Exciton-polariton modes arising from interaction between bound excitons in monolayer thin semiconductor sheets and photons in a Fabry-Perot microcavity are considered theoretically. We calculate the dispersion curves, mode lifetimes, Rabi splitting, and Hopfield coefficients of these structures for two nearly 2D semiconductor materials, MoS2 and WS2, and suggest that they are interesting for studying the rich physics associated with the Bose-Einstein condensation of exciton-polaritons. The large exciton binding energy and dipole allowed exciton transitions, in addition to the relatively easily controllable distance between the semiconductor sheets are the advantages of this system in comparison with traditional GaAs or CdTe based semiconductor microcavities. In particular, in order to mimic the rich physical properties of the quantum degenerate mixture of two bosonic species of dilute atomic gases with tunable inter-species interaction , we put forward a structure containing two semiconductor sheets separated by some atomic-scale distance (l) using a nearly 2D dielectric (e.g. h-BN), which offers the possibility of tuning the interaction between two exciton-polariton Bose-Enstein condensates. We show that the dynamics of this novel structure are ruled by two coupled Gross-Pitaevskii equations with the coupling parameter ∼ l −1 .

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We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is non-homogeneous and the collective excitations are characterized by a set of discrete confined phonon-like excitations. We derive a general convenient analytical description for the damping rate, which takes into account, the trapping potential and the optical lattice, for the Landau and Beliaev processes at any temperature, T . At high temperature or weak spatial confinement, we show that both mechanisms display linear dependence on T . In the quantum limit, we found that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of T . Our theoretical predictions for the damping rate under thermal regime is in completely correspondence with the experimental values reported for 1D condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive non-linear terms on the decay rate of the collective excitations. A general expression of the renormalized Goldstone frequency has been obtained as a function of the 1D non-linear self-interaction parameter, laser intensity and temperature.

We obtain the the long-wavelength polar optical vibrational modes of semiconductor core-shell nanowires by means of a phenomenological continuum model. A basis for the space of solutions is derived, and by applying the appropriate boundary conditions, the transcendental equations for the coupled and uncoupled modes are attained. Our results are applied to the study of the GaAs-GaP core-shell nanowire, for which we calculate numerically the polar optical modes, analyzing the role of strain in the vibrational properties of this nanosystem.

A detailed analysis of the uncoupled polar optical-phonon modes with cylindrical symmetry and translational invariance along the wire in core/shell semiconductor nanowires is presented, within the framework of a phenomenological continuum model. The effects of strain on confined longitudinal optical (LO) and transverse optical (TO) core-like and shell-like phonon modes in GaAs/GaP quantum wire are considered. The reported TO splitting together with LO confined modes may be used to extract information on the core and shell nanostructures, by comparison to Raman and infrared spectroscopy techniques. Employing recently reported experimental results on GaAsP/GaP core-shell nanowires, the ratio of the LO and TO Grüneisen mode parameters is determined.