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arXiv:0709.0847 · Physical Review A

Experimental position-time entanglement with degenerate single photons

Anthony J. Bennett, David Gevaux, Zhiliang L. Yuan, Andrew J. Shields, P. Atkinson, D. A. Ritchie

Published Feb 5, 2008• 9 citations
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Abstract

We report an experiment in which two-photon interference occurs between degenerate single photons that never meet. The two photons travel in opposite directions through our fiber-optic interferometer and interference occurs when the photons reach two different, spatially separated, two-by-two couplers at the same time. We show that this experiment is analogous to the conventional Franson-type entanglement experiment where the photons are entangled in position and time. We measure wave-function overlaps for the two photons as high as $94\ifmmode\pm\else\textpm\fi{}3%$.

DOI
10.1103/physreva.77.023803

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We report an experiment in which two-photon interference occurs between degenerate single photons that never meet. The two photons travel in opposite directions through our fiber-optic interferometer and interference occurs when the photons reach two different, spatially separated, two-by-two couplers at the same time. We show that this experiment is analogous to the conventional Franson-type entanglement experiment where the photons are entangled in position and time. We measure wave-function overlaps for the two photons as high as 94\ifmmode±\else\textpm\fi394\ifmmode\pm\else\textpm\fi{}3%94\ifmmode±\else\textpm\fi3.
We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no frequency entanglement. When unentangled polarization-correlated photons are used as an input state, the polarization entanglement is successfully recovered through the interferometer via delayed compensation.
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.
In a Franson interferometer two-photon interference fringes occur despite the photons never encountering each other [1]. This phenomenon is a fundamental demonstration of the nonlocal nature of quantum mechanics. It serves also as a direct proof of frequency-time-entanglement. Furthermore, it can benefit not only from local, but also nonlocal dispersion cancellation techniques [2], which is a very useful property when working with spectrally broad photon pairs. More specifically, one has to distinguish between dispersion occuring before the individual Mach-Zehnder interferometers (MZIs), which constitute the Franson interferometer, and within them. Analysis of influences up to second order has shown that no loss of contrast can be expected from dispersion before the Franson interferometer. Differential second-order dispersion inside the interferometer, however, can cause a reduction of contrast in the interferogram [3].
Many quantum advantages in metrology and communication arise from interferometric phenomena. Such phenomena can occur on ultrafast timescales, particularly when energy-time entangled photons are employed. These have been relatively unexplored as their observation necessitates time resolution much shorter than conventional photon counters. Integrating nonlinear optical gating with conventional photon counters can overcome this limitation and enable subpicosecond time resolution. Here, using this technique and a Franson interferometer, we demonstrate high-visibility quantum interference with two entangled photons, where the one- and two-photon coherence times are both subpicosecond. We directly observe the spectral and temporal interference patterns, measure a visibility in the two-photon coincidence rate of $(85.3\ifmmode\pm\else\textpm\fi{}0.4)%$, and report a Clauser--Horne--Shimony--Holt--Bell parameter of $2.42\ifmmode\pm\else\textpm\fi{}0.02$, violating the local-hidden variable bound by 21 standard deviations. The demonstration of energy-time entanglement with ultrafast interferometry provides opportunities for examining and exploiting entanglement in previously inaccessible regimes.