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Latin America Optics and Photonics Conference

Large photon number semiclassical asymptotics of the HOM interferometer with partially indistinguishable photons

Miguel Villalobos, Alejandra Valencia, Alonso Botero

Published Jan 1, 2024• 0 citations
Publisher

Abstract

The classical correspondence of the HOM interferometer with n → ∞ partially indistinguishable photons is shown to arise from a concentration phenomenon of the quantum state in a Hilbert-space sector that can be associated with a well-defined macroscopic fraction of effectively indisistinguishable photons.
DOI
10.1364/laop.2024.tu1a.5

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We propose a framework for computing multiphotonic scattering probabilities in a lossless multiport interferometer for arbitrary photon numbers and degrees of indistinguishability. By exploiting a toroidal expansion of multiphotonic states in tensor powers of single-particle states, the framework defines a map from a torus of relative phases to the probability simplex that governs the asymptotic behavior of scattering probabilities in the large-photon limit. Specifically, the probabilities concentrate on the "classically allowed region" defined by the map, and the slowly-varying part of the multiphotonic distribution reproduces a classical measure induced by the map. As a result, we are able to establish a new asymptotic formula for the multiphotonic probabilities in a general scenario of partially indistinguishable photons, while also providing a single-particle picture to explain the asymptotics of known multiphotonic transition amplitudes in the fully indistinguishable case. More broadly, our framework yields new, directly testable consequences in relation to asymptotic photon bunching patterns: it translates features of the classical map -- such as caustics and voids -- into direct predictions about regions of large or exponentially suppressed photon-distribution probability.
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The quantum statistics of particles is determined by both the spins and the indistinguishability of quantum states. Here we study the quantum statistics of partially distinguishable photons by defining the multiphoton indistinguishability. The photon-bunching coefficient is formulated based on the properties of permutation symmetry and a modified Bose-Einstein statistics is presented with an indistinguishability-induced photon-bunching effect. Moreover, the statistical transition of the photon state is studied for partially distinguishable photons and the results show that the indistinguishability exhibits the same role as that observed in the generation of laser. The results will fill the gap between Bose-Einstein and Poisson statistics for photons and a formula is presented for the study of multiphoton quantum information processes.