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Physics and High Technology

Quantum Interference of Different Photons and Indistinguishability of Probability Amplitudes

Young-Sik Ra, Yoon-Ho KIM

Published Mar 31, 2026• 0 citations
Publisher

Abstract

This article reviews the historical and conceptual evolution of quantum physics, challenging P.A.M. Dirac’s famous dictum, “Each photon then interferes only with itself. Interference between two different photons never occurs.” We trace the progression from the early experiments by Forrester et al. and Magyar & Mandel, which first questioned this notion, to the advent of Spontaneous Parametric Down-Conversion (SPDC) following the invention of the laser and nonlinear optics. The article elucidates how D. N. Klyshko’s quantum description of SPDC laid the groundwork for the landmark Shih-Alley and Hong-Ou-Mandel (HOM) experiments, which demonstrated two-photon quantum interference and entanglement. Finally, we address the common misconception that photons must physically overlap at a beam splitter for two-photon interference to occur. We illustrate that quantum interference arises solely from the indistinguishability of probability amplitudes leading to a joint detection event, even in configurations where the photons never locally interact at a beam splitter.

DOI
10.3938/phit.35.006

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This article reviews the historical and conceptual evolution of quantum physics, challenging P.A.M. Dirac’s famous dictum, “Each photon then interferes only with itself. Interference between two different photons never occurs.” We trace the progression from the early experiments by Forrester et al. and Magyar & Mandel, which first questioned this notion, to the advent of Spontaneous Parametric Down-Conversion (SPDC) following the invention of the laser and nonlinear optics. The article elucidates how D. N. Klyshko’s quantum description of SPDC laid the groundwork for the landmark Shih-Alley and Hong-Ou-Mandel (HOM) experiments, which demonstrated two-photon quantum interference and entanglement. Finally, we address the common misconception that photons must physically overlap at a beam splitter for two-photon interference to occur. We illustrate that quantum interference arises solely from the indistinguishability of probability amplitudes leading to a joint detection event, even in configurations where the photons never locally interact at a beam splitter.
Among the whole experiments using entangled pairs of photons, the famous experiment of two-photon interference known now as Hong-Ou-Mandel (HOM) interference, is probably one of the most fascinating. This ground-breaking experiment paved the way for a multitude of experiments showing the richness of the quantum properties of Spontaneous Parametric Down conversion (SPDC) and their applications to original communication protocols. Most of them use the coherence time property of a bi-photon state and measurement are mainly performed with bucket detectors and coincidence counters. While some studies report the spatial coherence of two-photon state, measurements are always performed in the temporal domain.
We have experimentally demonstrated two-photon interference between biphoton amplitudes arising from two well-separated pump pulses. It is important to note the following. 1) The pump pulse intensity was low enough so that single counting rates of the detectors were kept much smaller than pulse repetition rates: the probability of having one spontaneous parametric down conversion (SPDC) photon pair per pulse in our experiment is negligible. Hence the interference cannot be explained as two SPDC photons from two pump pulses (one SPDC photon pair from each pulse) interfering at the detectors. The two pump pulses simply provide two biphoton amplitudes which could result in coincidence counts, and interference occurs between these two biphoton amplitudes only when they are indistinguishable. 2) The BBO crystal in our experiment was only 100 /spl mu/m thick, so the two-pulse did not exist in BBO at the same time at any moment. 3) Due to the delays in the interferometer (/spl tau/ /spl tau//sub 1/), the signal-idler never met at the beamsplitter. Therefore, the existence of two-photon interference cannot be viewed as the interference between the signal and idler photons. These three points again emphasize the fact that it is the indistinguishability of the two-photon Feynman alternatives for the biphoton amplitudes which is responsible for the two-photon quantum interference effects.
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.
We analyze the interference of individual photons in two overlapping Mach–Zehnder interferometers joined via a common beam splitter. We show how two kinds of interference effects—single-photon Mach–Zehnder interference and two-photon Hong–Ou–Mandel interference—interfere with one another, partially canceling each other out. This configuration illustrates how quantum effects can combine nontrivially and, moreover, emphasizes that quantum interference happens at measurement. This work can serve as a bridge to more advanced quantum mechanical concepts, such as testing the predictions of quantum mechanics vs local realism.
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.
The Hong-Ou-Mandel effect is a paradigmatic quantum phenomenon demonstrating the interference of two indistinguishable photons that are linearly coupled at a 50:50 beam splitter. Here, we transpose such a two-particle quantum interference effect to the nonlinear regime, when two single photons are impinging on a parametric down-conversion crystal. Formally, this transposition amounts to exchanging space and time variables, giving rise to an unknown form of timelike quantum interference. The two-photon component of the output state is a superposition of the incident photons being either transmitted or reborn, that is, replaced by indistinguishable substitutes due to their interaction with the nonlinear crystal. We experimentally demonstrate the suppression of the probability of detecting precisely one photon pair when the amplification gain is tuned to 2, which arises from the destructive interference between the transmitted and reborn photon pairs. This heretofore unobserved quantum manifestation of indistinguishability in time pushes nonlinear quantum interference towards a new regime with multiple photons. Hence, composing this effect with larger linear optical circuits should provide a tool to generate multimode quantum non-Gaussian states, which are essential resources for photonic quantum computers.