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Physical Review A

First-quantization quantum-mechanical insight into the Hong-Ou-Mandel two-photon interferometer with polarizers and its role as a quantum eraser

Fedor Herbut, Milan Vujičić

Published Jul 1, 1997• 9 citations
Publisher

Abstract

A straightforward derivation of a first-quantization two-photon state vector is presented for the Hong-Ou-Mandel interferometer with a possible half-wave plate and possible linear analyzers in the ports. It is shown that one is dealing with a quantum eraser in a somewhat broader physical sense: It is not strictly the interference from version I of the experiment, the interference that has been suppressed by entanglement in version II, that is revived in version III; but it is an analogous interference. Besides, the coincidence probability for arbitrary-angle analyzers in the general case of arbitrary polarization in the lower arm of the interferometer is derived. The interference phenomenon of a complete decoupling of the partial loss of interference and the coincidence events in the ports is demonstrated. It is pointed out that the phenomenon of distant polarization (a special case of distant preparation) carries all the nonlocality between the two photons in the two ports.

DOI
10.1103/physreva.56.931

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A straightforward derivation of a first-quantization two-photon state vector is presented for the Hong-Ou-Mandel interferometer with a possible half-wave plate and possible linear analyzers in the ports. It is shown that one is dealing with a quantum eraser in a somewhat broader physical sense: It is not strictly the interference from version I of the experiment, the interference that has been suppressed by entanglement in version II, that is revived in version III; but it is an analogous interference. Besides, the coincidence probability for arbitrary-angle analyzers in the general case of arbitrary polarization in the lower arm of the interferometer is derived. The interference phenomenon of a complete decoupling of the partial loss of interference and the coincidence events in the ports is demonstrated. It is pointed out that the phenomenon of distant polarization (a special case of distant preparation) carries all the nonlocality between the two photons in the two ports.
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90\ifmmode^\circ\else\textdegree\fi{}. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
The Hong-Ou-Mandel effect lies at the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only a few works have considered polarization-frequency interaction within the interferometer. In this paper, we fill this gap. Our system of interest is a general biphoton polarization state that experiences effective dephasing noise by becoming entangled with the same photons' frequency state, as the photons propagate through birefringent media. The photons then meet at a beam splitter, where either coincidence or bunching occurs, after which the polarization-frequency interaction continues on the output paths. Along with performing extensive theoretical analysis on the coincidence probability and different polarization states, we outline multiple interesting applications that range from constructing Bell states to an alternative delayed choice quantum eraser.
Hong-Ou-Mandel effect lies in the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only few works have considered polarization-frequency interaction, i.e., noise, within the interferometer. In this paper, we fill this gap. Our system of interest consists of a general biphoton polarization state that becomes entangled with the same photons' frequency degrees of freedom as the photons propagate through birefringent media. The photons then meet at a beam splitter, where either coincidence or bunching occurs, after which the polarization-frequency interaction continues on the output paths. Alongside performing extensive theoretical analysis on the coincidence probability and different polarization states, we outline multiple interesting applications that range from constructing Bell states to an alternative delayed choice quantum eraser.
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.
We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no frequency entanglement. When unentangled polarization-correlated photons are used as an input state, the polarization entanglement is successfully recovered through the interferometer via delayed compensation.
We report a quantum-eraser experiment with frequency-entangled photon pairs generated by nondegenerate parametric down conversion. The relationship between which-path information and two-photon fringe visibility has been investigated by means of photon polarizations in a Hong-Ou-Mandel interferometer. Although photons are not of the same frequency and are not superposed at the beam splitter, the results of the experiment show the revival of the fringe pattern by removing the path information in the interferometer by means of polarizations in front of the detectors.