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Hyper Raman Scattering in Microcavity Quantum Wells: A Quantum Optical Process in the Strong Coupling Regime

Salvatore Savasta, R. Girlanda, Giovanna Martino

Published Nov 1, 1997• 22 citations
Publisher

Abstract

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.

DOI
10.1002/1521-396x(199711)164:1<85::aid-pssa85>3.0.co;2-#

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arXiv:0706.2241•Physical Review B•May 5, 2008•23 citations
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.
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.
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.
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.
Nonlinear optical phenomena in both semiconductor microcavities and sodium vapor are investigated. Systems displaying atomic and excitonic coupling are studied in detail in order to unravel underlying physical principles. Possible applications for these systems are evaluated where appropriate. Normal-mode coupling (NMC) in a semiconductor microcavity is achieved when a narrow-linewidth quantum well exciton resonance is coincident with the cavity mode of a high-finesse microcavity. This interaction leads to a double-peaked spectrum in either transmission, reflection, or photoluminescence (PL). The high-quality microcavities studied here at liquid-Helium temperatures reveal intensity dependent behavior that has not previously been observed. Nonlinear saturation of the exciton leads to a spectral broadening of the excitonic absorption without a significant loss in oscillator strength. This results in a reduction of the two transmission peaks with almost no change in the splitting between the peaks. Such behavior is easily explained using phenomenological nonlinear dispersion theory. In this nonlinear regime, the luminescence from the microcavity shows a gradual transition from the nonperturbative regime of NMC to lasing with increasing excitation. The observed behavior is explained by density-dependent changes in both the transmission of the microcavity and the bare-exciton emission, rather than a boson-condensation of excitons which has been previously proposed. An intermediate-finesse microcavity also modifies the emission distribution from a bulk-semiconductor at room temperature. Angularly resolved emission spectra and quantum efficiency measurements show the PL is strongly dependent on the reflectivity of the microcavity. Unfortunately, the enhancement in the decay rate of excitons due to high-reflectivity mirrors seen previously by our group does not result in an increased quantum efficiency. High-gain optical-wavefront amplification in atomic sodium vapor is demonstrated via both the three-photon effect and stimulated Raman scattering (SRS). In both cases, single-pass weak-field gain of nearly 400 is achieved with only 800 mW of pump power near 589 nm. In the case of SRS, phase preservation of the amplified wavefront, which is necessary in adaptive imaging applications, is also demonstrated.
We present a systematic theory of Coulomb-induced correlation effects in the nonlinear optical processes within the strong-coupling regime. In this paper, we shall set a dynamics controlled truncation scheme microscopic treatment of nonlinear parametric processes in semiconductor microcavities including the electromagnetic field quantization. It represents the starting point for the microscopic approach to quantum optics experiments in the strong-coupling regime without any assumption on the quantum statistics of electronic excitations (excitons) involved. We exploit a previous technique, which was used in the semiclassical context, which, once applied to four-wave mixing in quantum wells, allowed us to understand a wide range of observed phenomena. We end up with dynamical equations for exciton and photon operators, which extend the usual semiclassical description of Coulomb interaction effects in terms of a mean-field term plus a genuine noninstantaneous four-particle correlation to quantum optical effects.