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General rules for bosonic bunching in multimode interferometers
N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvao, A. Crespi, R. Ramponi, R. Osellame
TL;DR
Bosonic bunching is a well-known feature of bosonic systems, but its average behavior and full-bunching probabilities are distinct rules to test in multimode interferometers. The paper experimentally characterizes up to three photons in multimode circuits and verifies both rules, including a predicted 3.59 ± 0.15 full-bunching ratio for partially distinguishable three-photon inputs.
Problem
The paper examines how bosonic bunching behaves in multimode interferometers, including average bunching and events where all photons exit in one output mode.
Source: p. 1Method
The authors theoretically establish a full-bunching probability ratio and experimentally test bunching with distinguishable and indistinguishable photons in multimode interferometers.
Source: p. 1Results
The experiments agree with the average-bunching predictions and measure a three-photon full-bunching ratio of 3.59 ± 0.15 for partially distinguishable photons.
Source: p. 4Takeaways & Limitations
The full-bunching rule generalizes the Hong-Ou-Mandel effect to any interferometer and photon number, with enhancement up to n! when at most one boson enters each input mode.
Source: p. 3
Abstract
from arXiv · showhide
We perform a comprehensive set of experiments that characterize bosonic bunching of up to 3 photons in interferometers of up to 16 modes. Our experiments verify two rules that govern bosonic bunching. The first rule, obtained recently in [1,2], predicts the average behavior of the bunching probability and is known as the bosonic birthday paradox. The second rule is new, and establishes a n!-factor quantum enhancement for the probability that all n bosons bunch in a single output mode, with respect to the case of distinguishable bosons. Besides its fundamental importance in phenomena such as Bose-Einstein condensation, bosonic bunching can be exploited in applications such as linear optical quantum computing and quantum-enhanced metrology.
- Supplementary Material -
The supplementary material catalogs the tested interferometer architectures and reports experimental data for two-photon and three-photon bunching. It also describes the fermionic comparison and the effect of partial distinguishability on the three-photon full-bunching ratio.
Supplementary Figure S1
- The tested devices span two-mode couplers, tritters, random interferometers, and quantum walks up to 16 modes, with equal phases or static and dynamic disorder in some designs.The architectures include devices with up to eight layers.Source: Figure S1 · p. 7
Supplementary Table S1
- Supplementary Table S1 compares theoretical predictions with experimental two-photon bunching probabilities and ratios, including continuous-wave and pulsed-wave measurements.For pulsed measurements, expected two-photon visibilities are reduced by q ≃ 0.95 to account for imperfect indistinguishability; this correction is not shown in the table.Source: Table S1 · p. 8, - Supplementary Material - · p. 8
Supplementary Table S2
- Supplementary Table S2 compares theoretical and experimental two-fermion bunching probabilities using a continuous-wave source and polarization-entangled states to mimic fermions.A nonzero bunching probability for indistinguishable fermions is attributed to imperfect preparation of the polarization state |ψ−⟩.Source: Table S2 · p. 8, - Supplementary Material - · p. 8
Supplementary Table S3
- Supplementary Table S3 reports theoretical and experimental three-photon bunching data, including full-bunching ratios for partially distinguishable photons.The ratio combines the n! term for three indistinguishable photons and the (n−1)! term for two indistinguishable and one distinguishable photon.Source: Table S3 · p. 9, - Supplementary Material - · p. 9
Supplementary Tables
- With three photons of indistinguishability α = 0.63 ± 0.03, the full-bunching ratio is 3.59 ± 0.15, matching the predicted mixture of 3! and (3−1)! enhancements.The predictions using reconstructed device matrices are reported for chips 3–4, with reconstruction-error bars estimated by Monte Carlo simulation.Source: - Supplementary Material - · p. 9
I. EXPERIMENTAL DETAILS
The experiments use continuous-wave and pulsed photon sources to test integrated interferometer chips. The pulsed setup supports three-photon measurements and varies the delay between photons to control distinguishability.
Apparatus selection
- The measured chips and source configurations are divided between continuous-wave measurements and pulsed-wave measurements.The continuous-wave setup tests chips listed in Tables S1 and S2, while the pulsed setup tests chips listed in Tables S1 and S3.Source: §I · p. 9
Continuous-wave apparatus
- The continuous-wave apparatus uses polarization-entangled photon pairs, with waveplate rotations enabling simulated bosonic and fermionic behavior.The output is collected into multimode fibers, detected by single-photon counting modules, and recorded as coincidence counts.Source: §I · p. 9
Pulsed-source apparatus
- The pulsed setup measures two-photon interference visibilities of 0.952 ± 0.006 for photons from the same pair and 0.63 ± 0.03 for photons from different pairs.For three-photon measurements, one generated photon serves as a trigger while the other three enter the chip.Source: §I · p. 9
- The pulsed source uses delay lines to vary the interference regime between distinguishable and indistinguishable photons before coupling them into the chips.The setup uses a triggered three-photon input from a four-photon source.Source: §I · p. 9