The spectral properties of entangled photon pairs generated via quasi-phased matching in spontaneous parametric down-conversion are proposed and demonstrated experimentally.A general mathematical model for evaluating the spectral properties is developed to obtain the spectrum shape and range of down-converted photons.The model takes into account the effects of phase mismatching due to non-ideal pumping and the relationship between crystal periodic modulation function and the incidence angle of the pump beam.The spectrum curve shape is determined by the discrete Fourier transform of a Gaussian pump beam and the integration of parametric down-conversion generated by an individual plane wave.An experiment is carried out with a PPLN non-linear crystal and dispersing optics, which shows a good consistency in their spectral ranges and shapes with our model predictions within the spectrum of 600-633 nm.This therefore illustrates that both the simulation model and the experimental process are reasonable.This novel method has potential applications in high-accuracy calibration in the wide spectrum using correlated photons.
The spectral properties of entangled photon pairs generated via quasi-phased matching in spontaneous parametric down-conversion are proposed and demonstrated experimentally.A general mathematical model for evaluating the spectral properties is developed to obtain the spectrum shape and range of down-converted photons.The model takes into account the effects of phase mismatching due to non-ideal pumping and the relationship between crystal periodic modulation function and the incidence angle of the pump beam.The spectrum curve shape is determined by the discrete Fourier transform of a Gaussian pump beam and the integration of parametric down-conversion generated by an individual plane wave.An experiment is carried out with a PPLN non-linear crystal and dispersing optics, which shows a good consistency in their spectral ranges and shapes with our model predictions within the spectrum of 600-633 nm.This therefore illustrates that both the simulation model and the experimental process are reasonable.This novel method has potential applications in high-accuracy calibration in the wide spectrum using correlated photons.
Tailoring spectral properties of photon pairs is of great importance for optical quantum information and measurement applications. High-resolution spectral measurement is a key technique for engineering spectral properties of photons, making them ideal for various quantum applications. Here we demonstrate spectral measurements and optimization of frequency-entangled photon pairs produced via spontaneous parametric downconversion (SPDC), utilizing frequency-resolved sum-frequency generation (SFG), the reverse process of SPDC. A joint phase-matching spectrum of a nonlinear crystal around 1580 nm is captured with a 40 pm resolution and a > 40 dB signal-to-noise ratio, which is significantly improved compared to traditional frequency-resolved coincidence measurements. Moreover, our scheme is applicable to collinear degenerate sources whose characterization is difficult with previously demonstrated stimulated difference frequency generation (DFG). We also illustrate that the observed phase-matching function is useful for finding an optimal pump spectrum to maximize the spectral indistinguishability of SPDC photons. We expect that our precise spectral characterization technique will be useful tool for characterizing and tailoring SPDC sources for a wide range of optical quantum applications.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
Using a multidimensional Gaussian approximation of the wave function for the signal and idler light generated by spontaneous parametric down-conversion, we derive analytical expressions for the second-order coherence function and the fourth-order coherence function (which is proportional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widths determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these parameters are governed by the pump-beam waist, the pump spectral width, and the crystal length. We thereby derive relations analogous to the van Cittert--Zernike theorem and the Siegert relation for thermal light. We show that the normalized photon coincidence rate decreases sharply as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrically down-converted light obtained from a LiIO3 crystal pumped by Kr+-ion laser radiation at 413 nm. \textcopyright{}1996 The American Physical Society.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.
In this work we study the transverse spatial correlation of the pair of photons generated via the process of spontaneous parametric frequency down-conversion, in periodically poled non-linear crystals illuminated by a pulsed laser beam. It is well known that the two-photon state generated in quasi-phase matching (QPM) configurations depends explicitly on the characteristics of the pump beam, on the crystal modulated non-linearity, and on the detection geometry. This has allowed the development of several techniques for controlling the biphoton spectral and spatial properties. Here we discuss another technique for implementing the spatial entanglement modification in QPM gratings. We show, theoretically and experimentally, that in nearly collinear geometries, the spatial shape modulation of the pump beam allows for the control of the biphoton transverse spatial correlation.
Spontaneous Parametric Down-conversion (SPDC) is now routinely used to generate photon pairs for imaging, spectroscopy, and quantum information and metrology. However, the peculiar spectro-spatial properties of SPDC beams are not always known from the largest audience: they can give rise to ring-like beams, depending on the temperature, the wavelengths and pump focusing. This has to be considered for imaging or long-range applications. We will show examples of such beams created in 532-pumped PPLN or PPKTP and 1064-nm-pumped PPLN crystals. With a simple model of noncolinear phase matching we will give physical insight into the phenomena and explain the role of the signal/idler group delay. We will also explain how aperiodic crystals could be useful.