Many-Body and Correlation Effects on Parametric Polariton Amplification in Semiconductor Microcavities

Abstract

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...

Exciton polariton emission from a resonantly excited GaAs microcavity

“…The polarization dependence observed in this work shows directly the maintenance of the polarization during the e-p scattering process when generated from the lower e-p branch, which is not observed when we excite with smaller wave vector. This result corroborates with the coherence between the input laser and the output beam from the e-p scattering observed in the parametric amplification of the light by e-p microcavity [22]. The I/O curve, as well as the transition in the linewidth around the P th , show us an improvement of more than an order of magnitude in the β value (1% up to ∼ 17%) when an e-p was generated by exciting the lower branch.…”

Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

“…10, now including all vectorial polarization states. As discussed above, the polarization amplitudes are given in the X-Y basis, while the fields are given in the TE-TM basis.…”

“…No additional assumptions for the effective polariton-polariton interaction are needed, which is directly included in our theory via the frequency dependent and complex exciton-exciton scattering matrices. 10 Our theoretical analysis incorporates: (i) the well-established microscopic many-particle theory for the optically-induced QW polarization dynamics based on the dynamics-controlled truncation (DCT) formalism 26,27 , and (ii) the self-consistent coupling of this dynamics to the dynamics of the optical fields in the cavity modes 10,28,29 including all vectorial polarization state channels. The theory consistently includes all coherent third order (χ (3) ) nonlinearities and the resulting equations of motion are solved in a self-consistent fashion in the optical fields which includes a certain class of higherorder nonlinearities.…”

Coherent and incoherent aspects of polariton dynamics in semiconductor microcavities

“…This coherent term originates from the non-Markovian nature of the exciton-exciton interaction when going beyond the usual Hartree-Fock approximation and corresponds to four-particle correlations [22]. Lastly, several state of the art microscopic calculations show that the EID strength is highly energy dependent and becomes large when the energy of the two scattered polaritons exceeds twice the exciton energy [23][24][25][26][27]. This might also explain the onset of the lower polariton EID towards positive cavity detuning.…”