Spontaneous parametric down-conversion (SPDC) has shown great promise in the generation of pure and indistinguishable single photons. Photon pairs produced in bulk crystals are highly correlated in terms of transverse space and frequency. These correlations limit the indistinguishability of photons and result in inefficient photon sources. Domain-engineered crystals with a Gaussian nonlinear response have been explored to minimize spectral correlations. Here we study the impact of such domain engineering on spatial correlations of generated photons. We show that crystals with a Gaussian nonlinear response reduce the spatial correlations between photons. However, the Gaussian nonlinear response is not sufficient to fully eliminate the spatial correlations. Therefore, the development of a comprehensive method to minimize these correlations remains an open challenge. Our solution to this problem involves simultaneous engineering of the pump beam and crystal. We achieve purity of single-photon state up to 99% without any spatial filtering. Our findings provide valuable insights into the spatial waveform generated in structured SPDC crystals, with implications for applications such as boson sampling.
Spontaneous parametric down-conversion (SPDC) has shown great promise in the generation of pure and indistinguishable single photons. Photon pairs produced in bulk crystals are highly correlated in terms of transverse space and frequency. These correlations limit the indistinguishability of photons and result in inefficient photon sources. Domain-engineered crystals with a Gaussian nonlinear response have been explored to minimize spectral correlations. Here we study the impact of such domain engineering on spatial correlations of generated photons. We show that crystals with a Gaussian nonlinear response reduce the spatial correlations between photons. However, the Gaussian nonlinear response is not sufficient to fully eliminate the spatial correlations. Therefore, the development of a comprehensive method to minimize these correlations remains an open challenge. Our solution to this problem involves simultaneous engineering of the pump beam and crystal. We achieve purity of single-photon state up to 99% without any spatial filtering. Our findings provide valuable insights into the spatial waveform generated in structured SPDC crystals, with implications for applications such as boson sampling.
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.
Entanglement generated by Spontaneous Parametric Down Conversion (SPDC) involves multiple, often mutually correlated degrees of freedom. These degrees of freedom are often treated independently, overlooking the intrinsic correlation between them. We focus on the spatial spectral correlations that, if left uncontrolled, introduce distinguishability and reduce coherence, undermining applications such as high-dimensional OAM encoding. We analyze the spatio spectral structure of the biphoton and identify source configurations enabling a strong reduction of such correlations. We then quantify how spatial spectral coupling degrades OAM spatial purity, mapping high-purity regions as functions of OAM order, crystal length, and pump/collection waists. The resulting design parameters enable engineering bright, high purity OAM entangled sources, reducing the need for loss-introducing filtering and therefore supporting scalable high-dimensional photonic quantum technologies.
Summary form only given. Parametric downconversion (PDC) allows the generation of highly coherent, spectrally pure single photons for quantum photonics. In a typical heralded PDC source, the signal photon emerges in a spectrally mixed state due to strong (anti)correlation in the joint spectrum of PDC photon pairs.One method for reducing spectral correlations is spectral filtering, but this compromises the heralding efficiency and the brightness of the source. A more sophisticated method for increasing the heralded photon purity is group-velocity matching, which works by erasing part of the timing information between the pump and PDC photons. What group-velocity matching cannot address, however, are the remaining correlations in the joint spectrum that come from the sinc-shaped phase-matching function (PMF) typical to standard PDC crystals. Further source engineering is therefore required to remove these correlations. Several studies have introduced domain-engineering techniques for shaping the phase matching function (PMF) in periodically poled crystals to improve single photon purities [1-4]. We present a new technique for tailoring crystal nonlinearities which combines the advantages of a deterministic method for domain engineering [4] and an annealing method developed for classical applications in higher-harmonic generation [5]. In our method, we first choose each domain orientation such that the generated field amplitude along the crystal matches the target field amplitude obtained by integrating the desired nonlinearity profile. Using a one-block structure instead of a two-blocks structure (as in [4]) results in a higher flexibility of the algorithm in tracking the target function and yields to more accurate results. We then use an annealing algorithm to slightly vary the width of each domain, further improving the effective PMF. Our technique outperforms its predecessors, particularly for short crystals, leading to high single photon purities, as shown in Fig.1. We experimentally characterise our method through a high-precision measurement of multiphoton interference between two heralded photons generated by two independent sources.We also notice that by considering a complex target field amplitude function it is possible to generalise the algorithm in [5] to any constant domain width (not necessarily equal to the coherence length), leading to a better approximation of the desired phase matching function, especially in the very short crystal regime. Moreover, tracking both the real and imaginary components of the target function allows us to approximate more exotic cases such as chirped nonlinearity profiles. Since scalable quantum photonics will require integrated architectures in which nonlinear processes are typically employed for single-photon generation, it will be interesting to explore new techniques similar to in-fibre Bragg grating structures which might yield quasi-periodic four-wave mixing and apply our algorithm to these new platforms.
Single-mode-fiber-coupled spontaneous parametric down-conversion (SPDC) sources are a key resource for photonic quantum technologies, but in single-crystal geometries brightness, heralding efficiency, and spectral purity remain constrained by intrinsic trade-offs. Here, we show how nonlinear interference in a cascaded two-crystal type-II SPDC source can be used to engineer the modal structure of SPDC emission, improving the brightness--heralding-efficiency trade-off by more than one order of magnitude beyond the single-crystal limit. We further demonstrate two routes to near-unity spectral purity while retaining high brightness and/or heralding efficiency, even with standard periodically poled crystals, and study the additional advantages of aperiodic poling with Gaussian phase matching. Using a spectrally resolved Laguerre--Gauss modal decomposition, we show that these improvements arise from mode-selective interference of spatial-spectral SPDC modes within the nonlinear interferometer. We experimentally validate the model through sum-frequency-generation measurements of the spatial-spectral state.
Abstract Introducing structure into photon pair generation via spontaneous parametric down‐conversion (SPDC) is shown to be useful for controlling the output state and exploiting new degrees of freedom for quantum technologies. This paper presents a new method for simulating first‐ and second‐order correlations of the down‐converted photons in the presence of structured pump beams and shaped nonlinear photonic crystals. This method is nonperturbative, and thus accounts for high‐order effects, and can be made very efficient using parallel computing. Experimental results of photodetection and coincidence rates in complex spatial configurations are recovered quantitatively by this method. These include SPDC in 2D nonlinear photonic crystals, as well as with structured light beams such as Laguerre Gaussian and Hermite Gaussian beams. This simulation method reveals conservation rules for the down‐converted signal and idler beams that depend on the nonlinear crystal modulation pattern and the pump shape. This scheme can facilitate the design of nonlinear crystals and pumping conditions for generating non‐classical light with pre‐defined properties.
Photon sources based on spontaneous parametric down-conversion (SPDC) are central to experimental quantum optics and quantum technologies. Their performance is commonly quantified by three metrics: pair-collection probability, heralding efficiency, and spectral purity. In bulk-crystal SPDC, these metrics are known to be mutually constrained, yet the physical origin of the resulting trade-offs is often obscured. We show that these trade-offs originate from the frequency-dependent population of discrete spatial modes in the SPDC emission. By performing a Laguerre-Gauss mode decomposition at each frequency component, we show how spectral-spatial non-separability impacts collection probability, heralding efficiency, and purity. We apply this framework to two widely used quasi-phase-matching configurations: collinear degenerate type-0 and type-II SPDC in periodically poled bulk crystals, and quantify how different phase-matching functions shape the spectral-spatial mode structure. In particular, for type-II SPDC we compare standard periodically poled and aperiodically poled Gaussian phase matching. We experimentally validate some of our theoretical results using spatial- and spectral-projection measurements. This spectral-spatial mode analysis provides a quantitative and predictive framework for understanding and engineering bulk-crystal photon sources, enabling systematic multi-parameter optimization beyond qualitative design guidelines.