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arXiv:quant-ph/0503217 · Physical Review A

Hong-Ou-Mandel interferometer with cavities: Theory

C. Olindo, M. A. Sagioro, Carlos Henrique Monken, Sebastião Pádua, A. Delgado

Published Apr 19, 2006• 13 citations
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Abstract

We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam splitter exit is calculated. In the regime where the cavities lengths are larger than the one-photon coherence length, photon coalescence and anticoalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. The construction of an optical XOR gate is discussed as an application for the Hong-Ou-Mandel interferometer with two cavities.

DOI
10.1103/physreva.73.043806

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We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam splitter exit is calculated. In the regime where the cavities lengths are larger than the one-photon coherence length, photon coalescence and anticoalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. The construction of an optical XOR gate is discussed as an application for the Hong-Ou-Mandel interferometer with two cavities.
We herein study the rate of coincidences in a Hong–Ou–Mandel interferometer exit whose arms have been supplemented by two optical cavities which reflect the photons generated by parametric down conversion. The fourth-order correlation function at the beam-splitter exit is calculated. In the regime where the coherence length of the photons is larger than the cavities lengths, photon coalescence and anti-coalescence interferences are observed. In particular, complete anti-coalescence between photons generated by parametric down conversion Type I is evidenced. The photons reshaping as they are reflected by the cavities are also studied and path diagrams for the indistinguishable processes that lead to quantum interference are presented.
The interference of photons with the same polarization generated by spontaneous parametric down conversion in a Hong-Ou-Mandel interferometer, after one of them passed through a symmetric cavity, is demonstrated experimentally. In the regime where the cavity length is larger than the one-photon coherence length, photon coalescence and anticoalescence interference is observed. We show that by changing the cavity length, coincidence peaks can be transformed in dips and vice versa, even though the coherence length of the photon wave packet is smaller than the cavity length. The photon pair coalescence or anticoalescence at the beam splitter can be controlled by changing the length of the cavity.
We study the Hong-Ou-Mandel interferometer in the regime of spontaneous parametric down-conversion with high pump beam power at the crystal. In this regime one and two photons from a pump pulsed laser beam generate one and two pairs of photons, respectively. These photons are then directed to the beam splitter of the interferometer and detected at its exit in coincidence. An interesting phenomenon is observed: The reduction of the visibility of the Hong-Ou-Mandel coincidence peak (or dip) with the increase of pump power. We study the relation between the visibility of the fourth-order interference pattern and the power of the pumping laser beam for type I and type II phase-matching crystals. Our theoretical calculations are in good agreement with the experimental results.
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.
Using type I parametric down conversion, coincidence detection and the Hong-Ou-Mandel interferometer modified with the introduction of a Fabry-Perot cavity in one of its arms, we map the temporal distribution of the photon (one of those generated by the parametric down conversion), that pass through the cavity and we also measure the displacement of the peak of its temporal distribution after the cavity, in the photon longitudinal coherence length greater than the cavity length regime. We study the opposite regime, that is, where the cavity length is greater than the photon coherence length, and we found coalescence and anti-coalescence effects. The coincidence pattern, in this regime, is formed, in general, by peaks and dips which born from a constant value platform. The platform value depends only on the mirrors (that form the cavity) transmission and reflection coefficients, and it is proportional to the number of photons that cross the cavity. We complicated a little more, still in the cavity length greater than the photons coherence length regime, putting two cavities (each one in each of the interferometer arm), and we study the coincidence pattern for this case. The coincidence pattern is essentially the same of that found for the one cavity case. One of the main differences is that at this time the platform value depends also on the cavities lengths, and do not represents the number of the photons that cross the cavities anymore. We can simulate a C-NOT gate using this apparatus.Finally, using type II parametric down conversion, we study the case of two cavities which the transmission coefficients are polarization dependents. With this apparatus it is possible to distinguish conclusively the four Bell states: +, , _+ and _.
The spatial second-order interference of two independent pseudothermal light beams in a Hong-Ou-Mandel interferometer is studied experimentally and theoretically. The similar cosine modulation in the second-order coherence function as the one with entangled-photon pairs in a Hong-Ou-Mandel interferometer is observed. Two-photon interference based on Feynman's path integral theory is employed to interpret the results. The experimental results and theoretical simulations agree with each other very well.