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Optics Express

Modelling parametric down-conversion yielding spectrally pure photon pairs

Fabian Laudenbach, Hannes Hübel, Michael Hentschel, Philip John Walther, Andreas Poppe

Published Feb 2, 2016• 30 citations
Publisher

Abstract

Pair creation by spontaneous parametric down-conversion (SPDC) has become a reliable source for single-photon states, used in many kinds of quantum information experiments and applications. In order to be spectrally pure, the two photons within a generated pair should be as frequency-uncorrelated as possible. For this purpose most experiments use narrow bandpass filters, having to put up with a drastic decrease in count rates. This article elaborates (theoretically and by numerical evaluation) the alternative method to engineer a setup such that the SPDC-generated quantum states are intrinsically pure. Using pulsed pump lasers and periodically poled crystals this approach makes bandpass filtering obsolete and allows for significantly higher output intensities and therefore count rates in the detectors. After numerically scanning all common wavelength regimes, polarisation configurations and three different non-linear crystals, we present a broad variety of setups which allow for an implementation of this method.

DOI
10.1364/oe.24.002712

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Pair creation by spontaneous parametric down-conversion (SPDC) has become a reliable source for single-photon states, used in many kinds of quantum information experiments and applications. In order to be spectrally pure, the two photons within a generated pair should be as frequency-uncorrelated as possible. For this purpose most experiments use narrow bandpass filters, having to put up with a drastic decrease in count rates. This article elaborates (theoretically and by numerical evaluation) the alternative method to engineer a setup such that the SPDC-generated quantum states are intrinsically pure. Using pulsed pump lasers and periodically poled crystals this approach makes bandpass filtering obsolete and allows for significantly higher output intensities and therefore count rates in the detectors. After numerically scanning all common wavelength regimes, polarisation configurations and three different non-linear crystals, we present a broad variety of setups which allow for an implementation of this method.
Spontaneous parametric down-conversion (SPDC) is a reliable and robust source of photons for quantum information applications. For applications that involve operations such as entanglement swapping or single-photon heralding, two-photon states are required to be factorable (uncorrelated) in their spectral and spatial degrees of freedom. We report the design and experimental characterization of an SPDC source that has been optimized for high spectral and spatial purity. The source is pumped by the 776 nm output of a mode-locked Ti:Sapphire laser and consists of a periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal phase-matched for collinear type-II SPDC. The dispersive properties of PPKTP at these wavelengths is such that it is possible to minimize the spectral entanglement by matching the widths of the pump to the spectral phase-matching function. The spatial entanglement is minimized through careful control of the pump focus, yielding nearly single-mode emission. An advantage of this approach is that the emission rate into the collection modes is very high, resulting in a very bright SPDC source. We also report a scheme that employs the output of collinear sources such as these to produce polarization-entangled photon pairs. The scheme, which requires only simple polarization elements, can be scaled to N-photon GHZ states.
Spontaneous parametric downconversion (SPDC) sources are an essential element of quantum communication and quantum information processing systems. Their quality can be hampered by spectral, temporal, or spatial distinguishability of the two photons of a generated pair. Even when such defects have been corrected, the ultimate quality of the SPDC source is limited by the intrinsic multiple pair generation. In this paper, the effect of transmission, filtering and detection losses and asymmetrical spectral bandwidths in the photon pair paths on the visibility of the two-photon interference delivered by the SPDC source and its useful pair rate are investigated. In this investigation, two subcases are distinguished: deterministic and statistical splittings of the generated pairs, whatever the coherence of the multiple pairs. We show that the visibility is strongly degraded by a spectral bandwidth asymmetry, while the losses mainly affect the measured coincidence probability. The deterministic splitting configuration is shown to be generally more advantageous, although statistical splitting may present some advantages in applications with a narrow bandwidth requirement, such as those involving quantum memories. Moreover, while pump-induced optical noise only produces small visibility reductions, dark counts of the single-photon detectors are shown to limit the maximum possible visibility, particularly in the case of high-loss photon pair sources. Because our model quantifies the intrinsic limitations due to double pair emission in a simple way, the results presented can be used to optimize the design of SPDC sources and choose the optimum trade-offs between several key parameters such as visibility, generation probabilities, and spectral bandwidth, in particular for small bandwidth SPDC sources in the perspective of quantum networking and computing applications.
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.
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.
Spontaneous parametric down-conversion (SPDC) in nonlinear crystals is the most commonly used means to generate single photon pairs for quantum key distribution systems [1]. By using waveguides instead of bulk crystals, highly efficient devices can be obtained. Both, type-I and type-II phase-matched integrated devices have been demonstrated in periodically poled lithium niobate (PPLN) [2–4]. Although the type-II process is less efficient, it has two favourable properties: the spectrum of down-converted photons is narrower compared to type-I and orthogonally polarised photons are emitted.
Spontaneous parametric down-conversion (SPDC) is one of the most important sources for entangled or correlated photon pairs, which are the foundation of the emerging fields of quantum-optical imaging and spectroscopy. Using periodically poled materials as an SPDC-source allows broad emission spectra in widely tunable wavelength ranges in an efficient and walk-off-free process. For applications that employ nonlinear interference setups, maximum interferometric contrast is only achieved when signal and idler modes are overlapped precisely in the second crystal. Thus, accurate knowledge of the spectral-angular characteristic of SPDC is crucial for designing such devices.