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Optics

Hong–Ou–Mandel Interference on an Acousto-Optical Beam Splitter

Piotr Kwiek

Published Jun 5, 2025• 0 citations
Publisher

Abstract

This paper presents the results of theoretical and experimental investigations of a Hong–Ou–Mandel interferometer in which an optical beam splitter is replaced by an ultrasonic wave. The ultrasonic wave acts as an acousto-optical beam splitter for light, which is based on the phenomenon of Bragg diffraction on an ultrasonic wave. The Doppler effect was considered in the theoretical considerations and confirmed experimentally. It has been shown theoretically and experimentally that the Doppler effect changes the frequency of two-photon states at the outputs of an acousto-optical beam splitter. The frequency of the two-photon state in the positive diffraction order is increased by the frequency of the ultrasonic wave, whereas in the negative diffraction order, it is reduced by the frequency of the ultrasonic wave. It should be emphasized that there are no states 1112 in the outputs (diffraction orders), which disappear as a result of Hong–Ou–Mandel interference; consequently, the probability of detecting coincidences of photons between the plus first and minus first diffraction orders is zero, as it occurs in the Hong–Ou–Mandel interferometer. The frequency difference between the two-photon states at the outputs of the acousto-optical beam splitter was confirmed by recording the two-photon beat phenomenon. The obtained results changed the current view that the Doppler effect caused by ultrasonic waves can be neglected in the interaction of correlated pairs of photons with ultrasonic waves.

DOI
10.3390/opt6020025

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This paper presents the results of theoretical and experimental investigations of a Hong–Ou–Mandel interferometer in which an optical beam splitter is replaced by an ultrasonic wave. The ultrasonic wave acts as an acousto-optical beam splitter for light, which is based on the phenomenon of Bragg diffraction on an ultrasonic wave. The Doppler effect was considered in the theoretical considerations and confirmed experimentally. It has been shown theoretically and experimentally that the Doppler effect changes the frequency of two-photon states at the outputs of an acousto-optical beam splitter. The frequency of the two-photon state in the positive diffraction order is increased by the frequency of the ultrasonic wave, whereas in the negative diffraction order, it is reduced by the frequency of the ultrasonic wave. It should be emphasized that there are no states 1112 in the outputs (diffraction orders), which disappear as a result of Hong–Ou–Mandel interference; consequently, the probability of detecting coincidences of photons between the plus first and minus first diffraction orders is zero, as it occurs in the Hong–Ou–Mandel interferometer. The frequency difference between the two-photon states at the outputs of the acousto-optical beam splitter was confirmed by recording the two-photon beat phenomenon. The obtained results changed the current view that the Doppler effect caused by ultrasonic waves can be neglected in the interaction of correlated pairs of photons with ultrasonic waves.
The accurate theory describing interaction of two coherent light beams with ultrasonic wave where one of the light beam is incident at positive Bragg angle while the other at negative was developed by Leroy and Blomme in 1984 . The assumed geometry in this theory resembles an interferometer wherein ultrasonic beam plays a role of the output beam splitter of the light. The output light intensity is modulated with ultrasonic frequency as a result of interference between the light in diffraction orders in which the frequency is changed due to the Doppler effects with those diffracted with unchanged frequency. Temporal modulation of the light intensities in diffraction orders, that was foreseen by Leroy and Blomme, was confirmed experimentally and the results will be presented. In addition, the Leroy-Blomme theory has been extended to include the effect of the initial phase of the ultrasonic wave on the phase of modulation of light intensity in diffraction orders. According to the best knowledge of the author, Leroy and Blomme theory has not been verified experimentally, although many years have passed. This theory could be applied to the quantum optics phenomenon when pairs of entangled photons are incident on ultrasonic wave instead of two coherent light beams. The geometry of interaction of two coherent light beams with ultrasonic wave in Leroy-Blomme theory is the same as for Hong-Ou-Mandel interferometer wherein a beam splitter is replaced by the ultrasonic wave. Similarities and differences between Leroy-Blomme and Hong-Ou-Mandel interferometers will be presented.
Abstract The paper presents a classical and quantum description of the diffraction of two light beams incident on an ultrasonic wave at a positive and negative Bragg angle. The quantum description of the interaction with the ultrasonic wave was carried out for the two-photon NOON state. Study of diffraction of entangled pair of photon was performed in Mach–Zehnder interferometer wherein an output beam splitter is replaced by ultrasonic wave. It has been shown theoretically and experimentally that when a pair of photons generated from a parametric down-conversion was incident on two input ports of Mach–Zehnder interferometer with an acousto-optical beam splitter, then two-photon beats are observed at the output of the interferometer. The phenomenon of two-photon beats with the double frequency of the ultrasonic wave is the result of the Doppler effect on the ultrasonic wave. Time-correlated single-photon counting method was used to register the phenomenon of two-photon beats. The method of calibrating the interferometer with the use of an additional light source was presented in detail, which guarantees the observation of interaction of two-photon NOON state with ultrasonic wave. Graphical abstract
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection R=1/2R = 1/2R=1/2 and transmission $ T = 1/2 $. In this work, the general mechanism of the interaction of two photons in a beam splitter is considered using an analytical solution, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only $ R = 1/2 $ and $ T = 1/2 $, but also their root-mean-square fluctuations $ ΔR ^ 2, ΔT ^ 2 $, which arise due to the dependence of $R = R(ω_1, ω_2) $ and $ T = T (ω_1, ω_2) $ on the frequencies where ω1,ω2ω_1, ω_2ω1​,ω2​ are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations $ ΔR^2 $ and $ ΔT^2 $ can be neglected and $ R=T=1/2 $ is chosen, the developed theory coincides with previously known results.
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.
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. It is believed that the effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. In this work, it is shown that these fundamental provisions of the HOM interference may not always be fulfilled. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection [Formula: see text] and transmission [Formula: see text]. Here we consider the general mechanism of the interaction of two photons in a beam splitter, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only [Formula: see text] and [Formula: see text], but also their root-mean-square fluctuations [Formula: see text], which arise due to the dependence of [Formula: see text] and [Formula: see text] on the frequencies where [Formula: see text] are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations [Formula: see text] and [Formula: see text] can be neglected and [Formula: see text] is chosen, the developed theory coincides with previously known results.