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arXiv:1711.00080

Hong-Ou-Mandel Interference

Agata M. Brańczyk

Published Oct 31, 2017• 48 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1711.00080

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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.
Hong–Ou–Mandel interference is most dramatic when the photons involved are perfectly indistinguishable. Departures from this ideal scenario, however, are also interesting and useful to consider. In this tutorial, we analyze scenarios where the degree of the photons’ distinguishability depends on their spectral and temporal “overlap”. We first consider photons that are both spectrally pure and spectrally separable. We then generalize this to include spectrally entangled (but still spectrally pure) photons and spectrally mixed (but still spectrally separable) photons. This tutorial equips researchers with tools for a deeper understanding of this interesting phenomenon and its various applications.
The dip in the Hong–Ou–Mandel (HOM) experiment is frequently attributed to the interference of two indistinguishable photons. The width of the dip is inversely proportional to the spectral bandwidth of the light. We confirm that this width is unchanged regardless of where the bandwidth selection happens, i.e. prior to the photons combining in the beam splitter or just before the detectors; the latter case seemingly after the interference of the photons. The equivalence of the results from these two cases is a simple demonstration that the interference in the HOM experiment is not between photons, but rather between probability amplitudes.
The Hong–Ou–Mandel interference experiment is a fundamental demonstration of nonclassical interference and a basis for many investigations of quantum information. This experiment involves the interference of two photons reaching a symmetric beamsplitter. When the photons are made indistinguishable in all possible ways, an interference of quantum amplitudes results in both photons always leaving the same beamsplitter output port. Thus, a scan of distinguishable parameters, such as the arrival time difference of the photons reaching the beamsplitter, produces a dip in the coincidences measured at the outputs of the beamsplitter. The main challenge for its implementation as an undergraduate laboratory is the alignment of the photon paths at the beamsplitter. We overcome this difficulty by using a pre-aligned commercial fiber-coupled beamsplitter. In addition, we use waveplates to vary the distinguishability of the photons by their state of polarization. We present a theoretical description at the introductory quantum mechanics level of the two types of experiments, plus a discussion of the apparatus alignment and list of parts needed.
Recently a single-photon frequency converter by a nonlinear optical medium with a strong pump light [1] has been actively studied for quantum information processing [2]. The effective Hamiltonian of the process is described as a frequency-domain beamsplitter, which has two different frequency modes in its input and output. The transmittance is tunable by a pump power for the nonlinear optical effect. Such a frequency-domain beamsplitter is expected to cause an interference of two photons of different colors [3] in the context of a Hong–Ou–Mandel (HOM) experiment. In this study, we first observed the HOM dip in an optical range by using a frequency-domain beamsplitter.
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 Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.