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arXiv:cond-mat/0504554 · Physical Review B

Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies

Iacopo Carusotto, Cristiano Ciuti

Published Sep 21, 2005• 111 citations
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Abstract

We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.

DOI
10.1103/physrevb.72.125335

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We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.
The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviors is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behavior of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal, and idler frequencies.
The statistic of parametric photon emission in a one-dimensional semiconductor microcavity optical parametric oscillator is reported. We perform photon-counting experiments on signal and idler beams by means of a Hanbury Brown and Twiss setup for studying the second-order coherence. Under pulsed laser excitation at normal incidence, energy-degenerate signal and idler beams are emitted in a mirror-symmetric configuration and share the same excitonic/photonic composition. Moreover the two emissions share the same intensity and the same coherence properties. We show that the bunching visibility [i.e., the value of ${g}^{(2)}(\ensuremath{\tau}=0)$] changes across the parametric threshold and it is associated both to different spectral composition of the emission and to the buildup of coherence at high injection. Nevertheless, different from conventional optical parametric oscillators, a full coherence is never recovered.
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.
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 We report the observation of optical bistability in a semiconductor microcavity pumped at the “magic angle” above the parametric oscillation threshold. Experimental evidence is given in the form of a hysteresis cycle of the nonlinear emission as a function of the pump intensity. A model analogous to those developped for triply resonant Optical Parametric Oscillators (OPO) is in good agreement with the experimental findings. In the second part, we study the potential application of the parametric oscillation regime to quantum optics. The quantum correlations between the emitted “signal” and “idler” beams are computed. 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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We analyze the hyper Raman scattering process in a quantum well grown inside a semiconductor microcavity and present a microscopic calculation of emission spectra as a function of excitation energy, detuning, and angles. The exciton-photon coupling is treated non-perturbatively to include polariton effects and the Coulomb interaction between electrons is treated beyond the mean field approximation. The observation of hyper Raman scattering in semiconductor microcavities would represent an important step for the realization of non-classical optical states based on excitons. We find that the polaritons emitted in this scattering process are strongly correlated. This correlation,can be efficiently transferred to output photons, resulting in emission of two correlated non-classical light beams. As a probe of the quantum correlation we calculate the output spectrum of fluctuations in the intensity difference of the two beams generated in the hyper Raman process.