TY - JOUR A1 - Christ, Andreas A1 - Brecht, Benjamin A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine T1 - Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime JF - New Journal of Physics N2 - Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein–Podolsky–Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom–photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered. Y1 - 2013 U6 - https://doi.org/10.1088/1367-2630/15/5/053038 VL - 15 IS - 5 PB - IOP ER - TY - JOUR A1 - Coldenstrodt-Ronge, Hendrik B. A1 - Lundeen, Jeff S. A1 - Pregnell, Kenny L. A1 - Feito, Alvaro A1 - Smith, Brian J. A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine A1 - Eisert, Jens A1 - Plenio, Martin B. A1 - Walmsley, Ian A. T1 - A proposed testbed for detector tomography JF - Journal of Modern Optics N2 - Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators. Y1 - 2009 U6 - https://doi.org/10.1080/09500340802304929 VL - 56 IS - 2-3 SP - 432 EP - 441 PB - Taylor&Francis ER - TY - JOUR A1 - Mauerer, Wolfgang A1 - Avenhaus, Malte A1 - Helwig, Wolfram A1 - Silberhorn, Christine T1 - How colors influence numbers: Photon statistics of parametric down-conversion JF - Physical Review A (Phys. Rev. A) N2 - Parametric down-conversion (PDC) is a technique of ubiquitous experimental significance in the production of nonclassical, photon-number-correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this article, we explain the observation by an a priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement. Y1 - 2009 U6 - https://doi.org/10.1103/physreva.80.053815 VL - 80 IS - 5 PB - American Physical Society ER - TY - JOUR A1 - Rohde, Peter P. A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine T1 - Spectral structure and decompositions of optical states, and their applications JF - New Journal of Physics N2 - We discuss the spectral structure and decomposition of multi-photon states. Ordinarily 'multi-photon states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong–Ou–Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrödinger kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples. Y1 - 2007 U6 - https://doi.org/10.1088/1367-2630/9/4/091 VL - 9 IS - 4 PB - IOP Publishing ER - TY - JOUR A1 - Helwig, Wolfram A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine T1 - Multimode states in decoy-based quantum-key-distribution protocols JF - Physical Review A N2 - Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate. Y1 - 2009 U6 - https://doi.org/10.1103/physreva.80.052326 VL - 80 IS - 5 PB - American Physical Society ER - TY - JOUR A1 - Mauerer, Wolfgang A1 - Helwig, Wolfram A1 - Silberhorn, Christine T1 - Recent developments in quantum key distribution: Theory and practice JF - Annalen der Physik N2 - Quantum key distribution is among the foremost applications of quantum mechanics, both in terms of fundamental physics and as a technology on the brink of commercial deployment. Starting from principal schemes and initial proofs of unconditional security for perfect systems, much effort has gone into providing secure schemes which can cope with numerous experimental imperfections unavoidable in real world implementations. In this paper, we provide a comparison of various schemes and protocols. We analyse their efficiency and performance when implemented with imperfect physical components. We consider how experimental faults are accounted for using effective parameters. We compare various recent protocols and provide guidelines as to which components propose best advances when being improved. KW - experimental imperfections KW - quantum communication KW - Quantum cryptography Y1 - 2008 U6 - https://doi.org/10.1002/andp.200710284 VL - 17 IS - 2-3 SP - 158 EP - 175 PB - Wiley ER - TY - JOUR A1 - Avenhaus, Malte A1 - Coldenstrodt-Ronge, Hendrik B. A1 - Laiho, K. A1 - Mauerer, Wolfgang A1 - Walmsley, I. A. A1 - Silberhorn, Christine T1 - Photon Number Statistics of Multimode Parametric Down-Conversion JF - Physical Review Letters N2 - We experimentally analyze the complete photon number statistics of parametric down-conversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single-mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes. Y1 - 2008 U6 - https://doi.org/10.1103/physrevlett.101.053601 VL - 101 IS - 5 PB - American Physical Society ER - TY - JOUR A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine T1 - Quantum key distribution with passive decoy state selection JF - Physical Review A N2 - We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present day, nonideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical postprocessing. This allows one to improve the effective signal statistics and achievable distance. Y1 - 2007 U6 - https://doi.org/10.1103/physreva.75.050305 VL - 75 IS - 5 PB - American Physical Society ER - TY - CHAP A1 - Mauerer, Wolfgang A1 - Silberhorn, Christine T1 - Numerical Analysis of Parametric Downconversion T2 - AIP Conference Proceedings N2 - Parametric downconversion (PDC) is a popular technique to produce twin beams of photons that are entangled in multiple degrees of freedom. The generated states form the basis for numerous applications that require entanglement. An exact quantification of this resource is therefore essential, for instance for quantum cryptography that relies on a complete knowledge of the correlation contained in the state. While the determination of an entanglement monotone for the PDC process is only possible analytically in special cases, an exact calculation must usually be performed numerically. Recent work by Mikhailova et al. [2] analyses a certain class of PDC states for which the concurrence entanglement measure can be obtained by an analytical approximation. In this contribution, we analyse the validity of the approximation by comparison with exact numerical methods. Y1 - 2009 U6 - https://doi.org/10.1063/1.3131312 VL - 1110 IS - 1 PB - AIP Publishing ER -