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arXiv:1305.1469 · physica status solidi (b)

Polarization entanglement generation in microcavity polariton devices

L. Einkemmer, Z. Vörös, Gregor Weihs, S. Portolan

Published Mar 11, 2015• 6 citations
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Abstract

Entanglement generation by means of microcavity exciton-polaritons is an interesting application of the peculiar properties of these half-light/half-matter quasiparticles. In this paper, we theoretically investigate their luminescence dynamics and entanglement formation in single, and double cavities. We discuss the selection rules for polariton–polariton scattering in double cavities, and evaluate a number of possible parametric scattering schemes in terms of entanglement in the polarization degree of freedom, and identify the ones that are experimentally most promising.

DOI
10.1002/pssb.201451704

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Entanglement generation by means of microcavity exciton-polaritons is an interesting application of the peculiar properties of these half-light/half-matter quasiparticles. In this paper, we theoretically investigate their luminescence dynamics and entanglement formation in single, and double cavities. We discuss the selection rules for polariton–polariton scattering in double cavities, and evaluate a number of possible parametric scattering schemes in terms of entanglement in the polarization degree of freedom, and identify the ones that are experimentally most promising.
We show theoretically that polariton pairs with a high degree of polarization entanglement can be produced through parametric scattering. In our proposed scheme, varying the polarizations of the two pumps, we have a complete control over the symmetries of the produced state (i.e. singlet or triplet output). Our microscopic model shows how a tomographic reconstruction, based on two-time correlation functions, can provide a quantitative assessment of the level of entanglement produced under realistic experimental conditions. Our study provides a suggestive perspective towards hybrid all-optical quantum devices where quantum information can be efficiently generated and controlled within the same structure. This result puts forward the robustness of pair correlations in solid-state devices, even when noise dominates one-body correlations.
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. 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.
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.
The strong coupling of photons and quantum well excitons in semiconductor microcavities leads to the formation of new eigenstates called polaritons. Due to their peculiar dispersion curve and the convenient experimental accessibility, microcavity polaritons have gained considerable interest in the 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. This photon carries the whole information on the underlying polariton state.
Nonlinear optical response of cavity polaritons formed in high-g semiconductor microcavities has attracted much attention because of their potential applications to entangled-photon sources and other quantum information technologies. Theoretical ideas of entangled-photon generation, e.g., biexcitonic cavity quantum electrodynamics and polariton-polariton scattering, have been suggested, however these theories are limited in scope of target because they restrict two-exciton states to either biexciton or unbound two-exciton states. As for exciton system with small binding energy of biexciton, it is likely that the interplay between the biexciton and unbound two-exciton states have much impact on generation efficiency of entangled photons. The authors introduces a general model including both biexciton and unbound two-exciton states and discuss generation efficiency of entangled photons.