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Quantum Optoelectronics

Quantum Statistical Effects of Microcavity Exciton Polaritons

Hui W. Cao, Stanley Pau, F. Tassone, Robin K. Huang, Gunnar G. Bjork, Y. Yamamoto

Published Jan 1, 1997• 0 citations
Publisher

Abstract

In the past few years there has been extensive study on exciton-photon coupling in a quantum well (QW) embedded semiconductor microcavity [1, 2]. The strong coupling between the QW exciton state and the cavity photon state results in the new eigenstates of this coupled systems, i. e. the exciton-polariton states [3]. The microcavity exciton-polaritons, as new quasi particles, features interesting quantum statistics.

DOI
10.1364/qo.1997.qthb.1

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In the past few years there has been extensive study on exciton-photon coupling in a quantum well (QW) embedded semiconductor microcavity [1, 2]. The strong coupling between the QW exciton state and the cavity photon state results in the new eigenstates of this coupled systems, i. e. the exciton-polariton states [3]. The microcavity exciton-polaritons, as new quasi particles, features interesting quantum statistics.
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.
The exciton–photon effects on a microcavity are reported. In particular, the emission spectrum of a semiconductor quantum well embedded in a microcavity is obtained, including nonlinear effects such as exciton–exciton correlation. By solving the Heisenberg equations for the excitons and photons the polariton dispersion energy and the emission spectrum is calculated. It is shown the presence of collapses and revivals when the nonlinear interaction parameter is less than the exciton–photon coupling. For nonlinear exciton–exciton coupling values similar to exciton–photon coupling the results show that the time line shape is independent of the nonlinear term but the polariton peak position is blueshifted. Reasonable agreement is found with the experimental situation.
The quantum features of the temporal photon statistics of an exciton–cavity coupled system in a quantum-well semiconductor microcavity are investigated analytically. Under the secular approximation, if the nonlinear interactions, i.e. the exciton–exciton coupling and the phase-space filling, are much weaker than the exciton–photon interaction, the evolution of the Fano factor shows that the distribution of the photon numbers exhibits the feature of collapses–revivals (CRs), and the relevant revival time may be adjusted by several factors such as the total particle number, the detuning, and the nonlinear coupling strengths, etc. Especially, the ideal maximum antibunching with the minimum value 0 of the Fano factor occurs periodically for such a situation, with the dissipation of exciton–polariton being ignored.
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.
Abstract A quantum behavior of the light emitted by exciton polaritons excited in a pillar semiconductor microcavity with embedded quantum well is investigated. Considering the bare excitons and photon modes as coupled quantum oscillators allows for an accurate accounting of the nonlinear and dissipative effects. In particular, using the method of quantum states presentation in a quantum phase space via quasiprobability functions (namely, a P-function and a Wigner function), we study the effect of the laser and the exciton-photon detuning on the second order correlation function of the emitted photons. We determine the conditions for the phenomena of bunching, giant bunching, and antibunching of the emitted light. In particular, we predict the effect of a giant bunching for the case of a large exciton to photon population ratio. Within the domain of parameters supporting a bistability regime we demonstrate the effect of bunching of photons.