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arXiv:2512.07953 · Physical Review A

Exchange Symmetry in Multiphoton Quantum Interference

Shreya Kumar, Alex E Jones, Daniel Bhatti, Stefanie Barz

quant-phSubmitted Dec 8, 2025• Announced Dec 10, 2025• 0 citations
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Abstract

Photons are bosons, and yet, when prepared in specific entangled states, they can exhibit non-bosonic behaviour. While this phenomenon has so far been studied in two-photon systems, exchange symmetries and interference effects in multi-photon scenarios remain largely unexplored. In this work, we show that multi-photon states uncover a rich landscape of exchange symmetries. With three photons already, multiple pairwise combinations are possible, where each pair of photons can exhibit either bosonic, fermionic, or anyonic exchange symmetry. This gives rise to mixed symmetry systems that are not possible to achieve with two photon alone. We experimentally investigate how these symmetry configurations manifest themselves in the observed interference of three photons. We show that multi-photon interference can be effectively turned on and off by tuning the symmetry of the constituent pairs. The possibility of accessing and tuning new quantum statistics in a scalable photonic platform not only deepens our understanding of quantum systems, but is also highly relevant for quantum technologies that rely on quantum interference.

Comments
14 pages, 5 figures

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We study the impact of distinguishability and mixedness, two fundamental properties of quantum states, on quantum interference. We show that these can influence the interference of multiple particles in different ways, leading to effects that cannot be observed in the interference of two particles alone. This is demonstrated experimentally by interfering three independent photons in pure and mixed states and observing their different multiphoton interference, despite exhibiting the same two-photon Hong-Ou-Mandel interference. In addition to its fundamental relevance, our observation has important implications for quantum technologies relying on photon interference.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.
The wavefunction of two identical bosons remains invariant under particle exchange - a fundamental quantum symmetry that underlies Bose-Einstein statistics. We report the direct experimental observation of bosonic exchange symmetry in the temporal wavefunction of photon pairs generated via spontaneous four-wave mixing in a three-level cold atomic ensemble. The measured two-photon temporal correlations show excellent agreement with theoretical predictions based on symmetrized bosonic wavefunctions. In addition, we perform time-resolved two-photon interference to reconstruct the complex temporal wavefunction. Both the amplitude and phase profiles exhibit clear symmetry under photon exchange, providing a direct confirmation of bosonic exchange symmetry in the time domain.
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In previous work [Physical Review Letters, 136(6):060807, 2026], we developed a symmetry-based framework for generalized Hong-Ou-Mandel interference and its applications to quantum metrology. Here, we apply this framework to experimentally accessible configurations involving a few photons and explore how it sheds new light on a variety of existing results while suggesting new experimental perspectives. We first reinterpret a two-photon Mach-Zehnder interferometer as a generalized Hong-Ou-Mandel experiment and show how its photon-counting statistics and metrological performance follow from the spatial symmetry of an effective probe state. We then study two coherently pumped parametric photon-pair sources, derive their complete output distribution, and connect source indistinguishability with spatial symmetry. Finally, we extend the discussion to a three-mode interferometer and show that the same symmetry principles provide a natural description of three-photon interference in tritter configurations.