Single-photon generation and simultaneous observation of wave and particle properties

We describe an experiment in that generates single photons on demand and measures properties accounted to both particle and wave-like features of light. The measurement is performed by exploiting data that are sampled simultaneously in a single experimental run. INTRODUCTION The wave-particle duality of matter lies at the heart of quantum mechanics. With respect to light, the wave-like behavior is perceived as being classical and the particle aspect as being nonclassical, while for massive microscopic objects, like neutrons and atoms, the opposite holds. The occurrence of an interference pattern is a manifestation of the wave-nature of matter. In the frame of classical wave optics, standard first-order interference is explained by the superposition of the electric field strengths when two coherent partial beams merge. This superposition can be constructive or destructive and depends sensitively on the phase difference between the partial beams, thus giving rise to a spatial or temporal interference pattern when the latter varies. Already in 1909, soon after the introduction of the concept of the photon, it was observed experimentally that there is no deviation from the classically predicted interference pattern if a double-slit interference experiment is performed with very weak light, even if the intensity is so small that on average only a single photon is present inside the apparatus [1]. Later this observation was accounted for theoretically by quantum mechanics and was confirmed by more precise experiments [2, 3]. There exists an exact correspondence between the interference of the quantum probability amplitudes for each single photon to travel along either path in an interferometer on the one hand and the interference of the classical field strengths in the different paths on the other hand. Therefore, the outcome of any first-order interference experiment can be obtained by describing light as a classical electromagnetic wave, independent of the statistical distribution of the incident photons. Both waveand particle-aspect can be observed in a single experiment when with very small light intensities from a classical source the double-slit interference pattern is gradually built up by registering more and more spots on the screen. A small non-vanishing probability remains that such a spot is not caused by a single photon, but by two photons arriving at the same time, though. According to the principle of complementarity, it is impossible to simultaneously observe interference and to detect which path each photon travelled in the interferometer. In this paper we do not raise the question of complementarity, but report an experiment at the exact single-photon level to detect waveand particle-like properties of light in a single run. For this purpose we use the fact that the nonclassical, or corpuscular, aspect of light can be revealed by observing intensity correlations using a setup that was originally invented by Hanbury Brown and Twiss for determining the diameter of stars [4, 5]. In this scheme, intensity correlations between two partial beams are measured dependent on the path difference or the mutual time delay, respectively. These correlations correspond to delayed coincidences between the clicks of two detectors, each detecting the photons in one of the partial beams. Photon antibunching occurs when the coincidence probability increases with growing delay time. This effect cannot be explained by classical wave theory and is a clear indication for the particlelike nature of light (see e. g. [6]). Kimble et al. were the first to detect photon antibunching, using the light from atomic resonance fluorescence [7]. Later, Grangier et al. [8] performed a series of experiments with single photons from atomic decays. In a first step, they showed the single-photon character of the atomic emission by observing the corresponding antibunched behavior of the intensity correlation function. In a second step, they inserted the photons