PD Dr. Sonja Barkhofen - Contact (Paderborn University)

S. Barkhofen, B. Brecht, C. Silberhorn, Physik in unserer Zeit (2023), 54(1), pp. 10-11

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Dynamic conditioning of two particle discrete-time quantum walks

F. Pegoraro, P. Held, S. Barkhofen, B. Brecht, C. Silberhorn, Physica Scripta (2023), 98(3), 034005

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In real photonic quantum systems losses are an unavoidable factor limiting the scalability to many modes and particles, restraining their application in fields as quantum information and communication. For this reason, a considerable amount of engineering effort has been taken in order to improve the quality of particle sources and system components. At the same time, data analysis and collection methods based on post-selection have been used to mitigate the effect of particle losses. This has allowed for investigating experimentally multi-particle evolutions where the observer lacks knowledge about the system's intermediate propagation states. Nonetheless, the fundamental question how losses affect the behaviour of the surviving subset of a multi-particle system has not been investigated so far. For this reason, here we study the impact of particle losses in a quantum walk of two photons reconstructing the output probability distributions for one photon conditioned on the loss of the other in a known mode and temporal step of our evolution network. We present the underlying theoretical scheme that we have devised in order to model controlled particle losses, we describe an experimental platform capable of implementing our theory in a time multiplexing encoding. In the end we show how localized particle losses change the output distributions without altering their asymptotic spreading properties. Finally we devise a quantum civilization problem, a two walker generalisation of single particle recurrence processes.

Semiclassical formulae For Wigner distributions

S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical (2022), 55(24), 244007

Abstract

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arXiv

In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.

Scalable Generation of Multiphoton Entangled States by Active Feed-Forward and Multiplexing

E. Meyer-Scott, N. Prasannan, I. Dhand, C. Eigner, V. Quiring, S. Barkhofen, B. Brecht, M.B. Plenio, C. Silberhorn, Physical Review Letters (2022), 129(15), 150501

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Scalable Generation of Multiphoton Entangled States by Active Feed-Forward and Multiplexing

E. Meyer-Scott, N. Prasannan, I. Dhand, C. Eigner, V. Quiring, S. Barkhofen, B. Brecht, M.B. Plenio, C. Silberhorn, Physical Review Letters (2022), 129(15), 150501

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Quantum-state creation in nonlinear-waveguide arrays

C.S. Hamilton, R. Christ, S. Barkhofen, S.M. Barnett, I. Jex, C. Silberhorn, Physical Review A (2022), 105(4), 042622

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Driven Gaussian quantum walks

P. Held, M. Engelkemeier, S. De, S. Barkhofen, J. Sperling, C. Silberhorn, Physical Review A (2022), 105(4), 042210

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Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems

P. Schütte, T. Weich, S. Barkhofen, 2021

Abstract

arXiv

In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.

Experimental entanglement characterization of two-rebit states

N. Prasannan, S. De, S. Barkhofen, B. Brecht, C. Silberhorn, J. Sperling, Physical Review A (2021), 103

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Probing the topological Anderson transition with quantum walks

D. Bagrets, K.W. Kim, S. Barkhofen, S. De, J. Sperling, C. Silberhorn, A. Altland, T. Micklitz, Physical Review Research (2021)

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Transient subdiffusion via disordered quantum walks

A. Geraldi, S. De, A. Laneve, S. Barkhofen, J. Sperling, P. Mataloni, C. Silberhorn, Physical Review Research (2021)

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Experimental control of the degree of non-classicality via quantum coherence

A. Smirne, T. Nitsche, D. Egloff, S. Barkhofen, S. De, I. Dhand, C. Silberhorn, S.F. Huelga, M.B. Plenio, Quantum Science and Technology (2020), 04LT01

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Local Versus Global Two-Photon Interference in Quantum Networks

T. Nitsche, S. De, S. Barkhofen, E. Meyer-Scott, J. Tiedau, J. Sperling, A. Gábris, I. Jex, C. Silberhorn, Physical Review Letters (2020)

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Photonic quantum walks with four-dimensional coins

L. Lorz, E. Meyer-Scott, T. Nitsche, V. Potoček, A. Gábris, S. Barkhofen, I. Jex, C. Silberhorn, Physical Review Research (2019)

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Detailed study of Gaussian boson sampling

R. Kruse, C.S. Hamilton, L. Sansoni, S. Barkhofen, C. Silberhorn, I. Jex, Physical Review A (2019)

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Eigenvalue measurement of topologically protected edge states in split-step quantum walks

T. Nitsche, T. Geib, C. Stahl, L. Lorz, C. Cedzich, S. Barkhofen, R.F. Werner, C. Silberhorn, New Journal of Physics (2019), 043031

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A high dynamic range optical detector for measuring single photons and bright light

J. Tiedau, E. Meyer-Scott, T. Nitsche, S. Barkhofen, T.J. Bartley, C. Silberhorn, Optics Express (2019), 1

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Engineering integrated photon pair sources and multiplexed detectors (Conference Presentation)

E. Meyer-Scott, N. Prasannan, N. Montaut, J. Tiedau, C. Eigner, G. Harder, L. Sansoni, T. Nitsche, H. Herrmann, R. Ricken, V. Quiring, T. Bartley, S. Barkhofen, C. Silberhorn, in: Advances in Photonics of Quantum Computing, Memory, and Communication XII, 2019

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Experimental Reconstruction of Entanglement Quasiprobabilities

J. Sperling, E. Meyer-Scott, S. Barkhofen, B. Brecht, C. Silberhorn, Physical Review Letters (2019)

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Supersymmetric Polarization Anomaly in Photonic Discrete-Time Quantum Walks

S. Barkhofen, L. Lorz, T. Nitsche, C. Silberhorn, H. Schomerus, Physical Review Letters (2018)

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Proposal for Quantum Simulation via All-Optically-Generated Tensor Network States

I. Dhand, M. Engelkemeier, L. Sansoni, S. Barkhofen, C. Silberhorn, M. Plenio, Physical Review Letters (2018)

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Probing measurement-induced effects in quantum walks via recurrence

T. Nitsche, S. Barkhofen, R. Kruse, L. Sansoni, M. Štefaňák, A. Gábris, V. Potoček, T. Kiss, I. Jex, C. Silberhorn, Science Advances (2018)

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Engineering integrated sources of entangled photon pairs

E. Meyer-Scott, N. Prasannan, N. Montaut, J. Tiedau, G. Harder, L. Sansoni, H. Herrmann, C. Eigner, R. Ricken, V. Quiring, T. Bartley, S. Barkhofen, C. Silberhorn, in: Frontiers in Optics / Laser Science, 2018

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High-performance source of spectrally pure, polarization entangled photon pairs based on hybrid integrated-bulk optics

E. Meyer-Scott, N. Prasannan, C. Eigner, V. Quiring, J.M. Donohue, S. Barkhofen, C. Silberhorn, Optics Express (2018), 32475

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Gaussian Boson Sampling

C.S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, I. Jex, Physical Review Letters (2017)

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Measuring topological invariants in disordered discrete-time quantum walks

S. Barkhofen, T. Nitsche, F. Elster, L. Lorz, A. Gábris, I. Jex, C. Silberhorn, Physical Review A (2017)

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Limits of the time-multiplexed photon-counting method

R. Kruse, J. Tiedau, T. Bartley, S. Barkhofen, C. Silberhorn, Physical Review A (2017)

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Driven Boson Sampling

S. Barkhofen, T. Bartley, L. Sansoni, R. Kruse, C.S. Hamilton, I. Jex, C. Silberhorn, Physical Review Letters (2017)

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Driven discrete time quantum walks

C.S. Hamilton, S. Barkhofen, L. Sansoni, I. Jex, C. Silberhorn, New Journal of Physics (2016), 073008

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Quantum walks with dynamical control: graph engineering, initial state preparation and state transfer

T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, C. Silberhorn, New Journal of Physics (2016), 063017

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Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene

J. Böhm, M. Bellec, F. Mortessagne, U. Kuhl, S. Barkhofen, S. Gehler, H. Stöckmann, I. Foulger, S. Gnutzmann, G. Tanner, Physical Review Letters (2015)

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Compounding approach for univariate time series with nonstationary variances

R. Schäfer, S. Barkhofen, T. Guhr, H. Stöckmann, U. Kuhl, Physical Review E (2015)

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Quantum walk coherences on a dynamical percolation graph

F. Elster, S. Barkhofen, T. Nitsche, J. Novotný, A. Gábris, I. Jex, C. Silberhorn, Scientific Reports (2015)

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Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum

S. Barkhofen, F. Faure, T. Weich, Nonlinearity (2014), pp. 1829-1858

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Formation and interaction of resonance chains in the open three-disk system

T. Weich, S. Barkhofen, U. Kuhl, C. Poli, H. Schomerus, New Journal of Physics (2014), 033029

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Spectral properties of microwave graphs with local absorption

M. Allgaier, S. Gehler, S. Barkhofen, H. Stöckmann, U. Kuhl, Physical Review E (2014)

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Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum

S. Barkhofen, F. Faure, T. Weich, Nonlinearity (2014), 27(8), pp. 1829-1858

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arXiv

Formation and interaction of resonance chains in the open three-disk system

T. Weich, S. Barkhofen, U. Kuhl, C. Poli, H. Schomerus, New Journal of Physics (2014), 16(3), 033029

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arXiv

Disordered graphene and boron nitride in a microwave tight-binding analog

S. Barkhofen, M. Bellec, U. Kuhl, F. Mortessagne, Physical Review B (2013)

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Experimental Observation of the Spectral Gap in Microwave n-Disk Systems

S. Barkhofen, T. Weich, A. Potzuweit, H. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters (2013)

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First Experimental Realization of the Dirac Oscillator

J.A. Franco-Villafañe, E. Sadurní, S. Barkhofen, U. Kuhl, F. Mortessagne, T.H. Seligman, Physical Review Letters (2013)

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Experimental Observation of a Fundamental Length Scale of Waves in Random Media

S. Barkhofen, J.J. Metzger, R. Fleischmann, U. Kuhl, H. Stöckmann, Physical Review Letters (2013)

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Microwave Measurements on n-Disk Systems and Investigation of Branching in correlated Potentials and turbulent Flows

S. Barkhofen, Philipps-Universität Marburg, 2013

Abstract

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In this work we investigate the wave propagation in three different complex systems. In the first two systems we focus on the wave propagation through random potentials, the first one in a microwave and the second one in an acoustic setup. In both systems we focus on the non-Gaussian properties of the measured quantities. The third system is a paradigmatic example of a fully chaotic open system with a fractal repeller. Here the relation of the classical periodic orbits and quantum mechanical quantities is studied. In the first experiment we induce a potential into the microwave cavity by placing randomly distributed metallic scatterers on the bottom plate. Spatially resolved measurements of the full wave function reveal strong intensity fluctuations and a condensation of the wave flow along classical caustics. Additionally the scaling behavior of the branching with respect to the standard deviation of the potential is investigated and the predicted exponent of $-2/3$ is reproduced. As there are several open modes in the cavity due to the high frequency, effects of mode interference and mode coupling are found and explained, which go beyond the theoretical model. Perturbation theory of the Helmholtz equation for non-parallel top and bottom plate reveals extra source terms for the wave function, which are induced by the other open modes. These dynamics are also found in the experimental data. The second experiment deals with an acoustic setup, where the sound of a turbulent air flow is recorded. Here strong deviations from the central limit theorem, which predicts a Gaussian distribution of wave intensities, are observed. In a second experiment performed in a wind tunnel a monochromatic sound wave is sent through the air flow. The hope to learn something about the properties of the turbulence by investigating the modulations of the original sound is not met. But again non-Gaussian behavior is found. In the third part of this thesis another complex system is studied in a microwave setup: The emph{n}-disk system consists of emph{n} equal disks placed on an equilateral polygon in a two dimensional plane. Such an open systems provides complex resonances, which are extracted from our measured spectra via an elaborate algorithm, the harmonic inversion. The challenges of this extraction are discussed in detail and possible solutions for arising problems are suggested. The finally obtained resonances are used for the calculation of the counting function of the real parts, whose growth is predicted by the Hausdorff dimension as leading order. The distributions of the imaginary parts are studied with respect to the opening of the system. The largest (negative) imaginary part defines the spectral gap, which is compared to predictions, which can be calculated by using the periodic orbits of the system. By similar means a suggestions for the development of the maximum of this distribution is tested. Moreover the experimental data is compared to the quantum mechanical calculation of the system.

Experimental Observation of the Spectral Gap in Microwave n-Disk Systems

S. Barkhofen, T. Weich, A. Potzuweit, H. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters (2013), 110(16), 164102

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arXiv

Weyl asymptotics: From closed to open systems

A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H. Stöckmann, M. Zworski, Physical Review E (2012)

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Weyl asymptotics: From closed to open systems

A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H. Stöckmann, M. Zworski, Physical Review E (2012), 86(6), 066205

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arXiv

Dirac point and edge states in a microwave realization of tight-binding graphene-like structures

U. Kuhl, S. Barkhofen, T. Tudorovskiy, H. Stöckmann, T. Hossain, L. de Forges de Parny, F. Mortessagne, Physical Review B (2010)

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