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physica status solidi (b)

Quantum optics with interacting polaritons

Salvatore Savasta, Omar Di Stefano

Published Jul 27, 2006• 4 citations
Publisher

Abstract

Abstract Recent theoretical and experimental investigations evidencing quantum optical effects in semiconductor microcavities are reported. In particular the results of an experiment that probes polariton quantum correlations by exploiting quantum complementarity are described. In this experiment, it has been shown that polaritons in two distinct idler modes interfere if and only if they share the same signal mode so that which‐way information cannot be gathered, according to Bohr's quantum complementarity principle. The experimental results prove the existence of polariton pair correlations that store the which‐way information. This interpretation is confirmed by a theoretical analysis of the measured interference visibility in terms of quantum Langevin equations. The devised experimental scheme employs two frequency‐degenerate mutually‐coherent pump modes. It is shown that this kind of two‐pump parametric schemes can be exploited to realize a number of interesting tasks as the emission of polarization‐entangled cavity‐polariton states and the coherent control and trapping of parametric amplification in SMCs. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200668046

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Abstract Recent theoretical and experimental investigations evidencing quantum optical effects in semiconductor microcavities are reported. In particular the results of an experiment that probes polariton quantum correlations by exploiting quantum complementarity are described. In this experiment, it has been shown that polaritons in two distinct idler modes interfere if and only if they share the same signal mode so that which‐way information cannot be gathered, according to Bohr's quantum complementarity principle. The experimental results prove the existence of polariton pair correlations that store the which‐way information. This interpretation is confirmed by a theoretical analysis of the measured interference visibility in terms of quantum Langevin equations. The devised experimental scheme employs two frequency‐degenerate mutually‐coherent pump modes. It is shown that this kind of two‐pump parametric schemes can be exploited to realize a number of interesting tasks as the emission of polarization‐entangled cavity‐polariton states and the coherent control and trapping of parametric amplification in SMCs. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We present an experiment that probes polariton quantum correlations by exploiting quantum complementarity. Specifically, we find that polaritons in two distinct idler modes interfere if and only if they share the same signal mode so that ``which-way'' information cannot be gathered. The experimental results prove the existence of polariton pair correlations that store the which-way information. This interpretation is confirmed by a theoretical analysis of the measured interference visibility in terms of quantum Langevin equations.
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 discuss the quantum statistical properties of exciton-polaritons in semiconductor microcavities. The nonlinear dynamics is treated within a model of interacting bosons for the signal, pump and idler modes. We focus on the regime of parametric amplification below threshold. We present the time evolution of the signal and idler modes towards their stationary solutions and evaluate the amount of squeezing of the radiation emitted out of the microcavity in a configuration, which is relevant for experiments. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract After resuming the basic facts about Bose–Einstein condensation of weakly interacting systems, we review the main experimental and theoretical works aimed at the realization of this intriguing phenomenon in the system of microcavity polaritons. All the experimental results until present suggest that Bose–Einstein condensation is still eluding the experimentalists' efforts. On the theoretical side, only recently polaritons have been described within a quantum field theory of an interacting Bose gas, suggesting that polariton condensation might occur at least as a consequence of polariton parametric scattering under resonant excitation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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 present an extension of the previous descriptions based on the Dynamics Controlled Truncation Scheme of light‐matter interaction beyond mean‐field, including the microscopic description of the exciton‐photon interaction. This enables the microscopic analysis of the influence of decoherence and noise on the polariton quantum correlations originating from nonlinear optical processes. We expand the operators involved in the dynamics in terms of exact eigenstates of the electron system, the photon and phonon operators and treat phonon‐assisted transitions within the Markov approximation. In particular, we present quantum Heisenberg‐Langevin equations describing light‐induced excitations in semiconductor systems interacting with the phonon bath. This theoretical framework is applied to study the influence of dephasing and noise due to photoluminescence on polariton quantum correlations generated by parametric emission in microcavities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)