi_parallel$ and $chi_perp$, respectively. In particular, we show that od
d states bound to vacancy defects (VDs) lead to resonances in $chi_perp$ inside $E_{gperp}$ in MoS$_2$ SL with VDs. We use density functional theory, the tight-binding model, and the Dirac equation to study MoS$_2$ SL with three types of VDs: (i) Mo-vacancy, (ii) S$_2$-vacancy, and (iii) 3$times$MoS$_2$ quantum antidot. The resulting optical spectra identify and characterize the VDs.
We show that many-body correlations among excitons originating from the Pauli exclusion principle in a quantum well embedded inside a microcavity provide a possibility to produce pairs of entangled photons by ultrashort laser pulses with a yield of $
sim 10^{-2}$. The quantum-field theoretical two-particle density matrix in second quantization is used to calculate entanglement for arbitrary emission angles. %At time scales where the heavy-light hole splitting is resolved the resonances corresponding to different two-exciton %states develop, which allow for a simple kinematic theory relating the %states of the outgoing photons with the respective two-exciton states. Largest response can be expected at symmetric emission angles for resonances with the heavy-heavy and light-light two-exciton states with remarkably nontrivial dependence of entanglement on the emission angles and on the ellipticity parameters of the excitation. We show that the angle dependence can be tailored by means of the microcavity. Interestingly, the emitted entangled 2-photon states are always in a triplet state.
Non-perturbative phenomena in four-wave mixing spectra of semiconductors are studied using the exact solution of a widely used phenomenological non-linear equation of motion of the exciton polarization. It is shown that Coulomb interaction, included
in the nonlinearity, leads to two characteristic effects, which are essentially of dynamical origin, -- a split of the exciton peak and a non-monotonous dependence of the response at the exciton frequency on the magnitude of the external field. Relations between the spectral features and the parameters of the system is obtained. It is found that the transition from perturbative to non-perturbative regimes is controlled by parameters inversely proportional to the decay rate. It implies that the condition of low excitation density does not necessarily warrant applicability of the perturbational approach.
We studied the semiconductor response with respect to high intensity resonant excitation on short time scale when the contribution of the Fermi statistics of the electrons and holes prevails. We studied both the single and double pulse excitations. F
or the latter case we considered the time evolution of the multi-wave mixing exciton polarization. The main difference between the excitation by a single pulse or by two non-collinear pulses is that the Rabi oscillations of the multi-wave mixing response are characterized by two harmonics. Analyzing the operator dynamics governed by the external excitation we found that there are three invariant spin classes, which do not mix with the evolution of the system. Two classes correspond to the bright exciton states and one contains all dark states. We found that the dynamics of the classes is described by six frequencies and the Rabi frequencies are only two of them (one for each bright class). We discuss the effect of the dispersion of the electrons and holes and the Coulomb interaction describing the semiconductor by the semiconductor Bloch equation (SBE). We show that if initially the system is in the ground state then the SBE preserves the invariant spin classes thus proving absence of the dark excitons in the framework of this description. We found that due to the mass difference between holes of different kind additional Rabi frequencies, two of those present in the operator dynamics, should appear in the evolution of the exciton polarization.
