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

Abstract

We describe photonic crystal microcavities with very strong light-matter interaction to realize roomtemperature, equilibrium, exciton-polariton Bose-Einstein condensation (BEC). This goal 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 a moderate dielectric constant. This approach enables the formation of a long-lived, dense 10 − μm − 1 − cm-scale cloud of exciton polaritons with vacuum Rabi splitting 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 ℏΩ ¼ 55 meV (i.e., a vacuum Rabi splitting of 2ℏΩ ¼ 110 meV). The exciton-recombination energy of 1.65 eV corresponds to an optical wavelength of 750 nm. For N ¼ 106 QWs embedded in the cavity, the collective exciton-photon coupling per QW (ℏΩ= ffiffiffiffi N p ¼ 5.4 meV) is much larger than the state-of-the-art value of 3.3 meV, for the CdTe Fabry-Pérot 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 of approximately 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. The BEC transition temperature ranges as high as 500 K when the polariton density per QW is increased to ð11a B Þ −2 , where a B ≃ 3.5 nm is the exciton Bohr radius and the exciton-cavity detuning is increased to 30 meV. A high-quality PBG can suppress exciton radiative decay and enhance the polariton lifetime to beyond 150 ps at room temperature, sufficient for thermal equilibrium BEC.

Topological Polaritons

“…CdTebased quantum wells are a standard platform to reach the strong-coupling limit. Recently, exciton-photon couplings of up to Ω = |g q | √ 2 = 55meV have been reached using multiple CdTe-based quantum wells (Ω = 5.4meV for a single quantum well) embedded in a photoniccrystal-based microcavity [36]. For such large excitonphoton couplings, the size of the topological gap would essentially only be limited by the strength of the periodic exciton potential and the exciton Zeeman splitting.…”

Topological polaritons from photonic Dirac cones coupled to excitons in a magnetic field

“…Finally, the strong coupling between excitons and photons can be realized by forming a photonic cavity with an embedded exciton-supporting quantum well. The resulting couplings can be quite large, reaching g q = 4 meV [20,30] already for a single quantum well.…”

Polariton condensation in photonic crystals with high molecular orientation

“…It can be noted that there exist other materials, such as cyano-substituted compound 2,5-bis(cyano biphenyl-4-yl) thiophene, in which the transition dipole moment lies in the in-plane direction with respect to the crystal face. While such materials can be assumed to demonstrate strong coupling with the Fabry-Perot cavities or transverse electric (TE) modes of PCs [10], supporting Γ-point condensation in the reciprocal space, this case is trivial and beyond the scope of our manuscript. It should be noted that, unlike the nanostructure proposed in [10], here we study structures which fabrication is easier.…”

“…As it was shown in [10], fluctuations of shapes and sizes of the basic elements (such as pillars, holes, rods) forming the PC lead to the variation of the photonic bandgap edge. However, as it was shown, the randomness of around 20 nm leads to deviation of the PC band edge less than 2%.…”

“…This fact allows us to neglect the influence of the periodic structure of the 2D PC on the exciton wave function and consider non-uniform electric fields only. EPs emerge as mixed modes of the electromagnetic field and the exciton resonance, thus having the dispersion [10]:…”