@misc{MenzelHeuerMilonni2019,
  author    = {Menzel, Ralf and Heuer, Axel and Milonni, Peter W.},
  title     = {Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1077},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47354},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473542},
  pages     = {16},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2017,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Effect of polarization entanglement in photon-photon scattering},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {95},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2469-9926},
  doi       = {10.1103/PhysRevA.95.012101},
  pages     = {6},
  year      = {2017},
  abstract  = {It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in quantum electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces.},
  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{MenzelHeuerMilonni2019,
  author    = {Menzel, Ralf and Heuer, Axel and Milonni, Peter W.},
  title     = {Entanglement, Complementarity, and Vacuum Fields in Spontaneous Parametric Down-Conversion},
  series = {Atoms},
  volume    = {7},
  journal   = {Atoms},
  number    = {1},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2218-2004},
  doi       = {10.3390/atoms7010027},
  pages     = {14},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{GarzSandmannRadingetal.2012,
  author    = {Garz, Andreas and Sandmann, Michael and Rading, Michael and Ramm, Sascha and Menzel, Ralf and Steup, Martin},
  title     = {Cell-to-cell diversity in a synchronized chlamydomonas culture as revealed by single-cell analyses},
  series = {Biophysical journal},
  volume    = {103},
  journal   = {Biophysical journal},
  number    = {5},
  publisher = {Cell Press},
  address   = {Cambridge},
  issn      = {0006-3495},
  doi       = {10.1016/j.bpj.2012.07.026},
  pages     = {1078 -- 1086},
  year      = {2012},
  abstract  = {In a synchronized photoautotrophic culture of Chlamydomonas reinhardtii, cell size, cell number, and the averaged starch content were determined throughout the light-dark cycle. For single-cell analyses, the relative cellular starch was quantified by measuring the second harmonic generation (SHG). In destained cells, amylopectin essentially represents the only biophotonic structure. As revealed by various validation procedures, SHG signal intensities are a reliable relative measure of the cellular starch content. During photosynthesis-driven starch biosynthesis, synchronized Chlamydomonas cells possess an unexpected cell-to-cell diversity both in size and starch content, but the starch-related heterogeneity largely exceeds that of size. The cellular volume, starch content, and amount of starch/cell volume obey lognormal distributions. Starch degradation was initiated by inhibiting the photosynthetic electron transport in illuminated cells or by darkening. Under both conditions, the averaged rate of starch degradation is almost constant, but it is higher in illuminated than in darkened cells. At the single-cell level, rates of starch degradation largely differ but are unrelated to the initial cellular starch content. A rate equation describing the cellular starch degradation},
  language  = {en}
}
@misc{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90553},
  year      = {2016},
  abstract  = {The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {18},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Science},
  address   = {London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/2/023009},
  pages     = {1 -- 16},
  year      = {2016},
  abstract  = {The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2017,
  author    = {Raetzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light: The emission of counter-propagating laser pulses from an atom},
  series = {Physical review : D, Particles, fields, gravitation, and cosmology},
  volume    = {95},
  journal   = {Physical review : D, Particles, fields, gravitation, and cosmology},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0010},
  doi       = {10.1103/PhysRevD.95.084008},
  pages     = {11},
  year      = {2017},
  language  = {en}
}
@article{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light-the gravitational field of a laser pulse},
  series = {NEW JOURNAL OF PHYSICS},
  volume    = {18},
  journal   = {NEW JOURNAL OF PHYSICS},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/2/023009},
  pages     = {16},
  year      = {2016},
  abstract  = {The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {The effect of entanglement in gravitational photon-photon scattering},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {115},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/115/51002},
  pages     = {S12 -- S13},
  year      = {2016},
  abstract  = {The differential cross-section for gravitational photon-photon scattering calculated in perturbative quantum gravity is shown to depend on the degree of polarization entanglement of the two photons. The interaction between photons in the symmetric Bell state is stronger than between not entangled photons. In contrast, the interaction between photons in the anti-symmetric Bell state is weaker than between not entangled photons. The results are interpreted in terms of quantum interference, and it is shown how they fit into the idea of distance-dependent forces. Copyright (C) EPLA, 2016},
  language  = {en}
}