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Two-photon interference (TPI) lies at the heart of photonic quantum technologies. TPI is generally regarded as quantum interference stemming from the indistinguishability of identical photons, hence a common intuition prevails that TPI would disappear if photons are distinguishable. Here we disprove this perspective and uncover the essence of TPI. We report the first demonstration of TPI between distinguishable photons with their frequency separation up to $10^4$ times larger than their linewidths. We perform time-resolved TPI between an independent laser and single photons with ultralong coherence time ($>10\ \mu$s). We observe a maximum TPI visibility of $72\%\pm 2\%$ well above the $50\%$ classical limit indicating the quantum feature, and simultaneously a broad visibility background and a classical beat visibility of less than $50\%$ reflecting the classical feature. These visibilities are independent of the photon frequency separation and show no difference between distinguishable and indistinguishable photons. Based on a general wave superposition model, we derive the cross-correlation functions which fully reproduce and explain the experiments. Our results reveal that TPI as the fourth-order interference arises from the second-order interference of two photons within the mutual coherence time and TPI is not linked to the photon indistinguishability. This work provides new insights into the nature of TPI with great implications in both quantum optics and photonic quantum technologies., Comment: 7 pages, 5 figures. Comments are welcome. arXiv admin note: substantial text overlap with arXiv:2404.05158

Two-photon interference (TPI) is a fundamental phenomenon in quantum optics and plays a crucial role in quantum information science and technology. TPI is commonly considered as quantum interference with an upper bound of $100\%$ for both the TPI visibility and the beat visibility in contrast to its classical counterpart with a maximum visibility of $50\%$. However, this is not always the case. Here we report a simultaneous observation of quantum and classical TPI of single photons with ultralong coherence time which is longer than the photon correlation time by five orders of magnitude. We observe a TPI visibility of $94.3\%\pm 0.2\%$ but a beat visibility of $50\%$. Besides an anti-bunching central dip due to single-photon statistics, we observe two bunching side peaks in cross-correlation curves for indistinguishable photons. Using either classical wave superposition theory or quantum field approach, we derive the same expressions for the cross-correlation functions which reproduce and explain the experiments well. We conclude that quantum TPI with a stream of single photons is equivalent to classical TPI, both of which are the fourth-order interference arising from the second-order interference occurring on the time scale of photon coherence time., Comment: 7 pages, 4 figures, Comments are welcome

Laser light possesses perfect coherence, but cannot be attenuated to single photons via linear optics. An elegant route to convert laser light into single photons is based on photon blockade in a cavity with a single atom in the strong coupling regime. However, the single-photon purity achieved by this method remains relatively low. Here we propose an interference-based approach where laser light can be transformed into single photons by destructively interfering with a weak but super-bunched incoherent field emitted from a cavity coupling to a single quantum emitter. We demonstrate this idea by measuring the reflected light of a laser field which drives a double-sided optical microcavity containing a single artificial atom-quantum dot (QD) in the Purcell regime. The reflected light consists of a superposition of the driving field with the cavity output field. We achieve the second-order autocorrelation g2(0)=0.030+-0.002 and the two-photon interference visibility 94.3%+-0.2. By separating the coherent and incoherent fields in the reflected light, we observe that the incoherent field from the cavity exhibits super-bunching with g2(0)=41+-2 while the coherent field remains Poissonian statistics. By controlling the relative amplitude of coherent and incoherent fields, we verify that photon statistics of reflected light is tuneable from perfect anti-bunching to super-bunching in agreement with our predictions. Our results demonstrate photon statistics of light as a quantum interference phenomenon that a single QD can scatter two photons simultaneously at low driving fields in contrast to the common picture that a single two-level quantum emitter can only scatter (or absorb and emit) single photons. This work opens the door to tailoring photon statistics of laser light via cavity or waveguide quantum electrodynamics and interference., Comment: Comments are welcome

We reinterpret jet clustering as an axis-finding procedure which, along with the proton beam, defines the virtual-photon transverse momentum $q_T$ in deep inelastic scattering (DIS). In this way, we are able to probe the nucleon intrinsic structure using jet axes in a fully inclusive manner, similar to the Drell-Yan process. We present the complete list of azimuthal asymmetries and the associated factorization formulae at leading power for deep-inelastic scattering of a nucleon. The factorization formulae involve both the conventional time-reversal-even (T-even) jet function and the T-odd one, which have access to all transverse-momentum-dependent parton distribution functions (TMD PDFs) at leading twist. Since the factorization holds as long as $q_T \ll Q$, where $Q$ is the photon virtuality, the jet-axis probe into the nucleon structure should be feasible for machines with relatively low energies such as the Electron-Ion Collider in China (EicC). We show that, within the winner-take-all (WTA) axis-finding scheme, the coupling between the T-odd jet function and the quark transversity or the Boer-Mulders function could induce sizable azimuthal asymmetries at the EicC, the EIC and HERA. We also give predictions for the azimuthal asymmetry of back-to-back dijet production in $e^+e^-$ annihilation at Belle and other energies., Comment: 19 pages, 9 figures