Microscopic description of exciton-polaritons in microcavities

Abstract

We investigate the microscopic description of exciton-polaritons that involves electrons, holes and photons within a two-dimensional microcavity. We show that in order to recover the simplified exciton-photon model that is typically used to describe polaritons, one must correctly define the exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare microscopic parameters. For the case of unscreened Coulomb interactions, we find that the exciton-photon detuning is strongly shifted from its bare value in a manner akin to renormalization in quantum electrodynamics. Within the renormalized theory, we exactly solve the problem of a single exciton-polariton for the first time and obtain the full spectral response of the microcavity. In particular, we find that the electron-hole wave function of the polariton can be significantly modified by the very strong Rabi couplings achieved in current experiments. Our microscopic approach furthermore allows us to properly determine the effective interaction between identical polaritons, which goes beyond previous theoretical work. Our findings are thus important for understanding and characterizing exciton-polariton systems across the whole range of polariton densities. arXiv:1902.07966v1 [cond-mat.quant-gas]

Extremely imbalanced two-dimensional electron-hole-photon systems

“…To circumvent this problem, as in Ref. 34, we define the effective detuning δ eff and Rabi splitting Ω eff in a way analogous to an experimental procedure -by fitting the polariton dispersion to a coupled oscillator model. In particular, we employ a two-parameter least square fitting procedure to match the LP dispersion E Q evaluated numerically from Eqs.…”

“…In the presence of both light and matter degrees of freedom, the contact coupling term of our model,Ĥ e-h-C in Eq. (1d), implies an ultraviolet logarithmic divergence of the ground-state energy 34 . Since the details of the highmomentum physics, such as the band curvature due to the crystal lattice structure, are not included within our low-energy model, we will treat the ultraviolet physics via the process of renormalization.…”

“…To this end, we follow Ref. 34 and consider the most general superposition of a cavity photon at normal incidence and an electron-hole pair:…”

“…(9a) and (9b) recovers the coupled exciton-photon oscillator model in the limit g a X R X . The generalization to finite momentum is straightforward 34 , and one finds that the lowest eigenvalue E + E g of Eqs. (9a) and (9b) well matches the oneparticle lower polariton (LP) energy expression coming from the two-level coupled oscillator model,…”

“…As in Ref. 34, the renormalization procedure we consider is defined for the case at zero gating/doping (E F = 0). We then increase the density of majority particles while keeping the other parameters fixed.…”