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arXiv:cond-mat/0411314 · Physical Review Letters

Quantum Complementarity of Microcavity Polaritons

Salvatore Savasta, Omar Di Stefano, Vincenzo Savona, W. Langbein

Published Jun 20, 2005• 127 citations
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Abstract

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.

DOI
10.1103/physrevlett.94.246401

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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 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)
In this contribution, a novel geometry is investigated that eliminates the asymmetry between the signal and idler fields,using a nonlinear process that produces signal and idler polaritons with opposite wave vectors, hence the same photon content and the same linewidth, which allows maximal correlations between the signal and idler beams. It is studied theoretically in the Heisenberg-Langevin formalism and is found that perfect quantum correlations can be achieved for the polariton fields. The experimental observation of such nonlinear process is reported. A correlation of about 0.6 between the beams emitted with opposite planar wave vectors us measured. The measured correlations are classical, meaning that the intensity difference between the signal and idler beam is not squeezed. However, these results are very promising in view of the generation of quantum correlated polariton modes.
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.
We probe the principle of complementarity by performing a double-slit experiment based on entangled photons created by spontaneous parametric down-conversion from a pump mode in a TEM01-mode. Our setup brings out the need for a careful selection of the signal-idler photon pairs for our study of visibility and distinguishability. Indeed, when the signal photons interfering at the double-slit belong to this double-hump mode we obtain almost perfect visibility of the interference fringes and no "which-slit" information is available. However, when we break the symmetry between the two maxima of the mode by detecting the entangled idler photon, the paths through the slits become distinguishable and the visibility vanishes. It is the mode function of the photons selected by the detection system which decides if interference, or "which-slit" information is accessible in the experiment.
We investigate the role of the spatial mode function in a single-photon experiment designed to demonstrate the principle of complementarity. Our approach employs entangled photons created by spontaneous parametric downconversion from a pump mode in a TEM01 mode together with a double slit. Measuring the interference of the signal photons behind the double slit in coincidence with the entangled idler photons at different positions, we select signal photons of different mode functions. When the signal photons belong to the TEM01-like double-hump mode, we obtain almost perfect visibility of the interference fringes, and no “which slit” information is available in the idler photon detected before the slits. This result is remarkable because the entangled signal and idler photon pairs are created each time in only one of the two intensity humps. However, when we break the symmetry between the two maxima of the signal photon mode structure, the paths through the slits for these additional photons become distinguishable and the visibility vanishes. It is the mode function of the photons selected by the detection system that decides if interference or “which slit” information is accessible in the experiment.