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arXiv:cond-mat/0003145 · Physical review. B, Condensed matter

Signatures of the excitonic memory effects in four-wave mixing processes in cavity polaritons

Yuri P. Svirko, Makoto Kuwata‐Gonokami

Published Sep 15, 2000• 12 citations
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Abstract

We report the signatures of the exciton correlation effects with finite memory time in frequency domain degenerate four-wave mixing (DFWM) in semiconductor microcavity. By utilizing the polarization selection rules, we discriminate instantaneous, mean-field interactions between excitons with the same spins, long-living correlation due to the formation of biexciton state by excitons with opposite spins, and short-memory correlation effects in the continuum of unbound two-exciton states. The DFWM spectra give us the relative contributions of these effects and the upper limit for the time of the exciton-exciton correlation in the unbound two-exciton continuum. The obtained results reveal the basis of the cavity polariton scattering model for the DFWM processes in high-$Q$ GaAs microcavity.

DOI
10.1103/physrevb.62.6912

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Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.
A theory of degenerate four-wave mixing (DFWM) in the low density excitation limit at the semiconductor band edge is developed on the basis of the bosonic representation of the electron-hole Hamiltonian. By accounting for the exciton-exciton interactions of the lowest order we arrive at the practical few-level density matrix description of the third-order excitonic nonlinearity. The developed theory accounts phenomenologically for the phase space filling, and excitation induced dephasing effects and well reproduces the results of the recent DFWM experiments in high- and low-fineness microcavity. We show that polarization-sensitive four-wave mixing measurements enable to discriminate the contributions to the DFWM signal from the exciton-exciton interactions of different symmetry.
Summary form only given. Using a full microscopic many-body theory, based on the dynamics-controlled truncation (DCT) formalism, we compute four-wave mixing spectra of thin semiconductor quantum well microcavities within the lowest-order nonlinear regime (/spl chi//sup (3)/-regime). Specifically, we focus on heavy-hole 1s excitons and corresponding two-exciton correlations (coherent biexcitons and two-exciton continuum correlations). Within this approach, the linear optical response corresponding to hh-excitons with given absorption lineshapes are inputs to the calculation of the nonlinear FWM spectra.