Spontaneousparametric down-conversion (SPDC) is a well-developed tool to produce entangled photons for practical applications, such as quantum imaging [1][2][3], quantum key distribution [4,5] and quantum metrology [6,7], as well as for tests of quantum mechanics [8]. So far, SPDC sources have exclusively been used in the phase matched regime: when the emitted daughter photons conserve the momentum of the pump photon. Phase matched SPDC restricts both the choice of non-linear materials and the available states the daughter photons can occupy. This has prompted the search for SPDC where phase matching is absent [9][10][11][12]. Here we register over 1000 photon pairs per second generated in a micrometer-sized SPDC source continuously pumped at a moderate power. This is both the smallest SPDC source reported to date and, due to the relaxed phase matching, an entirely new type of two-photon radiation. Reducing the interaction length and localizing the position of the daughter photons creation leads to a huge uncertainty in their momentum. The uncertain momentum mismatch leads to a frequency-angular spectrum an order of magnitude broader than that of phase matched SPDC. This results in record breaking spatio-temporal correlation widths and huge entanglement. We believe that similar sources can be realized on thinner platforms, not only compounding the aforementioned effects, but also allowing easy integrability on optical chips.For SPDC, the probability of a pump photon, with momentum k p (wavevector k p ), to decay into two daughter photons, signal and idler with momenta k s,i (wavevectors k s,i ), strongly depends on the momentum (wavevector) mismatch ∆k ≡ k s + k i − k p . The allowed mismatch forms an uncertainty relation with the volume over which the non-linear interaction takes place. Its component parallel to the pump, or longitudinal mismatch ∆k || , is restricted by the inverse length of the nonlinear material. The component perpendicular to the pump, or transverse mismatch ∆k ⊥ , is restricted by the inverse non-linear interaction area, which is generally given by the Gaussian profile of the pump beam.In a phase-matched process, ∆k || = 0, the longitu-dinal momentum of the pump photon is conserved by the daughter photons. However, this is a special case and is only satisfied in a few non-linear materials with the appropriate electronic and optical properties. More generally ∆k || = 0, causing pairs to be generated in or out of phase with respect to pairs generated earlier in the non-linear material. The relative phase difference depends on the non-linear interaction length, L. If L is equal to an odd multiple of the so called coherence length, L c = π ∆k || [13], the interference between the emitted pairs is fully constructive leading to a local maximum in the emission probability. At L < L c , the pairs are always generated in phase. Moreover, with small length L, the allowed longitudinal mismatch can be very large, which leads to a very broad spectrum of emitted photons, both in frequency and in angle. F...
In counterfactual quantum key distribution (CQKD) information is transferred, in a secure way, between Alice and Bob even when no particle carrying the information is in fact transmitted between them. In this letter we fully implement the scheme for CQKD proposed in [1], demonstrating for the first time that information can be transmitted between two parties without the transmission of a carrier
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric downconversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.
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