@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{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{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} } @misc{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}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-395210}, 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{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{NiebuhrZinkJechowetal.2015, author = {Niebuhr, Mario and Zink, Christof and Jechow, Andreas and Heuer, Axel and Glebov, Leonid B. and Menzel, Ralf}, title = {Mode stabilization of a laterally structured broad area diode laser using an external volume Bragg grating}, series = {Optics express : the international electronic journal of optics}, volume = {23}, journal = {Optics express : the international electronic journal of optics}, number = {9}, publisher = {Optical Society of America}, address = {Washington}, issn = {1094-4087}, doi = {10.1364/OE.23.012394}, pages = {12394 -- 12400}, year = {2015}, abstract = {An external volume Bragg grating (VBG) is used for transverse and longitudinal mode stabilization of a broad area diode laser (BAL) with an on-chip transverse Bragg resonance (TBR) grating. The internal TBR grating defines a transverse low-loss mode at a specific propagation angle inside the BAL. Selection of the TBR mode was realized via the angular geometry of an external resonator assembly consisting of the TBR BAL and a feedback element. A feedback mirror provides near diffraction limited and spectral narrow output in the TBR mode albeit requiring an intricate alignment procedure. If feedback is provided via a VBG, adjustment proves to be far less critical and higher output powers were achieved. Moreover, additional modulation in the far field distribution became discernible allowing for a better study of the TBR concept. (C) 2015 Optical Society of America}, language = {en} } @article{HeuerMenzelMilonni2015, author = {Heuer, Axel and Menzel, Ralf and Milonni, P. W.}, title = {Complementarity in biphoton generation with stimulated or induced coherence}, series = {Physical review : A, Atomic, molecular, and optical physics}, volume = {92}, journal = {Physical review : A, Atomic, molecular, and optical physics}, number = {3}, publisher = {American Physical Society}, address = {College Park}, issn = {1050-2947}, doi = {10.1103/PhysRevA.92.033834}, pages = {8}, year = {2015}, abstract = {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.}, 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{HeuerRaabeMenzel2014, author = {Heuer, Axel and Raabe, S. and Menzel, Ralf}, title = {Phase memory across two single-photon interferometers including wavelength conversion}, series = {Physical review : A, Atomic, molecular, and optical physics}, volume = {90}, journal = {Physical review : A, Atomic, molecular, and optical physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1050-2947}, doi = {10.1103/PhysRevA.90.045803}, pages = {4}, year = {2014}, abstract = {Spontaneous parametric down-conversion (SPDC) in a nonlinear crystal generates two single photons (signal and idler) with random phases. Thus, no first-order interference between them occurs. However, coherence can be induced in a cascaded setup of two crystals if, e.g., the idler modes of both crystals are aligned to be indistinguishable. Due to the effect of phase memory it is found that the first-order interference of the signal beams can be controlled by the phase delay between the pump beams. Even for pump photon delays much larger than the coherence length of the SPDC photons, the visibility is above 90\%. The high visibilities reported here prove an almost perfect phase memory effect across the two interferometers for the pump and the signal photon modes.}, language = {en} }