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 obtain the effective interaction between identical polaritons for any light-matter coupling. Crucially, we show that the standard treatment of polariton-polariton interactions in the very strong coupling regime is incorrect, since it neglects the light-induced modification of the exciton size and thus greatly overestimates the effect of Pauli exclusion on the Rabi coupling, i.e., the saturation of exciton oscillator strength. Our findings thus provide the foundations for understanding and characterizing exciton-polariton systems across the whole range of polariton densities.
Highlights
A strong light-matter coupling is routinely achieved in experiment by embedding a semiconductor in an optical microcavity [1]
We have presented a microscopic theory of exciton-polaritons in a semiconductor planar microcavity that explicitly involves electrons, holes, and photons
We have shown that the light-matter coupling strongly renormalizes the cavity photon frequency in this model, a feature that has apparently been missed by all previous theoretical treatments
Summary
A strong light-matter coupling is routinely achieved in experiment by embedding a semiconductor in an optical microcavity [1]. When the coupling strength exceeds the energy scale associated with losses in the system, one can create hybrid light-matter quasiparticles called polaritons, which are superpositions of excitons and cavity photons [2,3,4]. For the case of polariton-polariton interactions, the exchange processes are complicated by the coupling to photons, and there are currently conflicting theoretical results in the literature [14,15,16,17] None of these previous works properly include light-induced modifications of the exciton wave function, which can be significant at strong light-matter coupling [18] and which are crucial for determining the polaritonpolariton interaction strength, as we show here. The form of Eq (7) ensures that photons only couple to electronhole states in s orbitals, since the coupling strength g is momentum independent, an approximation which is valid when Eg greatly exceeds all other energy scales in the problem
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