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Journal of the Optical Society of America B

Intrinsic limitations to the quality of pulsed spontaneous parametric downconversion sources for quantum information applications

Jean-Loup Smirr, Robert Frey, Eleni Diamanti, Romain Alléaume, Isabelle Zaquine

Published Mar 21, 2011• 10 citations
Publisher

Abstract

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.

DOI
10.1364/josab.28.000832

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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.
Fast characterization of pulsed spontaneous parametric down conversion (SPDC) sources is important for applications in quantum information processing and communications. We propose a simple method to perform this task, which only requires measuring the counts on the two output channels and the coincidences between them, as well as modeling the filter used to reduce the source bandwidth. The proposed method is experimentally tested and used for a complete evaluation of SPDC sources (pair emission probability, total losses, and fidelity) of various bandwidths. This method can find applications in the setting up of SPDC sources and in the continuous verification of the quality of quantum communication links.
Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which relies on the reduction of the duration time of the detection window, used for decreasing the number of registered errors. In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations this width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore, it can be applied in various implementations of quantum communication protocols. As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. The investigation was performed for the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance. The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.
An important open challenge in quantum information processing is to demonstrate a quantum device outperforming a classical computer. One of the most promising ways is by sending single photons through a passive linear-optical network, and sampling their output distribution [1]. However, this requires the nontrivial generation of many spectrally pure (indistinguishable) single photons. Most importantly, -spectral distinguishability reduces the visibility of quantum interference of the photons, but can be mitigated by filtering at the cost of optical losses. Unfortunately, losses are also detrimental to quantum interference. We recently quantified the combined role of spectral imperfections and loss in a multiphoton interference experiment [2]. We now apply these results to the problem of constructing spontaneous parametric down-conversion sources. In particular, we investigate the optimal filter bandwidth for different sources and optimize the down-conversion crystal parameters. Our results show that demonstrating a quantum advantage using photonics is difficult, but possible
Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which is based on the reduction of the duration time of the detection window, used for decreasing the number of registered errors. In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations the width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore it can be applied in various implementations of quantum communication protocols. As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. It was realized in the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance. The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.
Cavity-enhanced spontaneous parametric down-conversion (SPDC) can be used to implement heralded single-photon sources with narrow bandwidth down to tens of megahertz, thus compatible with atom-based quantum memories. In this work, we propose and study the cavities that are either singly resonant at the frequency of only one of the generated photons or doubly resonant at the frequency of one generated photon and for the pump field. We derive analytical expressions for the generation rate and the spectral brightness as a function of the main structure parameters. Our analysis shows that by exploiting counterpropagating SPDC inside a cavity with properly designed distributed Bragg reflectors, pure narrow-band heralded single photons can be generated. In particular, when a pulsed pump illuminates a 1-mm-long singly resonant cavity, the bandwidth of the resonant and the nonresonant photons will be 120 MHz and 5.7 GHz, respectively, with heralded single-photon purity as high as 0.993. Due to its small absorption probability inside the cavity, the heralding efficiency can approach unity if the nonresonant partner is used as a heralded single photon. Finally, we also show that continuous-wave excitation of a 1-cm-long cavity resonant for the pump and copropagating fields can provide photon pairs in a narrow bandwidth of 10 MHz with spectral brightness as high as $2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $({\text{s}\phantom{\rule{4.pt}{0ex}}\text{mW}\phantom{\rule{4.pt}{0ex}}\text{MHz})}^{\ensuremath{-}1}$. This source can efficiently couple with quantum memories and can find applications in quantum information processing and communication.
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.