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arXiv:2006.13288 · Physical Review Letters

High-Dimensional Two-Photon Interference Effects in Spatial Modes

Markus Hiekkamäki, Robert Fickler

Published Mar 22, 2021• 71 citations
arXivHTMLPDF

Abstract

Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analog of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anticoalescence in different three- and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.

DOI
10.1103/physrevlett.126.123601

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Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analog of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anticoalescence in different three- and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.
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.
Transverse spatial modes have become an increasingly popular degree-of-freedom for encoding quantum information owing to the compact implementation when compared to others such as path. Here we present the demonstration of two photon Hong-Ou-Mandel interference between the different transverse modes in a multimode silicon photonic chip using a compact inverse designed beam splitter with up to 99.56 0.64% interference visibility. We achieve high visibilities across both multiple copies of ±the same design and among different designs. This work demonstrates the potential of inverse designed devices for quantum information processing with transverse spatial modes.
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons - those with complex spatial profiles - under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions.
We present a general theory on the interference of a two-photon wave packet associated with spatial modes at a beam splitter. We find that the topological symmetry of the two-photon angular spectrum governs the nature of the two-photon interference. We distinguish between the coalescence interference and anticoalescence interference according to the decrease or increase of the coincidence probability in the absence of interference, respectively, and demonstrate that the symmetric and antisymmetric two-photon angular spectra are responsible for perfect coalescence interference and anticoalescence interference, respectively. Then we prove that anticoalescence interference never occurs for two independent photons, and it turns out that anticoalescence interference is the signature of two-photon entanglement. On the basis of this feature, we propose a special Mach-Zehnder interferometer, incorporated with two spiral phase plates, which can change the interference from a coalescence to an anticoalescence type only for a two-photon entangled state. The scheme is simple and straightforward compared with a test of Bell's inequality.
We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.
We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.