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arXiv:1304.7092 · Scientific Reports

Direct measurement of the biphoton Wigner function through two-photon interference

Tom Douce, A. Eckstein, Stephen Patrick Walborn, Antonio Zelaquett Khoury, S. Ducci, Arne Keller, T. Coudreau, P. Milman

Published Dec 18, 2013• 48 citations
arXivHTMLPDF

Abstract

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non-classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups.

DOI
10.1038/srep03530

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The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non-classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups.
Abstract Over the last several decades, quantum entanglement has been intensively studied for potential applications in quantum information science. The Hong-Ou-Mandel (HOM) dip is the most important test tool for direct proof of entanglement between paired photons, whose coincidence detection results in anticorrelation due to photon bunching on a beam splitter. Although anticorrelation is due to destructive quantum interference between paired photons, a wavelength-sensitive interference fringe has never been observed in any HOM-type experiments. Here, a typical HOM dip is investigated for entangled photon pairs generated by parametric down conversion processes (SPDC) to understand fundamental physics of anticorrelation. In addition, a pure coherence optics-based Hong-Ou-Mandel scheme is proposed and analyzed for general understanding of anticorrelation in an interferometric system. This study sheds light on deterministic quantum correlation control and opens the door to potential applications of on-demand quantum information science.
Hong–Ou–Mandel (HOM) interference is a quantum optics laboratory experiment that has recently become more accessible to undergraduate students. The experiment consists of two identical photons simultaneously entering a nonpolarizing beamsplitter, where the photon wavefunctions interfere. As a result, the photon pair exits from the same beamsplitter output, whereas classically, the two photons are equally likely to exit from the two different outputs. This effect is demonstrated by observation of a dip in coincidence counts measured between the two beamsplitter outputs. Due to the precision needed to achieve photon indistinguishability, the setup and alignment of this experiment is often considered to be too difficult and time consuming to be appropriate for the undergraduate instructional laboratory. Here, we present an alternative optical-fiber-based apparatus that gives a consistently reproducible experiment. In our approach, quantum interference occurs within a fused-fiber coupler, instead of within a traditional beamsplitter. We use a commercially available fiber-coupled biphoton source that requires minimal alignment and increases the interference coherence length. In addition, our biphoton source provides direct temperature-based control of the frequency degeneracy of the photon pairs, allowing students to investigate physical properties of HOM interference such as coherence length and interference visibility. Through use of standard optomechanical parts, combined with the commercially available fiber-integrated biphoton source, our apparatus is positioned midway between a completely built-from-scratch and a pre-aligned setup, making it ideal for the advanced instructional laboratory.
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.
Among the whole experiments using entangled pairs of photons, the famous experiment of two-photon interference known now as Hong-Ou-Mandel (HOM) interference, is probably one of the most fascinating. This ground-breaking experiment paved the way for a multitude of experiments showing the richness of the quantum properties of Spontaneous Parametric Down conversion (SPDC) and their applications to original communication protocols. Most of them use the coherence time property of a bi-photon state and measurement are mainly performed with bucket detectors and coincidence counters. While some studies report the spatial coherence of two-photon state, measurements are always performed in the temporal domain.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.