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Physical Review A

Spatial-mode two-photon interference at a beam splitter

Li-Ping Deng, Gui-Fang Dang, Kaige Wang

Published Dec 18, 2006• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.74.063819

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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.
A general theory is derived for the interference of a two-photon wavepacket in a beamsplitter. The theory is presented in the Schrödinger picture so that the quantum nature of the two-photon interference is explicitly revealed. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the nature of the two-photon interference, which may be distinguished by the increase or decrease of the coincidence probability in the absence of interference. However, two-photon entanglement can be identified by the nature of the interference. We demonstrate the necessary and sufficient conditions for perfect two-photon interference. It is shown that a two-photon entangled state with an anti-symmetric spectrum passes through a 50/50 beamsplitter with perfect transparency. The theory provides us with a unified understanding of the various two-photon interference effects.
We study theoretically the interference of a two-photon wavepacket in a beam splitter. We find that the spectrum symmetry for the two-photon wavepacket dominates the perfect coalescence and anti-coalescence interference. The coalescence interference is unrelated to photon entanglement. Only the anti-coalescence interference has evidence of photon entanglement. We prove that the two-photon wavepacket with an anti-symmetric spectrum is transparent to pass the 50/50 beam splitter, showing perfect anti-coalescence interference.
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.
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.
Fourth-order interference patterns of biphotons generated by type-I spontaneous parametric downconversion are examined for beams with partial angular and spectral entanglement, both for degenerate and nondegenerate constituent photons. Two-beam configurations using a single beam-splitter interferometer and a Mach-Zehnder interferometer are explicitly studied, as are four-beam configurations using pairs of beam splitters and Mach-Zehnder interferometers. The interference pattern generally comprises a number of harmonic functions of the path-length difference with frequencies and visibilities that usually depend on direction, and may have a finite or infinite duration (fourth-order coherence length). The relation between the visibility and the spectral indistinguishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are not washed out by the use of apertures of finite size.