TY - JOUR A1 - Menzel, Ralf A1 - Heuer, Axel A1 - Puhlmann, Dirk A1 - Dechoum, K. A1 - Hillery, M. A1 - Spaehn, M. J. A. A1 - Schleich, W. P. T1 - A two-photon double-slit experiment JF - Journal of modern optics N2 - 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. KW - complementarity KW - wave-particle dualism KW - Young's double-slit experiment KW - spontaneous parametric down conversion KW - TEM01 mode Y1 - 2013 U6 - https://doi.org/10.1080/09500340.2012.746400 SN - 0950-0340 VL - 60 IS - 1 SP - 86 EP - 94 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Schwarze, Thomas A1 - Garz, Andreas A1 - Teuchner, Klaus A1 - Menzel, Ralf A1 - Holdt, Hans-Jürgen T1 - Two-photon probes for metal ions based on phenylaza[18]crown-6 ethers and 1,2,3-triazoles as pi-linkers JF - ChemPhysChem : a European journal of chemical physics and physical chemistry KW - absorption KW - cations KW - click chemistry KW - dyes/pigments KW - fluorescence Y1 - 2014 U6 - https://doi.org/10.1002/cphc.201402232 SN - 1439-4235 SN - 1439-7641 VL - 15 IS - 12 SP - 2436 EP - 2439 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Heuer, Axel A1 - Raabe, S. A1 - Menzel, Ralf T1 - Phase memory across two single-photon interferometers including wavelength conversion JF - Physical review : A, Atomic, molecular, and optical physics N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1103/PhysRevA.90.045803 SN - 1050-2947 SN - 1094-1622 VL - 90 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Zink, Christof A1 - Werner, Nils A1 - Jechow, Andreas A1 - Heuer, Axel A1 - Menzel, Ralf T1 - Multi-wavelength operation of a single broad area diode laser by spectral beam combining JF - IEEE photonics technology letters N2 - Stabilized multi-wavelength emission from a single emitter broad area diode laser (BAL) is realized by utilizing an external cavity with a spectral beam combining architecture. Self-organized emitters that are equidistantly spaced across the slow axis are enforced by the spatially distributed wavelength selectivity of the external cavity. This resulted in an array like near-field emission although the BAL is physically a single emitter without any epitaxial sub-structuring and only one electrical contact. Each of the self-organized emitters is operated at a different wavelength and the emission is multiplexed into one spatial mode with near-diffraction limited beam quality. With this setup, multi-line emission of 31 individual spectral lines centered around and a total spectral width of 3.6 nm is realized with a 1000 mu m wide BAL just above threshold. To the best of our knowledge, this is the first demonstration of such a self-organization of emitters by optical feedback utilizing a spectral beam combining architecture. KW - Laser resonators KW - semiconductor lasers KW - optical feedback Y1 - 2014 U6 - https://doi.org/10.1109/LPT.2013.2291963 SN - 1041-1135 SN - 1941-0174 VL - 26 IS - 3 SP - 253 EP - 256 PB - Inst. of Electr. and Electronics Engineers CY - Piscataway ER - TY - JOUR A1 - Zink, Christof A1 - Niebuhr, Mario A1 - Jechow, Andreas A1 - Heuer, Axel A1 - Menzel, Ralf T1 - Broad area diode laser with on-chip transverse Bragg grating stabilized in an off-axis external cavity JF - Optics express : the international electronic journal of optics N2 - The emission characteristics of a novel, specially designed broad area diode laser (BAL) with on-chip transversal Bragg resonance (TBR) grating in lateral direction were investigated in an off-axis external cavity setup. The internal TBR grating defines a low loss transversal mode at a specific angle of incidence and a certain wavelength. By providing feedback at this specific angle with an external mirror, it is possible to select this low loss transverse mode and stabilize the BAL. Near diffraction limited emission with an almost single lobed far field pattern could be realized, in contrast to the double lobed far field pattern of similar setups using standard BALs or phase-locked diode laser arrays. Furthermore, we could achieve a narrow bandwidth emission with a simplified setup without external frequency selective elements. (C) 2014 Optical Society of America Y1 - 2014 U6 - https://doi.org/10.1364/OE.22.014108 SN - 1094-4087 VL - 22 IS - 12 SP - 14108 EP - 14113 PB - Optical Society of America CY - Washington ER - TY - JOUR A1 - Niebuhr, Mario A1 - Zink, Christof A1 - Jechow, Andreas A1 - Heuer, Axel A1 - Glebov, Leonid B. A1 - Menzel, Ralf T1 - Mode stabilization of a laterally structured broad area diode laser using an external volume Bragg grating JF - Optics express : the international electronic journal of optics N2 - 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 Y1 - 2015 U6 - https://doi.org/10.1364/OE.23.012394 SN - 1094-4087 VL - 23 IS - 9 SP - 12394 EP - 12400 PB - Optical Society of America CY - Washington ER - TY - JOUR A1 - Heuer, Axel A1 - Menzel, Ralf A1 - Milonni, P. W. T1 - Complementarity in biphoton generation with stimulated or induced coherence JF - Physical review : A, Atomic, molecular, and optical physics N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevA.92.033834 SN - 1050-2947 SN - 1094-1622 VL - 92 IS - 3 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Elsner, Robert A1 - Puhlmann, Dirk A1 - Pieplow, Gregor A1 - Heuer, Axel A1 - Menzel, Ralf T1 - Transverse distinguishability of entangled photons with arbitrarily shaped spatial near- and far-field distributions JF - Journal of the Optical Society of America : B, Optical physics N2 - 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 Y1 - 2015 U6 - https://doi.org/10.1364/JOSAB.32.001910 SN - 0740-3224 SN - 1520-8540 VL - 32 IS - 9 SP - 1910 EP - 1919 PB - Optical Society of America CY - Washington ER - TY - GEN A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light BT - the gravitational field of a laser pulse N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 222 KW - electromagnetic radiation KW - general relativity KW - gravity KW - laser pulses KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-90553 ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light BT - the gravitational field of a laser pulse JF - New journal of physics : the open-access journal for physics N2 - 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. KW - gravity KW - general relativity KW - laser pulses KW - electromagnetic radiation KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/2/023009 SN - 1367-2630 VL - 18 SP - 1 EP - 16 PB - IOP Science CY - London ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light-the gravitational field of a laser pulse JF - NEW JOURNAL OF PHYSICS N2 - 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. KW - gravity KW - general relativity KW - laser pulses KW - electromagnetic radiation KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/2/023009 SN - 1367-2630 VL - 18 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - The effect of entanglement in gravitational photon-photon scattering JF - epl : a letters journal exploring the frontiers of physics N2 - 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 Y1 - 2016 U6 - https://doi.org/10.1209/0295-5075/115/51002 SN - 0295-5075 SN - 1286-4854 VL - 115 SP - S12 EP - S13 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Puhlmann, Dirk A1 - Henkel, Carsten A1 - Heuer, Axel A1 - Pieplow, Gregor A1 - Menzel, Ralf T1 - Characterization of a remote optical element with bi-photons JF - Physica scripta : an international journal for experimental and theoretical physics N2 - 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. KW - quantum optics KW - quantum eraser KW - entanglement KW - bi-photons Y1 - 2016 U6 - https://doi.org/10.1088/0031-8949/91/2/023006 SN - 0031-8949 SN - 1402-4896 VL - 91 SP - 113 EP - 114 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Sandmann, Michael A1 - Garz, Andreas A1 - Menzel, Ralf T1 - Physiological response of two different Chlamydomonas reinhardtii strains to light-dark rhythms JF - Botany N2 - Cells of a cell-wall deficient line (cw15-type) of Chlamydomonas reinhardtii and of the corresponding wild type were grown during repetitive light-dark cycles. In a direct comparison, both lines showed approximately the same relative biomass increase during light phase but the cw-line produced significantly more, and smaller, daughter cells. Throughout the light period the average cellular starch content, the cellular chlorophyll content, the cellular rate of dark respiration, and the cellular rate of photosynthesis of the cw-line was lower. Despite this, several non-cell volume related parameters like the development of starch content per cell volume were clearly different over time between the strains. Additionally, the chlorophyll-based photosynthesis rates were 2-fold higher in the mutant than in the wild-type cells, and the ratio of chlorophyll a to chlorophyll b as well as the light-saturation index were also consistently higher in the mutant cells. Differences in the starch content were also confirmed by single cell analyses using a sensitive SHG-based microscopy approach. In summary, the cw15-type mutant deviates from its genetic background in the entire cell physiology. Both lines should be used in further studies in comparative systems biology with focus on the detailed relation between cell volume increase, photosynthesis, starch metabolism, and daughter cell productivity. KW - cell wall deficient mutant KW - diurnal rhythm KW - nonlinear microscopy KW - photosynthesis KW - single-cell analysis Y1 - 2016 U6 - https://doi.org/10.1139/cjb-2015-0144 SN - 1916-2790 SN - 1916-2804 VL - 94 SP - 53 EP - 64 PB - NRC Research Press CY - Ottawa ER - TY - JOUR A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Effect of polarization entanglement in photon-photon scattering JF - Physical review : A, Atomic, molecular, and optical physics N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevA.95.012101 SN - 2469-9926 SN - 2469-9934 VL - 95 IS - 1 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Raetzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light: The emission of counter-propagating laser pulses from an atom JF - Physical review : D, Particles, fields, gravitation, and cosmology Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevD.95.084008 SN - 2470-0010 SN - 2470-0029 VL - 95 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Menzel, Ralf A1 - Puhlmann, Dirk A1 - Heuer, Axel T1 - Complementarity in single photon interference – the role of the mode function and vacuum fields JF - Journal of the European Optical Society-Rapid N2 - 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. KW - Quantum optics KW - Complementarity KW - Mode function KW - Vacuum fields Y1 - 2017 U6 - https://doi.org/10.1186/s41476-017-0036-x SN - 1990-2573 VL - 13 PB - Springer ER - TY - GEN A1 - Menzel, Ralf A1 - Puhlmann, Dirk A1 - Heuer, Axel T1 - Complementarity in single photon interference – the role of the mode function and vacuum fields N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 333 KW - Complementarity KW - Mode function KW - Quantum optics KW - Vacuum fields Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-395210 ER - TY - GEN A1 - Menzel, Ralf A1 - Heuer, Axel A1 - Milonni, Peter W. T1 - Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1077 KW - complementarity KW - vacuum fields KW - entanglement KW - Hong-Ou-Mandel effect KW - spontaneous parametric down-conversion Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473542 SN - 1866-8372 IS - 1077 ER - TY - JOUR A1 - Menzel, Ralf A1 - Marx, Robert A1 - Puhlmann, Dirk A1 - Heuer, Axel A1 - Schleich, Wolfgang T1 - The photon BT - the role of its mode function in analyzing complementarity JF - Journal of the Optical Society of America : B, Optical physics N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1364/JOSAB.36.001668 SN - 0740-3224 SN - 1520-8540 VL - 36 IS - 6 SP - 1668 EP - 1675 PB - Optical Society of America CY - Washington ER - TY - JOUR A1 - Menzel, Ralf A1 - Heuer, Axel A1 - Milonni, Peter W. T1 - Entanglement, Complementarity, and Vacuum Fields in Spontaneous Parametric Down-Conversion JF - Atoms N2 - 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. KW - complementarity KW - vacuum fields KW - entanglement KW - Hong-Ou-Mandel effect KW - spontaneous parametric down-conversion Y1 - 2019 U6 - https://doi.org/10.3390/atoms7010027 SN - 2218-2004 VL - 7 IS - 1 PB - MDPI CY - Basel ER -