Photonic Crystal Architecture for Room Temperature Equilibrium Bose-Einstein Condensation of Exciton-Polaritons

We describe photonic crystal microcavities with very strong light-matter interaction to realize room-temperature, equilibrium, exciton-polariton Bose-Einstein condensation (BEC). This is achieved through a careful balance between strong light-trapping in a photonic band gap (PBG) and large exciton density enabled by a multiple quantum-well (QW) structure with moderate dielectric constant. This enables the formation of long-lived, dense 10~$\mu$m - 1~cm scale cloud of exciton-polaritons with vacuum Rabi splitting (VRS) that is roughly 7\% of the bare exciton recombination energy. We introduce a woodpile photonic crystal made of Cd$_{0.6}$Mg$_{0.4}$Te with a 3D PBG of 9.2\% (gap to central frequency ratio) that strongly focuses a planar guided optical field on CdTe QWs in the cavity. For 3~nm QWs with 5~nm barrier width the exciton-photon coupling can be as large as \hbar\Ome=55~meV (i.e., vacuum Rabi splitting 2\hbar\Ome=110~meV). The exciton recombination energy of 1.65~eV corresponds to an optical wavelength of 750~nm. For $N=$106 QWs embedded in the cavity the collective exciton-photon coupling per QW, \hbar\Ome/\sqrt{N}=5.4~meV, is much larger than state-of-the-art value of 3.3~meV, for CdTe Fabry-P\'erot microcavity. The maximum BEC temperature is limited by the depth of the dispersion minimum for the lower polariton branch, over which the polariton has a small effective mass $\sim 10^{-5}m_0$ where $m_0$ is the electron mass in vacuum. By detuning the bare exciton recombination energy above the planar guided optical mode, a larger dispersion depth is achieved, enabling room-temperature BEC

On the uniform perfectness of the boundary of multiply connected wandering domains

We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to examples of multiply connected wandering domains given by Baker. We also provide examples of infinitely connected wandering domains whose boundary is uniformly perfect.Comment: 19 page

Linear and Nonlinear Mesoscopic Thermoelectric Transport with Coupling to Heat Baths

Decades of research on thermoelectrics stimulated by the fact that nano- and meso-scale thermoelectric transport could yield higher energy conversion efficiency and output power has recently uncovered a new direction on inelastic thermoelectric effects. We introduce the history, motivation, and perspectives on mesoscopic inelastic thermoelectric effects.Comment: Invited by Comptes Rendu