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Recently, great progress has been made in the entanglement of multiple photons at various wavelengths and in different degrees of freedom for optical quantum information applied in diverse scenarios. However, multi-photon entanglement in the transmission window of green light under the water has not been reported yet. Here, by combining femtosecond laser based multi-photon entanglement and entanglement-maintaining frequency upconversion techniques, we successfully generate a green two-photon polarization-entangled Bell state and a green three-photon Greenberger-Horne-Zeilinger (GHZ) state, whose state fidelities are 0.893$\mathbf{\pm}$0.002 and 0.595$\mathbf{\pm}$0.023, respectively. Our result provides a scalable method to prepare green multi-photon entanglement, which may have wide applications in underwater quantum information., Comment: 8 pages, 4 figures

High-order quantum coherence reveals the statistical correlation of quantum particles. Manipulation of quantum coherence of light in temporal domain enables to produce single-photon source, which has become one of the most important quantum resources. High-order quantum coherence in spatial domain plays a crucial role in a variety of applications, such as quantum imaging, holography and microscopy. However, the active control of high-order spatial quantum coherence remains a challenging task. Here we predict theoretically and demonstrate experimentally the first active manipulation of high-order spatial quantum coherence by mapping the entanglement of spatially structured photons. Our results not only enable to inject new strength into current applications, but also provide new possibilities towards more wide applications of high-order quantum coherence., Comment: 11 pages, 5 figures

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., Comment: Accepted by Physical Review Letters

Optical orbital angular momentum (OAM), as an important degree of freedom of light, has been attracted extensive attention, due to its intrinsic feature of natural discrete infinite dimension. Manipulation of OAM spectra is crucial for many impressive applications from classical to quantum realms, in particular, nonlinear manipulation of OAM spectra. Here we realized the nonlinear manipulation of OAM spectra by using the simultaneous second- and third-harmonic generation in a single nonlinear crystal of quasi-periodically poled potassium titanyl phosphate, for fundamental waves with a variety of OAM spectra, especially for customized OAM spectra of the second and third harmonics. The experimental results confirmed the theoretical predictions. Our approach not only provides a novel way to manipulate OAM spectra at new shorter wavelengths that are hard to be directly generated, but also may find new applications towards multiplexing in classical optics and high-dimensional information processing in quantum optics., Comment: 5 pages, 4 figures

Nonlinear optical processes of spatially structured light, including optical vortex and vector optical fields, have stimulated a lot of interesting physical effects and found a variety of important applications ranging from optical imaging to quantum information processing. However, high harmonic generation of vector optical fields with space-varying polarization states is still a challenge. Here we demonstrate third harmonic generation of spatially structured light including vector optical fields, in a nonlinear Sagnac interferometer containing a carefully designed quasi-periodically poled potassium titanyl phosphate for the first time. The experimental results are in good agreement with the theoretical predictions. Our results will enable to manipulate spatially structured light or photons at new wavelengths and carrying higher orbital angular momentum. Our approach has the potential applications for the research of optical skyrmions and may open up new opportunities to produce spatially structured entangled photons for quantum communication and computation., Comment: 5 pages, 3 figures