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Physical Review A

Multipartite polariton entanglement in semiconductor microcavities

T. C. H. Liew, Vincenzo Savona

Published Sep 1, 2011• 43 citations
Publisher

Abstract

We study the entanglement of multiple polariton modes, which results in continuous variable cluster states suitable for quantum computation. Schemes are based on parametric scattering between spin-polarized lower and upper polariton branches in planar microcavities or spin-polarized orbital angular momentum states in mesa structures. Such systems are modeled by numerical solution of truncated density matrices and compared to the solution of the Heisenberg equations for the set of field correlators up to third order. Four-body entanglement is evidenced by violation of the van Loock--Furusawa quadripartite inequalities. We show that the entanglement is able to withstand a realistic strength of pure dephasing present in typical systems.

DOI
10.1103/physreva.84.032301

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We study the entanglement of multiple polariton modes, which results in continuous variable cluster states suitable for quantum computation. Schemes are based on parametric scattering between spin-polarized lower and upper polariton branches in planar microcavities or spin-polarized orbital angular momentum states in mesa structures. Such systems are modeled by numerical solution of truncated density matrices and compared to the solution of the Heisenberg equations for the set of field correlators up to third order. Four-body entanglement is evidenced by violation of the van Loock--Furusawa quadripartite inequalities. We show that the entanglement is able to withstand a realistic strength of pure dephasing present in typical systems.
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.
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.
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.
Recently, the possibility of generating nonclassical polariton states by means of parametric scattering has been demonstrated. Excitonic polaritons propagate in a complex interacting environment and contain real electronic excitations subject to scattering events and noise affecting quantum coherence and entanglement. Here, we present a general theoretical framework for the realistic investigation of polariton quantum correlations in the presence of coherent and incoherent interaction processes. The proposed theoretical approach is based on the nonequilibrium quantum Langevin approach for open systems applied to interacting-electron complexes described within the dynamics controlled truncation scheme. It provides an easy recipe to calculate multitime correlation functions which are key quantities in quantum optics. As a first application, we analyze the buildup of polariton parametric emission in semiconductor microcavities including the influence of noise originating from phonon-induced scattering.
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.
A scheme is proposed for the generation of polarization- and frequency-entangled photons in a semiconductor planar microcavity. Photon entanglement can be achieved by converting two lower polariton branches with symmetric in-plane momenta into lower and upper polariton branches with zero in-plane momentum via a biexciton state. The phase-matching condition is satisfied for a microcavity with cavity detuning equal to the biexciton binding energy. The generation efficiency and energy control of the entangled photons are demonstrated for a CuCl microcavity as an example.