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Time-frequency duality plays a pivotal role in modern optical science and engineering. Conventional duality, which is connected by one-dimensional Fourier transformation, is insufficient for characterizing quantum mechanical correlations in the time-frequency behavior of multiple photons; a higher-dimensional treatment is required. The authors directly measure the two-photon distributions of generated biphotons in both frequency and time domains, and show that they satisfy the Fourier-limited condition in two-dimensional time and frequency space, but not in conventional one-dimensional space. This study helps to pave the way to tomorrow's quantum optical technologies.

Multiparticle interference is a fundamental phenomenon in the study of quantum mechanics.It was discovered in a recent experiment [Ra, Y.-S. et al, Proc. Natl Acad. Sci. USA \textbf{110}, 1227(2013)] that spectrally uncorrelated biphotons exhibited a nonmonotonic quantum-to-classical transition in a four-photon Hong-Ou-Mandel (HOM) interference. In this work, we consider the same scheme with spectrally correlated photons.By theoretical calculation and numerical simulation, we found the transition not only can be nonmonotonic with negative-correlated or uncorrelated biphotons, but also can be monotonic with positive-correlated biphotons. The fundamental reason for this difference is that the HOM-type multi-photon interference is a differential-frequency interference. Our study may shed new light on understanding the role of frequency entanglement in multi-photon behavior., Comment: 8 pages, 2 figures

We report on the experimental generation of an entangled state with a spectrally pure heralded single-photon state and a weak coherent state. By choosing group-velocity matching in the nonlinear crystal, our system for producing entangled photons was 60 times brighter than that in the earlier experiment [Phys. Rev. Lett. 90, 240401 (2003)], with no need of bandpass filters. This entanglement system is useful for quantum information protocols that require indistinguishable photons from independent sources., Comment: 7 pages, 5 figures

We demonstrate a Hong-Ou-Mandel interference between two independent, intrinsically pure, heralded single photons from spontaneous parametric down-conversion (SPDC) at telecommunication wavelength. A visibility of $85.5\ifmmode\pm\else\textpm\fi{}8.3%$ was achieved without using any bandpass filter. Thanks to the group-velocity-matched SPDC and superconducting nanowire single-photon detectors (SNSPDs), the fourfold coincidence counts are one order higher than that in the previous experiments. The combination of bright single-photon sources and SNSPDs is a crucial step for future practical quantum infocommunication systems at telecommunication wavelength.

We present an experiment of nonclassical interference between an intrinsically pure heralded single-photon state and a weak coherent state. Our experiment demonstrates that, without the use of bandpass filters, spectrally pure single photons can have high-visibility ($89.4\ifmmode\pm\else\textpm\fi{}0.5%$) interference with photons from a weak coherent field. Our scheme lays the groundwork for future experiments requiring quantum interference between photons in nonclassical states and those in coherent states.

Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the measurement of the photonic de Broglie wavelength of entangled photon pairs (biphotons) generated by spontaneous parametric down-conversion. The observed interference manifests the concept of the photonic de Broglie wavelength. We also discuss the phase uncertainty obtained from the experiment.