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arXiv:1601.07817 · Physical Review A

Clearer visibility of the Hong-Ou-Mandel effect with a correlation function based on rates rather than intensities

Krzysztof Rosołek, Kamil Kostrzewa, Arijit Dutta, Wiesław Laskowski, Marcin Wieśniak, Marek Żukowski

Published Apr 17, 2017• 3 citations
arXivHTMLPDF

Abstract

We test ideas put forward, e.g., by \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski et al. [M. \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski et al., Phys. Rev. A 95, 042113 (2017)], which suggest that using rates in quantum optics can lead to better indicators of nonclassicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered photons in a given detector to the total number of detected photons in all detectors in a run of the experiment. For the Hong-Ou-Mandel effect for parametric down-conversion fields, we show that by using two detector correlation functions, which are defined in terms of averages of products of measured rates, rather than usual intensities, one can observe nonclassical visibilities beyond $1/2$ for significantly higher pump rates. At such rates we already have the partially stimulated emission, which leads to significant amplitudes for multiple pairs production, still the approach allows us to clearly see the nonclassical dip. We consider both the perfect and imperfect detection efficiency.

DOI
10.1103/physreva.95.042119

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We test ideas put forward, e.g., by \ifmmode \dot{Z}\else .{Z}\fi{}ukowski et al. [M. \ifmmode \dot{Z}\else .{Z}\fi{}ukowski et al., Phys. Rev. A 95, 042113 (2017)], which suggest that using rates in quantum optics can lead to better indicators of nonclassicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered photons in a given detector to the total number of detected photons in all detectors in a run of the experiment. For the Hong-Ou-Mandel effect for parametric down-conversion fields, we show that by using two detector correlation functions, which are defined in terms of averages of products of measured rates, rather than usual intensities, one can observe nonclassical visibilities beyond 1/21/21/2 for significantly higher pump rates. At such rates we already have the partially stimulated emission, which leads to significant amplitudes for multiple pairs production, still the approach allows us to clearly see the nonclassical dip. We consider both the perfect and imperfect detection efficiency.
We analyse how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, nonphoton-number resolving detections on the Cauchy–Schwarz parameter, on the second-order auto-correlation and cross-correlation functions, and on the visibilities of both Hong–Ou–Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.
Abstract We generalize a new approach to entanglement conditions for light of undefined photons numbers given in Żukowski et al (2017 Phys. Rev. A 95 042113) for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one to perform experiments based upon multiport beamsplitters. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into modes (beams), one can have perfect EPR-like correlations of numbers of photons emitted into ‘conjugate modes’ which can be monitored at spatially separated detection stations. We provide entanglement conditions for experiments involving three modes on each side, and three-input-three-output multiport beamsplitters, and show their violations by bright squeezed vacuum states. We show that a condition expressed in terms of averages of observed rates is a much better entanglement indicator than a related one for the usual intensity variables. Thus, the rates seem to emerge as a powerful concept in quantum optics, especially for fields of undefined intensities.
Summary form only given. In any optical system, quantum and classical theory yield identical predictions for the mean intensity. The quantum mechanical predictions diverge from the classical theory only for higher order correlations. For this reason, typical quantum-interference experiments are performed by measuring coincidence rates between two or more detectors. The usual approximation, following Glauber, is that a single-photon counter fires at a rate proportional to the intensity, or number of incident photons per unit time. This approximation is so good and so entrenched that one routinely assumes that all singles-detection rates are insensitive to quantum effects. However, if one of these detectors fires, it cannot fire again for a characteristic time, called the dead-time. This characteristic of the detectors makes them highly nonlinear over times shorter than the dead-time, and thus sensitive to the higher order intensity correlations. In other words the detector has a different response for two photons arriving at different times, than for two photons arriving at the same time. We use the process of spontaneous parametric-downconversion (SPDC) to create correlated photon-pairs and send them through a polarization-based Hong-Ou-Mander interferometer. This quantum interferometer allows us to change the photon statistics without changing the intensity of the beams.
Abstract We extensively discuss the Hong–Ou–Mandel experiment by taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field’s quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that make explicit the differences between a classical Hong–Ou–Mandel-like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down conversion, but our results can be extended to other analogous experimental systems and to various degrees of freedom. Graphical Abstract The Hong–Ou–Mandel experiment is a landmark in quantum optics, showing the bunching of indistinguishable bunch. In the present contribution, we give another perspective to this experiment based on a phase space representation of the continuous degrees of freedom of the single photons sent into the input arms of such interferometer. We show that the coincidence detection in the output ports of an Hong– Ou–Mandel interferometer is a direct measurement of the Wigner function of the produced photons in a given region of space, and we discuss how continuous degrees of freedom of single photons can be used in continuous variables quantum protocols, as quantum error correction and metrology. Our results open the perspective of broadening even more the applications of single photon-based quantum information-related protocols.
We extensively discuss the Hong-Ou-Mandel experiment taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field's quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that explicit the differences between a classical Hong-Ou-Mandel like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down-conversion, but our results can be extended to other analogous experimental systems and to different degrees of freedom.
Normalized quantum Stokes operators introduced in Phys. Rev. A 95, 042113 (2017) enable one to better observe non-classical correlations of entangled states of optical fields with undefined photon numbers.For a given run of an experiment the new quantum Stokes operators are defined by the differences of the measured intensities (or photon numbers) at the exits of a polarizer divided by their sum.It is this ratio that is to be averaged, and not the numerator and the denominator separately, as it is in the conventional approach.The new approach allows to construct more robust entanglement indicators against photon-loss noise, which can detect entangled optical states in situations in which witnesses using standard Stokes operators fail.Here we show an extension of this approach beyond phenomena linked with polarization.We discuss EPR-like experiments involving correlations produced by optical beams in a multi-mode bright squeezed vacuum state.EPR-inspired entanglement conditions for all prime numbers of modes are presented.The conditions are much more resistant to noise due to photon loss than similar ones which employ standard Glauber-like intensity, correlations.