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arXiv:1512.05930

Complementarity in single photon interference - the role of mode functions and vacuum fields

R. W. Menzel, Dirk Puhlmann, Axel Heuer

Published Dec 18, 2015• 0 citations
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Abstract

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. In earlier experiments the role of the vacuum fields could be demonstrated in induced coherence experiments as the source of complementarity \cite{Heu14}. Here the spatial coherence properties of these vacuum fields are measured and as the physical reason for complementarity in single photon quantum optics demonstrated.

DOI
10.48550/arxiv.1512.05930

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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. In earlier experiments the role of the vacuum fields could be demonstrated in induced coherence experiments as the source of complementarity \cite{Heu14}. Here the spatial coherence properties of these vacuum fields are measured and as the physical reason for complementarity in single photon quantum optics demonstrated.
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.
It is well established that spontaneous parametric down-conversion with induced coherence across two coupled interferometers results in high-visibility single-photon interference. We describe experiments in which additional photon channels are introduced such that "which-path" information is made possible and the fringe visibility in single-photon interference is reduced in accordance with basic notions of complementarity. However, these additional pathways result in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these observations and attributes them directly to the vacuum fields at the different crystals.
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.
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.
The visibilities of second-order (one-photon) and fourth-order (two-photon) interference have been observed in a Young's double-slit experiment using light generated by spontaneous parametric down-conversion and a photon-counting intensified charge-coupled device camera. Coherence and entanglement underlie one- and two-photon interference, respectively. As the effective source size is increased, coherence is diminished while entanglement is enhanced, so that the visibility of one-photon interference decreases while that of two-photon interference increases. This experiment demonstrates the complementarity between one- and two-photon interference (coherence and entanglement) in the spatial domain.