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arXiv:1808.01127

Quantum statistics of polariton parametric interactions

M. Sassermann, Vörös, Zoltán, Mohsen Razavi, W. Langbein, Gregor Weihs

Published Aug 3, 2018• 3 citations
arXivHTMLPDF

Abstract

Using a high-quality GaAs planar microcavity, we optically generate polariton pairs, and verify their correlations by means of time-resolved single-photon detection. We find that correlations between the different modes are consistently lower than identical mode correlations, which is attributed to the presence of uncorrelated background. We discuss a model to quantify the effects of such a background on the observed correlations. Using spectral and temporal filtering, the background can be suppressed and a change in photon statistics towards non-classical correlations is observed. These results improve our understanding of the statistics of polariton-polariton scattering and background mechanisms, and pave the way to the generation of entangled polariton pairs.

DOI
10.48550/arxiv.1808.01127

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Using a high-quality GaAs planar microcavity, we optically generate polariton pairs, and verify their correlations by means of time-resolved single-photon detection. We find that correlations between the different modes are consistently lower than identical mode correlations, which is attributed to the presence of uncorrelated background. We discuss a model to quantify the effects of such a background on the observed correlations. Using spectral and temporal filtering, the background can be suppressed and a change in photon statistics towards non-classical correlations is observed. These results improve our understanding of the statistics of polariton-polariton scattering and background mechanisms, and pave the way to the generation of entangled polariton pairs.
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.
It has been proposed that parametric scattering of microcavity polaritons can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy [1], or the polarization degree of freedom [2]. In order to establish, whether a particular scheme is practically feasible, one has to take into account not only the parametric processes in question, but the polaritons' interaction with their environment. It is clear that any such interaction is going to reduce the quality of the entanglement produced by the desired parametric process.
Summary form only given. Several theoretical studies have recently suggested that the scattering of microcavity polaritons can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy (branch index) [1], or the polarization degree of freedom [2]. Even cluster states can be generated [3]. Motivated by the above-mentioned proposals for the creation of entangled photon pairs, we studied parametric polariton scattering in 2D coupled planar and ID micro-cavities grown by molecular beam epitaxy (Fig. 1, left hand side). The advantage of these structures is that the polariton branches involved in the parametric scattering are located energetically below the exciton reservoir, thus the particles are protected from excitonic losses, as shown in Fig. 1.In this paper, we are going to experimentally explore entanglement schemes similar to that in Fig. 1. These measurements are carried out using time-correlated photon counting and utilizing the flexible excitation scheme developed in our group [4]. We also compare the experimental results to numerical calculations which are based on the extension of the microscopic theory of Portolan et al. [5]. Our model allows us to optimize the samples for particular scattering schemes.
We propose and theoretically analyze a new scheme for generating hyperentangled photon pairs (EPPs) in a system of polaritons in coupled planar microcavities.Starting from a microscopic model, we evaluate the relevant parametric scattering processes and numerically simulate the phonon-induced noise background under continuous-wave excitation.Our results show that, compared to other polariton entanglement proposals, our scheme enables the generation of photon pairs that are entangled in both the path and polarization degrees of freedom, and simultaneously leads to a strong reduction in the photoluminescence noise background.This can significantly improve the fidelity of the EPPs under realistic experimental conditions.
Recent theoretical studies of quantum nonlinear dynamics of laser-driven semiconductor microcavities in presence of a lateral photonic potential are reviewed. The following effects are discussed: (i) polariton parametric interactions can be tailored in photonic microstructures (e.g., photonic wires) to generate peculiar entangled states, which are efficiently coupled to the extra-cavity field and which are conveniently protected from the excitonic reservoir, (ii) the peculiar polariton superfluid behavior can be probed through the angle-resolved resonant Rayleigh scattering produced by point defects, (iii) polaritonic "circuits" can be designed to produce efficiently non-classical states of light as output.
The importance of interaction effects in determining the temporal coherence of spectrally and spatially isolated single modes of the microcavity optical parametric oscillator (OPO) is demonstrated. As a function of macroscopic occupancy, the coherence time (tau c) first increases linearly and then exhibits saturation behavior, reaching maximum values of up to 500 ps. Good agreement is found with a model including fluctuations in polariton number and polariton-polariton interactions between the OPO states. tau c is a property of the coupled OPO system, a result confirmed by the finding of equal coherence times for signal and idler, even though the idler is subject to strong additional scattering.