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The European Physical Journal D

The Hong–Ou–Mandel experiment: from photon indistinguishability to continuous-variable quantum computing

Nicolas Fabre, Maria I. Amanti, F. Baboux, Arne Keller, S. Ducci, P. Milman

Published Oct 1, 2022• 8 citations
Publisher

Abstract

Abstract We extensively discuss the Hong–Ou–Mandel experiment by taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field’s quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that make explicit the differences between a classical Hong–Ou–Mandel-like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down conversion, but our results can be extended to other analogous experimental systems and to various degrees of freedom. Graphical Abstract The Hong–Ou–Mandel experiment is a landmark in quantum optics, showing the bunching of indistinguishable bunch. In the present contribution, we give another perspective to this experiment based on a phase space representation of the continuous degrees of freedom of the single photons sent into the input arms of such interferometer. We show that the coincidence detection in the output ports of an Hong– Ou–Mandel interferometer is a direct measurement of the Wigner function of the produced photons in a given region of space, and we discuss how continuous degrees of freedom of single photons can be used in continuous variables quantum protocols, as quantum error correction and metrology. Our results open the perspective of broadening even more the applications of single photon-based quantum information-related protocols.

DOI
10.1140/epjd/s10053-022-00525-0

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Abstract We extensively discuss the Hong–Ou–Mandel experiment by taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field’s quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that make explicit the differences between a classical Hong–Ou–Mandel-like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down conversion, but our results can be extended to other analogous experimental systems and to various degrees of freedom. Graphical Abstract The Hong–Ou–Mandel experiment is a landmark in quantum optics, showing the bunching of indistinguishable bunch. In the present contribution, we give another perspective to this experiment based on a phase space representation of the continuous degrees of freedom of the single photons sent into the input arms of such interferometer. We show that the coincidence detection in the output ports of an Hong– Ou–Mandel interferometer is a direct measurement of the Wigner function of the produced photons in a given region of space, and we discuss how continuous degrees of freedom of single photons can be used in continuous variables quantum protocols, as quantum error correction and metrology. Our results open the perspective of broadening even more the applications of single photon-based quantum information-related protocols.
We extensively discuss the Hong-Ou-Mandel experiment taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field's quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that explicit the differences between a classical Hong-Ou-Mandel like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down-conversion, but our results can be extended to other analogous experimental systems and to different degrees of freedom.
We use time-frequency continuous variables as the standard framework to describe states of light in the subspace of individual photons occupying distinguishable auxiliary modes. We adapt to this setting the interplay between metrological properties and the phase-space picture already extensively studied for quadrature variables. We also discuss in details the Hong-Ou-Mandel interferometer, which was previously shown to saturate precision limits, and provide a general formula for the coincidence probability of a generalized version of this experiment. From the obtained expression, we systematically analyze the optimality of this measurement setting for arbitrary unitary transformations applied to each one of the input photons. As concrete examples, we discuss transformations which can be represented as translations and rotations in time-frequency phase space for some specific states.
The quality of individual photons and their ability to interfere are traditionally tested by measuring the Hong-Ou-Mandel photon bunching effect. However, this phase-insensitive measurement only tests the particle aspect of the quantum interference, leaving out the phase-sensitive aspects relevant for continuous-variable processing. To overcome these limitations we formulate a witness capable of recognizing both the indistinguishability of the single photons and their quality with regard to their continuous-variable utilization. We exploit the conditional nonclassical squeezing and show that it can reveal both the particle and the wave aspects of the quantum interference in a single set of direct measurements. We experimentally test the witness by applying it to a pair of independent single photons retrieved on demand.
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.
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.
Hong-Ou-Mandel effect lies in the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only few works have considered polarization-frequency interaction, i.e., noise, within the interferometer. In this paper, we fill this gap. Our system of interest consists of a general biphoton polarization state that becomes entangled with the same photons' frequency degrees of freedom as the photons propagate through birefringent media. The photons then meet at a beam splitter, where either coincidence or bunching occurs, after which the polarization-frequency interaction continues on the output paths. Alongside performing extensive theoretical analysis on the coincidence probability and different polarization states, we outline multiple interesting applications that range from constructing Bell states to an alternative delayed choice quantum eraser.