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Physical Review A

Exploring the quantum nature of the radial degree of freedom of a photon via Hong-Ou-Mandel interference

Ebrahim Karimi, Daniel Giovannini, Eliot Bolduc, Nicolas Bent, Filippo M. Miatto, Miles J. Padgett, Robert W. Boyd

Published Jan 23, 2014• 103 citations
Publisher

Abstract

In quantum information, quantum systems and their properties offer unprecedented opportunities. Being able to harness additional degrees of freedom adds power and flexibility to quantum algorithms and protocols. In this work, we demonstrate that the radial transverse mode of a single photon constitutes one such degree of freedom. We do so by showing that we can tune the two-photon interference, a quintessential quantum effect and the basic constituent of many quantum protocols, by manipulating its radial transverse modal profiles. Our work, in addition to allowing for greater versatility of existing protocols and significantly increasing the information channel capacity, can inspire novel quantum information tasks.

DOI
10.1103/physreva.89.013829

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In quantum information, quantum systems and their properties offer unprecedented opportunities. Being able to harness additional degrees of freedom adds power and flexibility to quantum algorithms and protocols. In this work, we demonstrate that the radial transverse mode of a single photon constitutes one such degree of freedom. We do so by showing that we can tune the two-photon interference, a quintessential quantum effect and the basic constituent of many quantum protocols, by manipulating its radial transverse modal profiles. Our work, in addition to allowing for greater versatility of existing protocols and significantly increasing the information channel capacity, can inspire novel quantum information tasks.
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We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong–Ou–Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
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.
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.
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.
The celebrated Hong--Ou--Mandel effect illustrates the richness of two-photon interferometry. In this work, we demonstrate that this extends to the realm of time-frequency interferometry. Taking advantage of the mathematical analogy which can be drawn between the frequency and quadrature degrees of freedom of light when there is a single photon in each auxiliary mode, we consider the equivalent of the Hong--Ou--Mandel effect in the frequency domain. In this setting, the nnn-Fock state becomes equivalent to a single-photon state with a spectral wave function given by the nthn^{th}nth Hermite--Gauss function and destructive interference corresponds to vanishing probability of detecting single photons with an order one Hermite--Gauss spectral profile. This compelling analogy motivates us to propose an interferometric strategy that uses a frequency-engineered two-photon state to achieve enhanced phase precision that scales inversely with the number of modes. Finally, we generalise the Gaussian Boson Sampling model to time-frequency degrees of freedom of single photons.