Mean-field description of multicomponent exciton-polariton superfluids

This is a review of spin-dependent (polarization) properties of multicomponent exciton-polariton condensates in conditions when quasi-equilibrium mean-field Gross-Pitaevskii description can be applied. Mainly two-component (spin states $\pm1$) polariton condensates are addressed, but some properties of four-component exciton condensates, having both the bright (spin $\pm1$) and the dark (spin $\pm2$) components, are discussed. Change of polarization state of the condensate and phase transitions in applied Zeeman field are described. The properties of fractional vortices are given, in particular, I present recent results on the warping of the field around half-vortices in the presence of longitudinal-transverse splitting of bare polariton bands, and discuss the geometrical features of warped half-vortices (in the framework of the lemon, monstar, and star classification).Comment: 21 pages, 3 figures. Chapter submitted to the book "Quantum fluids: hot topics and new trends", Springer Solid State Physics series, edited by A. Bramati and M. Modugn

Quantum Exciton-Polariton Networks through Inverse Four-Wave Mixing

We demonstrate the potential of quantum operation using lattices of exciton-polaritons in patterned semiconductor microcavities. By introducing an inverse four-wave mixing scheme acting on localized modes, we show that it is possible to develop non-classical correlations between individual condensates. This allows a concept of quantum exciton-polariton networks, characterized by the appearance of multimode entanglement even in the presence of realistic levels of dissipation.Comment: 5 pages, 4 figures, pre-review version of manuscrip

Exciton-Polariton Oscillations in Real Space

We introduce and model spin-Rabi oscillations based on exciton-polaritons in semiconductor microcavities. The phase and polarization of oscillations can be controlled by resonant coherent pulses and the propagation of oscillating domains gives rise to phase-dependent interference patterns in real space. We show that interbranch polariton-polariton scattering controls the propagation of oscillating domains, which can be used to realize logic gates based on an analogue variable phase.Comment: 6 page

Comment on "Topological stability of the half-vortices in spinor exciton-polariton condensates"

We show that recent paper by Flayac et al. [Phys. Rev. B 81, 045318 (2010) and arXiv:0911.1650] is misleading. We demonstrate the existence of static half-quantum vortices in exciton-polariton condensates and calculate the warping of their polarization texture produced by TE-TM splitting of polariton band.Comment: 4 pages, 1 figure. More material was added (in particular, on the current flow)

Spontaneous polariton currents in periodic lateral chains

We predict spontaneous generation of superfluid polariton currents in planar microcavities with lateral periodic modulation of both potential and decay rate. A spontaneous breaking of spatial inversion symmetry of a polariton condensate emerges at a critical pumping, and the current direction is stochastically chosen. We analyse the stability of the current with respect to the fluctuations of the condensate. A peculiar spatial current domain structure emerges, where the current direction is switched at the domain walls, and the characteristic domain size and lifetime scale with the pumping power.Comment: 6+6 pages, 4+1 figures (with supplemental material

Vortices in exciton-polariton condensates with polarization splitting

The presence of polarization splitting of exciton-polariton branches in planar semiconductor microcavities has a pronounced effect on vortices in polariton condensates. We show that the TE-TM splitting leads to the coupling between the left and right half-vortices (vortices in the right and left circular components of the condensate), that otherwise do not interact. We analyze also the effect of linear polarization pinning resulted from a fixed splitting between two perpendicular linear polarizations. In this case, half-vortices acquire strings (solitons) attached to them. The half-vortices with strings can be detected by observing the interference fringes of light emitted from the cavity in two circular polarizations. The string affects the fringes in both polarizations. Namely, the half-vortex is characterized by an asymmetric fork-like dislocation in one circular polarization; the fringes in the other circular polarization are continuous, but they are shifted by crossing the string.Comment: 4 pages, 2 figs, Optics of Excitons in Confined Systems 11 (Madrid, 7-11 september 2009

Portefólio: instrumento de avaliação e desenvolvimento profissional de professores do 1.º ciclo em formação contínua em matemática

Este trabalho surge no contexto do Programa de Formação Contínua em Matemática (PFCM) para professores do 1.º Ciclo que está a ser desenvolvido desde 2005, a nível nacional, por várias instituições de ensino superior. No distrito de Viseu, a formação é dinamizada, pelo segundo ano consecutivo, pela Escola Superior de Educação.Ministério da Educaçã