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arXiv:1204.2687 · Physical Review A

Second-order superposition operations via Hong-Ou-Mandel interference

Su-Yong Lee, Hyunchul Nha

Published Apr 10, 2012• 46 citations
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Abstract

We propose an experimental scheme to implement a second-order nonlocal superposition operation ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}2}+{e}^{i\ensuremath{\varphi}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}^{\ifmmode\dagger\else\textdagger\fi{}2}$ and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement properties of continuous variable states. We discuss the feasibility of our proposed scheme considering realistic experimental conditions such as on-off photodetectors with nonideal efficiency and imperfect single-photon sources.

DOI
10.1103/physreva.85.043816

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Abstract The Hong−Ou−Mandel (HOM) effect was long believed to be a two-photon interference phenomenon. It describes the fact that two indistinguishable photons mixed at a beam splitter will bunch together to one of the two output modes. Considering the two single-photon emitters such as trapped ions, we explore a hidden scenario of the HOM effect, where entanglement can be generated between the two ions when a single photon is detected by one of the detectors. A second photon emitted by the entangled photon sources will be subsequently detected by the same detector. However, we can also control the fate of the second photon by manipulating the entangled state. Instead of two-photon interference, the phase of the entangled state is responsible for the photon’s path in our proposal. Toward a feasible experimental realization, we conduct a quantum jump simulation on the system to show its robustness against experimental errors.
We propose an optical scheme to generate a superposition of coherent states with enhanced size adopting an interferometric setting at the single-photon level currently available in the laboratory. Our scheme employs a nondegenerate optical parametric amplifier together with two beam splitters so that the detection of single photons at the output conditionally implements the desired superposition of second-order photonic operations. We analyze our proposed scheme by considering realistic on-off photodetectors with nonideal efficiency in heralding the success of conditional events. A high-quality performance of our scheme is demonstrated in view of various criteria such as quantum fidelity, mean output energy, and measure of quantum interference.
The second-order intensity correlation of entangled photons has been intensively studied for decades, particularly for the Hong-Ou-Mandel (HOM) effect and nonlocal correlation -- key quantum phenomena that have no classical counterparts. Recently, a path-entangled two-photon state has been experimentally demonstrated for both bosonic (symmetric) and fermionic (anti-symmetric) HOM effects by manipulating the photon phase at one input port. Entanglement represents a quantum superposition of path- or energy-correlated two-photon states with a relative phase. According to the conventional quantum mechanics, this phase is not an individual property but collective attribute of interacting photons. Here, the wave nature of photons is employed to coherently analyze the phase-controlled HOM effects recently observed in npj Quantum Info. 5, 43 (2019). A pure coherence approach is applied to derive a general solution for these phase-controlled HOM effects. Consequently, the quantum mystery of HOM effects, traditionally interpreted through the particle nature of quantum mechanics, is revealed as a coherent phenomenon between entangled photons via a selective choice of correlated photons.
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.