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The complexity induced by the Coulomb interaction between electrons determines the noninstantaneous character of exciton-exciton collisions. We show that the exciton-photon coupling in semiconductor microcavities is able to alter the exciton dynamics during collisions strongly affecting the effective scattering rates. Our analysis clarifies the origin of the great enhancement of parametric gain observed when increasing the polariton splitting. It also demonstrates that exciton-exciton collisions in semiconductors can be controlled and engineered to produce almost decoherence-free collisions for the realization of all-optical microscopic devices. DOI: 10.1103 The phase-coherent amplification of light-matter waves (cavity polaritons) recently observed is one of the most exciting developments in the field of semiconductor nonlinear optics [1][2][3][4][5][6][7]. It operates with analogous principles (but under very different conditions) of matterwave amplifiers based on ultracold atoms [8,9]. Very recently it has been shown that a semiconductor microcavity (SMC) can amplify (via phase-coherent amplification of polaritons) a weak light pulse more than 5000 times [7].Cavity polaritons are two-dimensional eigenstates of SMCs which result from the strong resonant coupling between cavity-photon modes and two-dimensional excitons in embedded quantum wells (QWs) [10]. The dynamics and hence the resulting energy bands of these mixed quasiparticles are highly distorted with respect to those of bare excitons and cavity photons (Fig. 1). The exciton-photon coupling rate V determines the splitting (2V) between the two polariton energy bands. Coherent amplification of polaritons requires a coupling mechanism able to transfer polaritons from a reservoir (in this case provided by polaritons resonantly excited by a pump laser pulse on the lower polariton dispersion) to the signal mode, while conserving energy and momentum. Polaritons of different modes are coupled via their excitonic content, the coupling being provided mainly by the Coulomb interaction between excitons (also the anharmonic part of the exciton-photon interaction contributes). The microscopic theory of parametric polariton amplification [11] shows that the resulting Coulomb coupling strength is given by the exciton-exciton (XX) scattering rate [12] V XX ' 1:52E b a 2 0 (E b is the exciton binding energy and a 0 is the exciton Bohr radius) times the exciton fraction of the interacting polariton modes. This effective polariton-polariton interaction scatters a pair of pump polaritons into the lowest-energy state and into a higher-energy state (usually known as the idler mode). Energy and momentum conservation requires 2! k ! 0 ! 2k , where ! k is the energy of a pump polariton injected with an in-plane wave vector k as shown in Fig. 1. The scattering process is stimulated by a weak signal beam injected perpendicular to the cavity (k 0) that is thus greatly amplified. It has recently been shown that increasing the exciton-photon coupling V by inserting a large number...

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We present a quantum theory of light scattering for the analysis of the quantum statistical and fluctuation properties of light scattered or emitted by micrometric and nanometric three-dimensional structures of arbitrary shape. We obtain general three-dimensional quantum-optical input-output relations providing the output photon operators in terms of the input photon operators and of the noise currents of the scattering system. These relations hold also for photon operators associated with evanescent fields, for anisotropic scattering systems and/or for media with a nonlocal susceptibility. We find that the commutation relations of the output photon operators, carrying all the information on the scattering and/or the emission process, result to be fixed by energy conservation and reciprocity. We prove that this quantization scheme is consistent with QED commutation rules by using a novel relationship between vacuum and thermal fluctuations. This theoretical framework has been applied to analyze the spectral density of light close to a point scatterer under different nonequilibrium conditions.