We investigate the methods to obtain maximum correlated photon pairs generated in Type I spontaneous parametric down conversion (SPDC) with focused pump beam. We study the effect of pump focusing on the photon collection efficiency of signal and idler modes. The correlated photon pair collection efficiency decreases asymptotically with input pump beam focusing parameter [1]. The results obtained here are expected to be useful in designing appropriate optical fibers for generating efficient entangled photon sources for quantum information applications.
We investigate the methods to obtain maximum correlated photon pairs generated in Type I spontaneous parametric down conversion (SPDC) with focused pump beam. We study the effect of pump focusing on the photon collection efficiency of signal and idler modes. The correlated photon pair collection efficiency decreases asymptotically with input pump beam focusing parameter [1]. The results obtained here are expected to be useful in designing appropriate optical fibers for generating efficient entangled photon sources for quantum information applications.
Both correlated-mode coupling efficiency and photon pair flux (brightness) of spontaneous parametric down-conversion (SPDC) coupled into single-mode fibers are key parameters for various quantum information science applications. We present an experimental investigation on the optimization of the correlated-mode coupling efficiency and the brightness of frequency-degenerated SPDC photon pairs into single-mode optical fibers. Using photon pairs generated from a type-I phase-matched bulk $\ensuremath{\beta}$-barium borate crystal pumped by a continuous-wave laser, we carefully evaluated both the correlated-mode coupling efficiency and the brightness of SPDC light coupled to a single-mode optical fiber, while continuously changing the focusing of the pump and collection modes, experimenting with Rayleigh lengths from 3 to 280 (for the pump) and 0.2 to 20 (for the collection) times the crystal length. The measured data suggest that the correlated-mode coupling efficiency can be close to unity for any pump focus, however, the optimal Rayleigh length of the collection mode depends on the pump focus parameter, and the brightness can be increased by tightening the pump focus, provided that the Rayleigh length of the collection mode is precisely adjusted. A maximal correlated-mode coupling efficiency of $99.0\ifmmode\pm\else\textpm\fi{}1.3%$ was experimentally achieved. These results will be useful for photonic quantum science and technology using SPDC sources with high heralding efficiencies.
I investigate the properties of spontaneous parametric down-conversion (SPDC) involving collinear Gaussian spatial modes for the pump and the photon collection optics. Approximate analytical and numerical results are obtained for the peak spectral density, photon bandwidth, pair collection probability, heralding ratio, and spectral purity as a function of crystal length and beam-focusing parameters. I address the optimization of these properties individually as well as jointly, and find focusing conditions that simultaneously bring the pair collection probability, heralding ratio, and spectral purity to near-optimal values. These properties are also found to be nearly scale invariant, that is, ultimately independent of crystal length. The results obtained here are expected to be useful for designing SPDC sources with high performance in multiple categories for the next generation of SPDC applications.
Photon modes have an important role in characterizing the quantum sources of light. Proper coupling of various photon modes obtained in spontaneous parametric down conversion (SPDC) process in optical fibers is essential to generate an effective source of entangled photons. The two main pre-detection factors affecting the biphoton mode coupling in SPDC are the pump beam focusing parameter and the crystal thickness. We present the numerical and experimental results on the effect of pump focusing on conditional down-converted photon modes for a Type-I BBO crystal. We experimentally verify that biphoton coupling efficiency decreases asymptotically with pump beam focusing parameter. We attribute this behaviour to (a) the asymmetry in the spatial distribution of down-converted photons with the pump beam focusing parameter and (b) the ellipticity of biphoton modes introduced due to the focusing of the pump beam. We also show experimentally the ellipticity as well as quantify the asymmetry with the pump focusing parameter. These results may be useful in selecting optimum conditions in the down-conversion process for generating efficient sources of entangled photons for quantum information applications.
From quantum computation to quantum key distribution, many quantum-enhanced applications rely on the ability to generate pure single photons. Even though the process of spontaneous parametric downconversion (SPDC) is widely used as the basis for photon-pair sources, the conditions for pure heralded single-photon generation, taking into account both spectral and spatial degrees of freedom, have not been fully described. We present an analysis of the spatio-temporal correlations present in photon pairs produced by type-I, non-collinear SPDC. We derive a set of conditions for full factorability in all degrees of freedom—required for the heralding of pure single photons—between the signal and idler modes. In this paper, we consider several possible approaches for the design of bright, fiber-coupled and factorable photon-pair sources. We show through numerical simulations of the exact equations that sources based on: (i) the suppression of spatio-temporal entanglement according to our derived conditions and (ii) a tightly focused pump beam together with optimized fiber-collection modes and spectral filtering of the signal and idler photon pairs, lead to a source brightness of the same order of magnitude. Likewise, we find that both of these sources lead to a drastically higher factorable photon-pair flux, compared to an unengineered source.
Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.
Spontaneous parametric down-conversion (SPDC) is a widely used process to prepare entangled photon pairs. In SPDC, a second-order nonlinear crystal is pumped by a coherent laser beam to generate photon pairs. The photon pairs are usually detected by single-mode fibers (SMF), where only photons in a Gaussian mode can be collected. The collection modes possess typical Gaussian parameters, namely a beam waist and a focal plane position. The collection efficiency of photons highly depends on the choice of both parameters. The exact focal plane position of the pump beam relative to those of the detection modes is difficult to determine in a real experiment. Usually, theoretical and experimental studies assume that the focal plane positions of the pump and the generated beams are positioned in the center of the crystal. The displacement of beam focal planes can lead to deviations from expected results and the coupling efficiency into SMF can increase or decrease. In this work, we consider variable positions of focal planes and investigate how shifts of these focal planes influence the spatial and temporal properties of photon pairs. We present SPDC arrangements, in which the knowledge of the exact position of the focal planes is essential, as well as scenarios, where focal plane displacements do not contribute significantly to experimental outcomes. These findings are of particular interest for achieving higher efficiency in SPDC experiments.