The precise knowledge of one of two complementary experimental outcomes prevents us from obtaining complete information about the other one. This formulation of Niels Bohr's principle of complementarity when applied to the paradigm of wave-particle dualism-that is, to Young's double-slit experiment-implies that the information about the slit through which a quantum particle has passed erases interference. In the present paper we report a double-slit experiment using two photons created by spontaneous parametric down-conversion where we observe interference in the signal photon despite the fact that we have located it in one of the slits due to its entanglement with the idler photon. This surprising aspect of complementarity comes to light by our special choice of the TEM 01 pump mode. According to quantum field theory the signal photon is then in a coherent superposition of two distinct wave vectors giving rise to interference fringes analogous to two mechanical slits.T he double-slit experiment has served as a source of inspiration for more than two centuries. Indeed, Thomas Young (1) has used it to argue in favor of the wave theory of light rather than the corpuscular one of Isaac Newton (2). In the early days of quantum mechanics it was central to the dialogue (3) between Albert Einstein and Bohr on epistemological problems in atomic physics. Moreover, it was the starting point of the path integral formulation (4) of quantum mechanics by Richard Feynman.Today the question of "which-slit" versus "interference" in the double-slit configuration (5) is as fascinating and relevant (6) as it was in the early days of quantum mechanics. In particular, the understanding of the physical origin (7) of the disappearance of the fringes in the presence of which-slit information has come a long way. Werner Heisenberg in the context of the uncertainty relation (8), Bohr in his discussion with Einstein (3) on the recoiling slit, and others (9) have argued in favor of an uncontrollable momentum transfer (7). However, the Gedanken experiments of the quantum eraser (10) and the micromaser "welcher Weg" detector (11) have identified entanglement and the availability of information as the main culprit. Indeed, the seminal atom interferometer experiment (12) as well as the realization (13) of the quantum eraser have made a clear decision against momentum transfer in favor of entanglement. As a result, today the principle of complementarity (14) is widely accepted (15) in the form (16): "If information on one complementary variable is in principle available even if we choose not to 'know' it… we will lose the possibility of knowing the precise value of the other complementary variable."In the present paper we report the results of a double-slit experiment that brings out an additional layer of this principle. We employ the entanglement between the signal and the idler photon created in spontaneous parametric down-conversion (SPDC) (17) to obtain by a coincidence measurement of the two photons which-slit information about the signal ...

We employ a photon pair created by spontaneous parametric down conversion (SPDC) where the pump laser is in the TEM 01 mode to perform a Young's double-slit experiment. The signal photon illuminates the two slits and displays interference fringes in the far-field while the idler photon measured in the near-field in coincidence with the signal photon provides us with 'which-slit' information. We explain the results of these experiments with the help of an analytical expression for the second-order correlation function derived from an elementary model of SPDC. Our experiment emphasizes the crucial role of the mode function in the quantum theory of radiation.

Space momentum entangled photon pairs are generated from type II parametric down conversion in a beta barium borate crystal. The correlations in the positions of photons in the near field and far field planes with regard to the generating crystal are observed in both transverse dimensions using scanning fiber probes. The space-momentum correlation is characterized using a covariance description for a bivariate normal distribution and tested for non-separability with Mancini's criterion. The role of higher order spatial modes to observe spatial entanglement between the two photons is discussed.

Entangled photons generated by spontaneous parametric down conversion inside a nonlinear crystal exhibit a complex spatial photon count distribution. A quantitative description of this distribution helps with the interpretation of experiments that depend on this structure. We developed a theoretical model and an accompanying numerical calculation that includes the effects of phase matching and the crystal properties to describe a wide range of spatial effects in two-photon experiments. The numerical calculation was tested against selected analytical approximations. We furthermore performed a double-slit experiment where we measured the visibility V and the distinguishability D and obtained D 2 + V 2 = 1.43. The numerical model accurately predicts these experimental results.

We present a simple setup that exploits the interference of entangled photon pairs. 'Signal' photons are sent through a Mach-Zehnder-like interferometer, while 'idlers' are detected in a variable polarization state. Two-photon interference (in coincidence detection) is observed with very high contrast and for significant time delays between signal and idler detection events. This is explained by quantum erasure of the polarization tag and a delayed choice protocol involving a non-local virtual polarizer. The phase of the two-photon fringes is scanned by varying the path length in the signal beam or by rotating a birefringent crystal in the idler beam. We exploit this to characterize one beam splitter of the signal photon interferometer (reflection and transmission amplitudes including losses), using only information about coincidences and control parameters in the idler path. This is possible because our bi-photon state saturates the Greenberger-Yelin-Englert inequality between contrast and predictability.