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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Bimodal Hong-Ou-Mandel Interference in Symmetric and Asymmetric Optical Systems

Cody C. Leary, Thomas Gilliss, Deepika Sundarraman

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We investigate Hong-Ou-Mandel interference in symmetric and asymmetric interferometers, with the input photons prepared in arbitrary first-order spatial modes. We find that Hong-Ou-Mandel interference may occur in conjunction with mode transformation, and between distinguishable inputs.
DOI
10.1364/cqo.2013.m6.05

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The Hong-Ou-Mandel interferometer is a foundational tool in quantum optics with both fundamental and practical significance. Earlier works identified that input-state symmetry under exchange of the two spatial modes is fundamental in the understanding of the Hong-Ou-Mandel effect. We now show that this notion of symmetry is central to generalizing this effect. In particular, this point of view enables the construction of extensions beyond the standard two single-photon case to arbitrary input states, as well as to configurations with more than two spatial modes via a natural generalization of the beam splitter to a discrete Fourier transform interferometer. Beyond its conceptual significance, this framework offers direct insights into quantum metrology, showing how symmetry properties of input states allow for the computation of explicit precision bounds. By focusing on symmetry, we provide a perspective that simplifies and unifies a range of known results while paving the way for new developments in quantum interference and sensing.
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.
This article is a detailed introduction to Hong-Ou-Mandel (HOM) interference, in which two photons interfere on a beamsplitter in a way that depends on the photons' distinguishability. We begin by considering distinguishability in the polarization degree of freedom. We then consider spectral distinguishability, and show explicitly how to calculate the HOM dip for three interesting cases: 1) photons with arbitrary spectral distributions, 2) spectrally entangled photons, and 3) spectrally mixed photons.
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 investigate the connection between biphoton states involving photons in product modes of their spin and orbital degrees of freedom and those involving photons in hybrid spin-orbit modes, as mediated by Hong-Ou-Mandel interference (HOMI) in an asymmetric Mach-Zehnder interferometer. We predict that two input photons in balanced superposition states of both their spin and orbital degrees of freedom will exhibit HOMI while undergoing a simultaneous mode conversion from product spin-orbit input modes to hybrid output modes bearing orbital angular momentum. These hybrid outputs contain a spatially varying polarization structure which may be controllably rotated about the photonic beam axis by varying the relative phase between the vertical and horizontal components of each input photon's polarization. Additionally, a type of coupling of the spin and orbital degrees of freedom is exhibited in this system: the transverse spatial profile of the output photons may be continuously manipulated by tuning the polarization parameters of the input photons, in such a way that the HOMI between the photons remains stable. An interesting corollary to this work is the possibility of demonstrating in a simple experimental system that HOMI may occur between distinguishable input modes.