Electron-Photon Interaction in Microcavities

M. Yamanishi, Y. Lee

振龍 張

Renju Rajan, P. Ramesh Babu, Krishnamoorthy Senthilnathan

In this paper, a mathematical model for photon condensation in an optical microcavity is considered based on Gross-Pitaevskii equation. The interaction of photons with fluorescent dye molecules in an optical microcavity resembles electron-ion interaction in a periodic lattice. The system is modelled analogous to Kronig-Penney model for electrons in a one-dimensional periodic lattice. The laser used as the light source gives rise to nonlinearity due to the deformation of electron orbits in the fluorescent dye. To accommodate the optical Kerr effect which arises due to this nonlinear interaction, the resultant Schrödinger equation is modified, which assumes the form of Gross-Pitaevskii equation. The model is validated using equation of state, whose virial coefficients can be evaluated from grand canonical ensemble scheme taking into account the interaction between photons and fluorescent dye molecules.

Helmut Schwarz

Bich Ha Nguyen

Abstract A quantum system consisting of a single-mode microcavity and a two-level quantum dot or atom placed inside this microcavity, the interaction of monoenergetic photons in the microcavity with the electron in the two-level quantum dot or atom being the allowed electrical dipole transition between two energy levels, is a basic element of prospective devices for quantum information processing. Its time evolution is governed by cavity quantum electrodynamics (CQED). The photon–electron coupling induces the shifts of energy levels of the electron in the two-level quantum dot or atom. If there is no photon in the microcavity, then the shift of electron energy levels is induced by the radiative corrections and it is called the Lamb shift. The presence of photons in the microcavity induces another type of electron energy level shift—the ac Stark shift. In this paper, we present the exact derivation of the formulae for the Lamb and ac Stark shifts of electron energy levels in the two-level quantum dot or atom placed inside a single-mode microcavity.

José Luis Figueiredo, José Tito Mendonça, Hugo Terças

Supersolidity - simultaneous superfluid flow and crystalline order - has been realized in quantum atomic systems but remains unexplored in purely photonic platforms operating at weak light-matter coupling. We predict a supersolid phase of light in a plasma-filled optical microcavity, where photons acquire effective mass and interact via nonlocal, plasma-mediated nonlinearities. By deriving a Gross-Pitaevskii equation with a tunable photon-photon interaction kernel, we show that under coherent driving the cavity light field can spontaneously crystallize into a supersolid lattice via modulational instability. Crucially, this supersolid arises from a weak photon-electron coupling enabled by virtual electronic transitions, and it does not require hybrid polariton formation. Using doped semiconductor microcavities, we identify feasible conditions (electron densities $\sim 10^{10}- 10^{11}~\mathrm{cm}^{-2}$ and optical intensities $\sim 10^{2}-10^{4}~\mathrm{W/cm}^{2}$) for experimental realization. This work establishes plasmonic cavities as a platform for correlated photonic matter with emergent quantum order.