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arXiv:cond-mat/0505639 · Physical Review Letters

Four Wave Mixing Oscillation in a Semiconductor Microcavity: Generation of Two Correlated Polariton Populations

Marco Romanelli, Charles Leyder, Jean‐Philippe Karr, E. Giacobino, Alberto Bramati

Published Mar 7, 2007• 93 citations
arXivHTMLPDF

Abstract

We demonstrate a novel kind of polariton four wave mixing oscillation. Two pump polaritons scatter towards final states that emit two beams of equal intensity, separated both spatially and in polarization with respect to the pumps. The measurement of the intensity fluctuations of the emitted light demonstrates that the final states are strongly correlated.

DOI
10.1103/physrevlett.98.106401

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We demonstrate a novel kind of polariton four wave mixing oscillation. Two pump polaritons scatter towards final states that emit two beams of equal intensity, separated both spatially and in polarization with respect to the pumps. The measurement of the intensity fluctuations of the emitted light demonstrates that the final states are strongly correlated.
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.
The quantum correlations between the beams generated by polariton pair scattering in a semiconductor microcavity above the parametric oscillation threshold are computed analytically. The influence of various parameters, including the cavity-exciton detuning, the intensity mismatch between the signal and idler beams, and the amount of spurious noise, is analyzed. We show that very strong quantum correlations between the signal and idler polaritons can be achieved. However, the quantum effects in the outgoing light fields are strongly reduced due to the large mismatch in the coupling of the signal and idler polaritons to the external photons.
We report squeezed polariton generation using parametric polariton four-wave mixing in semiconductor microcavities in thestrong coupling regime. The geometry of the experiment corresponds to degenerate four-wave mixing, which gives rise to abistability threshold. Spatial effects in the nonlinear regime are evidenced, and spatial filtering is required in orderto optimize the measured squeezing. By measuring the noise of the outgoing light, we infer a 9 percent squeezing on thepolariton field close to the bistability turning point.
Investigations of quantum effects in semiconductor quantum-well microcavities interacting with laser light in the strong-coupling regime are presented. Modifications of quantum fluctuations of the outgoing light are expected due to the non-linearity originating from coherent exciton–exciton scattering. In the strong-coupling regime, this scattering translates into a four-wave mixing interaction between the mixed exciton–photon states, the polaritons. Squeezing and giant amplification of the polariton field and of the outgoing light field fluctuations are predicted. However, polariton–phonon scattering is shown to yield excess noise in the output field, which may destroy the non-classical effects. Experiments demonstrate evidence for giant amplification due to coherent four-wave mixing of polaritons. Noise reduction below the thermal noise level was also observed.
Nonlinear optical effects such as four-wave mixing and generation of squeezed light are ubiquitous in optical devices and light sources. For new devices operating at low optical power, the resonant nonlinearity arising from the two-photon sensitive bound biexciton in a semiconductor microcavity is an interesting prospective platform. Due to the particularly strong Coulomb interaction in atomically thin semiconductors, these materials have strongly bound biexcitons and operate in the visible frequency range of the electromagnetic spectrum. To remove the strong pump laser from the generated light in optical devices or to simultaneously excite nondegenerate polaritons, a bichromatic-pump configuration with two spectrally separated pump lasers is desirable. In this paper, we theoretically investigate spontaneous four-wave mixing and quadrature-squeezing in a bichromatically pumped atomically thin semiconductor microcavity. We explore two different configurations that support degenerate and nondegenerate scattering from polaritons into bound biexcitons, respectively. We find that these configurations lead to the generation of strongly single- and two-mode quadrature-squeezed light.
We investigate experimentally one of the main features of a quantum fluid constituted by exciton polaritons in a semiconductor microcavity, that is, quantum degeneracy of a macroscopic fraction of the particles. We show that resonant pumping allows us to create a macroscopic population of polaritons in one quantum state. Furthermore, we demonstrate that parametric polariton scattering results in the transfer of a macroscopic population of polariton from one single quantum state into another one. Finally, we briefly outline a simple method which provides direct evidence of the first-order spatial coherence of the transferred population.