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Journal of the Optical Society of America B

The photon: the role of its mode function in analyzing complementarity

Ralf Menzel, Robert Marx, Dirk Puhlmann, Axel Heuer, Wolfgang P. Schleich

Published May 28, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1364/josab.36.001668

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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.
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 employ a photon pair created by spontaneous parametric down conversion (SPDC) where the pump laser is in the TEM01 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.
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.
Particle and wave like properties of photons can impressively be demonstrated in Young’s double slit experiment. Usually, measurements behind the slit provide information either about the path of the single photons or interference can be observed. Today the question of “which-slit” versus “interference” in the double-slit configuration is as relevant as it was in the early days of quantum mechanics. To gain deeper insight we set up an experiment using a pair of photons generated by SPDC pumped with a higher order mode (TEM 01 ). One of the SPDC photons, the signal photon, was used to illuminate the double slit and measure the single photon interference behind it. The other photon, the idler photon, was used in a reference measurement at the position of the slit using a polarizing beam splitter. First, the signal photons were obtained at the position of the slit as a function of the position of the entangled idler photons in a coincidence measurement. From this coincidence measurement the “which-slit” information is available. In a second coincidence measurement the far field interference fringes were obtained for signal photons passing through one of the slits, only, selected by the position of the reference detector measuring the entangled idler photons. The newest results will be presented and discussed. This may provide new insights in the wave-particle dualism and thus inspire the discussion about the nature of photons.
We report a two-photon double-slit interference experiment. Two correlated photons, generated by spontaneous parametric downconversion and traveling in different directions, are made to pass through a double slit in such a way that the path of one photon can be identified with that of the other photon. No single-photon interference pattern is observed even if the path is not actually identified, but a spatial interference pattern appears in the joint detection counting rates of the photon pairs. It can easily be shown that these nonlocal phenomena cannot be exhibited by any kind of classical field.
In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015). Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode function in quantum optics regarding the complementarity principle. Here the spatial coherence properties of these vacuum fields are demonstrated as the physical reason for complementarity in these single photon quantum optical experiments. These results are directly connected to the mode picture in classical optics. The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics.