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arXiv:1410.0941 · IEEE Journal of Selected Topics in Quantum Electronics

Enhancing Heralding Efficiency and Biphoton Rate in Type-I Spontaneous Parametric Down-Conversion

Hannah E. Guilbert, Daniel J. Gauthier

Published Nov 26, 2014• 9 citations
arXivHTMLPDF

Abstract

The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.

DOI
10.1109/jstqe.2014.2375161

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The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.
One method to produce pure heralded single photons (HSP) when using the optical process of spontaneous parametric down-conversion (SPDC) is by modifying the joint spectrum of the photon pairs by means of spectral filters. In this work, we characterize the dependence, with the bandwidth of such filters, of the spectral purity and heralding efficiency of the HSP generated in a bulk SPDC. The values we report for the purity and heralding efficiency are obtained from measurements of the joint spectrum. Our results are in agreement with the theoretical model that predicts a trade-off between the purity and heralding efficiency, and they complement similar measurements that have been done for HSP produced by other types of sources.
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.
The generation of high purity single photons and entangled photon pairs is a crucial first step in many quantum optics experiments, including those that require quantum teleportation [1], entanglement swapping [2], and the generation of multi-photon entanglement [3]. The most widely used and established approach for creating photon pairs is spontaneous parametric down conversion (SPDC) - where pump photons undergo a non-linear optical process to create a down-converted photon pair [4]. Traditionally, the generation of high-purity heralded single photons required severe spectral filtering, introducing additional loss. However, through careful engineering of spectral correlations of the down-converted photon pairs one can circumvent the need for filtering and avoid the accompanying reduction in heralding efficiency.
We demonstrate theoretically that correlated bi-photons can be generated with high heralding efficiency and high spectral purity for non-collinear Type-I spontaneous parametric down-conversion. In Type-I down-conversion, the generated photons have the same linear polarization that is perpendicular to the linear pump polarization. Previously, it was thought that high efficiency and purity could not be obtained for this configuration. We show that the non-collinear geometry gives an additional degree-of-freedom that allows for simultaneous optimization of these source metrics. We predict near-unity (≈0.97\approx0.97≈0.97) heralding efficiency and single-photon spectral purity by adjusting the beam focal parameters, which can be obtained over a wide range of pump, signal, and idler wavelengths without requiring special crystal dispersion characteristics. As an example, we predict a heralding efficiency of 0.97, a single-photon purity of 0.97, and a pair production rate of 0.50 pairs/(s ~ mW ~ THz) using a 400-μμμm-long βββ-barium borate crystal pumped by a 355-nm-wavelength pulsed laser with a bandwidth of 8-THz. Our work offers a simple and universal approach for producing high-quality quantum photonic states for a wide variety of quantum information science applications.
The creation and manipulation of biphotons is important for many applications in quantum optics and quantum information. Topics that benefit from efficient biphoton sources range from the most fundamental quantum science experiments to the highly applied fields of quantum communication and quantum computation. Biphoton sources have long been hailed as one of the leading methods for creating entangled photon pairs for tests of Bell's inequality, creating heralded photon pairs that are used in on-demand single-photon sources and heralded measurement techniques, and for quantum communication protocols to name a few. Specifically for quantum communication, biphoton sources are commonly used for cutting edge quantum key distribution (QKD) protocols. In the first part of the thesis, I focus on realizing an efficient biphoton source that produces high yield photon pairs. More specifically, I develop an optimized biphoton source using the nonlinear optical process of spontaneous parametric down-conversion in a second-order nonlinear crystal. I develop a formalism for predicting the two important metrics of a biphoton source: the heralding efficiency and joint count rate. I show how, from a large parameter space, one can tailor the phase matching of the nonlinear interaction to create a high quality biphoton source that produces both high heralding efficiency and high joint count rate. I achieve heralding efficiencies of 86$\\pm555\\%$ and joint count rates of 2.58$\\pm0.6kHzpermWpumppower.Ishowthatusingacollinearnondegenerategeometryallowsforheraldingefficienciesofupto99.70.6 kHz per mW pump power. I show that using a collinear nondegenerate geometry allows for heralding efficiencies of up to 99.70.6kHzpermWpumppower.Ishowthatusingacollinearnondegenerategeometryallowsforheraldingefficienciesofupto99.7\\%$ assuming no loss in the system. I verify the theoretical model with experimental results and find good agreement. In the second part of the thesis I turn to manipulating the single photons born from the biphoton source for applications in creating single-photon spectrometers and time-frequency QKD systems. The security of QKD is only guaranteed if the two parties have access to a set of states called mutually unbiased states. I create a set of these states in time and their conjugate states in the frequency basis and show that I can manipulate single photon correlations in time and frequency so that an eavesdropper can be detected if she localizes a photon to a 1 ns time interval. Additionally, in these experiments, I stretch a single photon wavepacket of 5-ps-width to a wavepacket of 8.3-ns-width and subsequently recompress it to at least the resolution of the detectors (sim\\simsim 300 ps). This demonstrates a stretch factor of >1600 for a single-photon pulse using a group velocity dispersive material. To my knowledge, this is the largest reported stretch factor for a single-photon wavepacket produced by a biphoton source. The ability to stretch and recompress a single photon by this amount has applications in creating high-resolution, high-efficiency, single-photon spectrometers as well as advancing time-frequency QKD systems and other temporal pulse shaping applications.
Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the nonseparability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing.