Hong-Ou-Mandel Interference between Two Hyper-Entangled Photons Enables Observation of Symmetric and Anti-Symmetric Particle Exchange Phases

TL;DR

This paper demonstrates two-photon Hong-Ou-Mandel interference across multiple degrees of freedom, revealing symmetric and anti-symmetric exchange phases, and expands the Hilbert space to measure phases previously unobservable.

Contribution

It introduces a method to observe hyper-entangled two-photon interference in polarization and OAM, enabling measurement of exchange phases in expanded Hilbert space.

Findings

Observed hyper-entangled two-photon interference in polarization and OAM.

Measured symmetric exchange phases close to theoretical predictions.

Demonstrated anti-symmetric exchange phase consistent with theory.

Abstract

Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The exiting researches on two-photon interference were mainly limited in one degree of freedom (DoF), hence it is still a challenge to realize the quantum interference in multiple DoFs. Here we demonstrate the HOM interference between two hyper-entangled photons in two DoFs of polarization and orbital angular momentum (OAM) for all the sixteen hyper-entangled Bell states. We observe hyper-entangled two-photon interference with bunching effect for ten symmetric states (nine Boson-Boson states, one Fermion-Fermion state) and anti-bunching effect for six anti-symmetric states (three Boson-Fermion states, three Fermion-Boson states). More interestingly, expanding the Hilbert space by introducing an extra DoF for two photons enables to transfer the unmeasurable external phase in the initial DoF to a measurable internal phase in the expanded two DoFs. We directly measured the symmetric exchange phases being $0.012 \pm 0.002$, $0.025 \pm 0.002$ and $0.027 \pm 0.002$ in radian for the three Boson states in OAM and the anti-symmetric exchange phase being $0.991 \pi \pm 0.002$ in radian for the other Fermion state, as theoretical predictions. Our work may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DoFs.