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arXiv:1609.08248 · Journal of the Optical Society of America B

Second-order fermionic interference with independent photons

Jianbin Liu, Hui Chen, Yu Zhou, Huaibin Zheng, Fuli Li, Zhuo Xu

Published May 19, 2017• 3 citations
arXivHTMLPDF

Abstract

The experimental study of second-order interference with fermions is much more difficult than that with bosons. Inspired by the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics [Phys. Rev. A88, 012130 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012130], we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown–Twiss and Hong–Ou–Mandel interferometers, respectively. The experimental results are consistent with the theoretical predictions, which may serve as guidance for future interference experiments with fermions. The employed method offers an interesting and convenient way to study the coherence of fermions.

DOI
10.1364/josab.34.001215

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The experimental study of second-order interference with fermions is much more difficult than that with bosons. Inspired by the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics [Phys. Rev. A88, 012130 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012130], we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown–Twiss and Hong–Ou–Mandel interferometers, respectively. The experimental results are consistent with the theoretical predictions, which may serve as guidance for future interference experiments with fermions. The employed method offers an interesting and convenient way to study the coherence of fermions.
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According to the identity principle in quantum theory, states of a system consisted of identical particles should maintain unchanged under interchanging between two of the particles. The whole wavefunction should be symmetrized or antisymmetrized. This leads to statistical correlations between particles, which exhibit observable effects. We design an experiment to directly observe such effects for bosons. The experiment is performed with two photons. The effect of statistical correlations is clearly observed when the wavepackets of two photons are completely overlapped, and this effect varies with the degree of overlapping. The results of our experiment substantiate the statistical correlation in a simple way. Experiment reported here can also be regarded as another kind of two-photon Hong-Ou-Mandel interference, occurs in the polarization degree of freedom of photon.
Usually fermions and bosons behave very differently. Regarding distinguishability, they behave in one and the same way. Two-identical-particle quantum theory is discussed on the example of the deuteron and that of distant correlations, as well as on the example of the real interference and quantum erasure experiments in the Hong–Ou–Mandel two-photon interferometer (with and without polarizers and analyzers). Distinguishability and indistinguishability of two identical photons in the experiments are illustrated. It is demonstrated, using a simple formalism valid simultaneously for fermions and for bosons, that there exists an isomorphism giving theoretical foundation to distinguishing two identical particles. But the distinguishing has a limited range of exact applicability. In most cases of interest, only the indistinguishability approach has a first-principle (and universal) validity.
The second-order interference of two independent photons with different spectra in a Shih–Alley/Hong–Ou–Mandel interferometer is studied in Feynman’s path integral theory. There is a second-order interference pattern for photons with different spectra if the photons are indistinguishable for the employed detection system. The conditions to observe the second-order temporal beating with photons of different spectra are analyzed. The influence of the response time of the detection system on the observed second-order interference pattern is also discussed. It is a direct result of that measurement in quantum mechanics is dependent on the employed measuring apparatus. The results are helpful to understand the physics of two-photon interference in different schemes.