@article{MenzelHeuerPuhlmannetal.2013,
  author    = {Menzel, Ralf and Heuer, Axel and Puhlmann, Dirk and Dechoum, K. and Hillery, M. and Spaehn, M. J. A. and Schleich, W. P.},
  title     = {A two-photon double-slit experiment},
  series = {Journal of modern optics},
  volume    = {60},
  journal   = {Journal of modern optics},
  number    = {1},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0950-0340},
  doi       = {10.1080/09500340.2012.746400},
  pages     = {86 -- 94},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@article{PuhlmannHenkelHeueretal.2016,
  author    = {Puhlmann, Dirk and Henkel, Carsten and Heuer, Axel and Pieplow, Gregor and Menzel, Ralf},
  title     = {Characterization of a remote optical element with bi-photons},
  series = {Physica scripta : an international journal for experimental and theoretical physics},
  volume    = {91},
  journal   = {Physica scripta : an international journal for experimental and theoretical physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0031-8949},
  doi       = {10.1088/0031-8949/91/2/023006},
  pages     = {113 -- 114},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{MenzelPuhlmannHeuer2017,
  author    = {Menzel, Ralf and Puhlmann, Dirk and Heuer, Axel},
  title     = {Complementarity in single photon interference - the role of the mode function and vacuum fields},
  series = {Journal of the European Optical Society-Rapid},
  volume    = {13},
  journal   = {Journal of the European Optical Society-Rapid},
  publisher = {Springer},
  issn      = {1990-2573},
  doi       = {10.1186/s41476-017-0036-x},
  pages     = {7},
  year      = {2017},
  abstract  = {Background 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). Methods 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. Results 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. Conclusion The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics.},
  language  = {en}
}
@article{OstermeyerPuhlmannKorn2009,
  author    = {Ostermeyer, Martin and Puhlmann, Dirk and Korn, Dietmar},
  title     = {Quantum diffraction of biphotons at a blazed grating},
  issn      = {0740-3224},
  year      = {2009},
  abstract  = {Correlations between photons are interesting for a number of applications and concepts in metrology, in particular for resolution improvements in different methods of quantum imaging. We demonstrate the application of a blazed grating for the characterization of the degree of spatial correlation of biphotons. The biphotons are generated by type II parametric downconversion. Compared to an ordinary transmission grating, a blazed grating shows a high diffraction efficiency only for a single order of diffraction. Thus, higher intensities in the Fraunhofer far field behind the grating, and easier photon counting, can be achieved. The distribution of the two-photon rate in the Fraunhofer far field of the blazed grating can show one additional order of diffraction with a visibility related to the degree of correlation of the biphotons. The number of spatial modes that are populated by the biphoton beam can be directly altered in our experiments. The relation of the spatial mode order of the photon propagation to the observable degree of spatial correlation of the biphotons is investigated and related to the Schmidt number of spatially entangled modes.},
  language  = {en}
}
@article{MenzelMarxPuhlmannetal.2019,
  author    = {Menzel, Ralf and Marx, Robert and Puhlmann, Dirk and Heuer, Axel and Schleich, Wolfgang},
  title     = {The photon},
  series = {Journal of the Optical Society of America : B, Optical physics},
  volume    = {36},
  journal   = {Journal of the Optical Society of America : B, Optical physics},
  number    = {6},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {0740-3224},
  doi       = {10.1364/JOSAB.36.001668},
  pages     = {1668 -- 1675},
  year      = {2019},
  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.},
  language  = {en}
}
@article{ElsnerPuhlmannPieplowetal.2015,
  author    = {Elsner, Robert and Puhlmann, Dirk and Pieplow, Gregor and Heuer, Axel and Menzel, Ralf},
  title     = {Transverse distinguishability of entangled photons with arbitrarily shaped spatial near- and far-field distributions},
  series = {Journal of the Optical Society of America : B, Optical physics},
  volume    = {32},
  journal   = {Journal of the Optical Society of America : B, Optical physics},
  number    = {9},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {0740-3224},
  doi       = {10.1364/JOSAB.32.001910},
  pages     = {1910 -- 1919},
  year      = {2015},
  abstract  = {Entangled photons generated by spontaneous parametric downconversion are ubiquitous in quantum optics. In general, they exhibit a complex spatial photon count distribution. This spatial structure is responsible for seemingly surprising results concerning, e.g., complementarity such as the apparent simultaneous observation of interference fringes V and which-way information D at a double slit, as recently reported by Menzel et al. [Proc. Natl. Acad. Sci. USA 109, 9314 (2012)]. We implement a complete quantitative model of the SPDC interaction that fully incorporates the effects of crystal anisotropies, phase matching, and the pump beam structure and allows for arbitrary manipulations of the SPDC light in the near and far fields. This enables us to establish an upper bound D-2 + V-2 <= 1.47 for the experimental parameters reported by Menzel et al. We report new experimental results that agree excellently with these theoretical predictions. The new model enables a detailed quantitative analysis of this surprising result and the fair sampling interpretation of biphotons passing a double slit. (C) 2015 Optical Society of America},
  language  = {en}
}
@article{OstermeyerKornPuhlmannetal.2009,
  author    = {Ostermeyer, Martin and Korn, Dietmar and Puhlmann, Dirk and Henkel, Carsten and Eisert, Jens},
  title     = {Two-dimensional characterization of spatially entangled photon pairs},
  issn      = {0950-0340},
  doi       = {10.1080/09500340903359962},
  year      = {2009},
  abstract  = {We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down- conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space-momentum entanglement. The role of higher- order spatial modes for observing spatial entanglement between the two photons is discussed.},
  language  = {en}
}
@article{MenzelPuhlmannHeueretal.2012,
  author    = {Menzel, Ralf and Puhlmann, Dirk and Heuer, Axel and Schleich, Wolfgang P.},
  title     = {Wave-particle dualism and complementarity unraveled by a different mode},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {109},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {24},
  publisher = {National Acad. of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1201271109},
  pages     = {9314 -- 9319},
  year      = {2012},
  abstract  = {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 TEM01 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.},
  language  = {en}
}