5Th Workshop on Quantum Chaos and Localisation Phenomena

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5th Workshop on Quantum Chaos and Localisation Phenomena

May 20–22, 2011, Warsaw, Poland organised by Institute of Physics Polish Academys, of Science Center for Theoretical Physics Polish Academy of Sciences, and Pro Physica Foundation PROGRAMME Organising Committee

Szymon Bauch ([email protected]) Sunday, May 22 Oleh Hul ([email protected]) INVITED TALKS Marek Kuś ([email protected]) 9:00–9:35 Uzy Smilansky (Rehovot, Israel) Michał Ławniczak ([email protected]) Stationary scattering from a nonlinear network Leszek Sirko – chairman ([email protected]) 9:35–10:10 Yan V. Fyodorov (Nottingham, UK) Level curvature distribution at the spectral edge of random Hermitian matrices 10:10–10:45 Pavel Kurasov (Stockholm, Sweden) Magnetic Schrödinger operators on graphs: spectra, Objectives inverse problems and applications 10:45–11:20 Karol Życzkowski (Warsaw, Poland) To assess achievements and to formulate directions of new research Level spacing distribution revisited on quantum chaos and localisation 11:20–11:50 coffee break To bring together prominent experimental and theoretical physicists 11:50–12:25 Andreas Buchleitner (Freiburg, Germany) who share a common interest in quantum chaos and localisation Transport, disorder, and entanglement phenomena 12:25–13:00 Jan Kˇríž (Hradec Králové, Czech Republic) Chaos in the brain 13:00–13:35 Agnès Maurel (Paris, France) Experimental study of waves propagation using Fourier Transform Profilometry Scope 13:35–14:30 lunch break CONTRIBUTED TALKS Presentations will focus on the following topics: 14:30–14:50 Filip Studniˇcka (Hradec Králové, Czech Republic) Quantum chaos and nonlinear classical systems Analysis of biomedical signals using differential geometry invariants Quantum and microwave billiards 14:50–15:10 Michał Ławniczak (Warsaw, Poland) Quantum and microwave graphs Investigation of Wigner reaction matrix, cross- and velocity Atoms in strong electromagnetic fields – experiment and theory correlators for microwave networks Chaos vs. coherent effects in multiple scattering 15:10–15:30 Maciej Janowicz (Warsaw, Poland) Anderson localisation Quantum properties of coupled generalized logistic map Random lasers lattices Quantum chaos and quantum computing 15:30–15:40 Closing remarks Entanglement and noise PROGRAMME INVITED TALKS

Friday, May 20 Fading statistics in communications – a random 19:00–21:00 Welcome party matrix approach Saturday, May 21 Jen-Hao Yeh, Thomas Antonsen, Edward Ott, Steven M. Anlage 9:00–9:10 Leszek Sirko (Warsaw, Poland) Opening Physics Department, University of Maryland, College Park, MD 20742-4111, USA INVITED TALKS 9:10–9:45 Achim Richter (Darmstadt, Germany) Fading is the observation of variations in signal strength measured at Simulating graphene with a microwave photonic crystal a receiver due to time-dependent variations in the propagation of waves 9:45–10:20 Steven M. Anlage (College Park, USA) from the source, or due to multi-path scattering and interference. It is Fading statistics in communications – a random matrix well known that the quantitative statistical theory of wave chaos – random approach matrix theory (RMT) – can be successfully applied to predict statistical 10:20–10:55 Jakub Zakrzewski (Cracow, Poland) properties of many quantities, such as the scattering matrix, of a wave Extraction of information from dynamics for strongly chaotic system. Here we start from the statistical model of the scatter- correlated systems ing matrix [1] to establish a general fading model. The model provides 10:55–11:30 Heinerich Kohler (Madrid, Spain) a first-principles understanding of the most common statistical model used Fidelity in chaotic and random systems in the communications field, namely Rayleigh fading, and shows that the statistical properties are governed by a single quantity related to the loss 11:30–12:00 coffee break or de-phasing parameter of RMT. We also combine the RMT fading 12:00–12:35 Dima Shepelyansky (Toulouse, France) model with our random coupling model (RCM) that takes into account Wigner crystal in snaked nanochannels system-specific features such as direct and short orbits [2–4], to build 12:35–13:10 Bart van Tiggelen (Grenoble, France) a more general fading model that includes Rician fading. In the high 3D Anderson localization of ultrasound and cold atoms loss-parameter limit, our model agrees with the Rayleigh/Rice models, 13:10–13:45 Gregor Tanner (Nottingham, UK) however it shows significant deviations from the Rayleigh/Rice distribu- Wave intensity distributions in complex structures tion in the limit of low loss. We have performed experiments with two ray-chaotic microwave cavities [3,4] to test the RMT/RCM fading model 13:45–14:45 lunch break over a wide range of loss parameter values. 14:45–16:00 POSTER SESSION Work funded by the ONR/Maryland AppEl Center Task A2 (contract No. CONTRIBUTED TALKS N000140911190), the AFOSR under grant FA95500710049. 16:00–16:20 Lock Yue Chew (Singapore) [1] P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. B 55, 4695 (1997). The quantum signature of chaos through the dynamics [2] James A. Hart, T.M. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009). of entanglement [3] Jen-Hao Yeh et al., Phys. Rev. E 81, 025201(R) (2010). 16:20–16:40 Adam Sawicki (Warsaw, Poland and Bristol, UK) [4] Jen-Hao Yeh et al., Phys. Rev. E 82, 041114 (2010). Scattering from isospectral graphs 16:40 Warsawtourandconferencedinner

1 INVITED TALKS NOTES

Transport, disorder, and entanglement

Andreas Buchleitner Quantum optics and statistics, Institute of Physics, Albert-Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany

In many areas of physics we witness dramatic differences between classical and quantum transport – from the theory of charge or heat conduction in the solid state, over radiation transport in multiple scattering media, to energy transport in various scenarios of light-matter interaction. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the environment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional ef- ficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such ef- ficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal coherent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex.

2 PARTICIPANTS AND AUTHORS INVITED TALKS

Bart van Tiggelen (invited speaker), p. 12 CNRS/Laboratoire de Physique et Modelisation des Milieux Condeses, Universite Level curvature distribution at the spectral edge Joseph Fourier, Maison des Magisteres, BP 166, F-38042 Grenoble Cedex 9, of random Hermitian matrices France e-mail: [email protected] Yan V. Fyodorov Mathematical Physics, School of Mathematical Sciences, Tomasz Tkocz (co-author), p. 14 University of Nottingham, NG72RD Nottingham, UK Dept. of Physics, Warsaw University, Hoża 69, 00-681 Warsaw, Poland Level curvature is a measure of sensitivity of eigenvalues of a disor- Maciej Wołoszyn (poster), p. 42 dered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures Dept. of Applied Informatics and Computational Physics, AGH University to be given by Zakrzewski–Delande expressions. Motivated by growing of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland interest in statistics of extreme (maximal or minimal) eigenvalues of dis- e-mail: [email protected] ordered systems of various nature, it is natural to ask about the associated level curvatures. I show how calculating the distribution for the curva- Jen-Hao Yeh (co-author), p. 1 tures of extreme eigenvalues in GUE ensemble can be reduced to study- Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA ing asymptotics of orthogonal polynomials appearing in a recent work by e-mail: [email protected] Nadal and Majumdar. The corresponding asymptotic analysis being yet outstanding, I instead will discuss solution of a related, but somewhat Jakub Zakrzewski (invited speaker), p. 13 simpler problem of calculating the level curvature distribution averaged over all the levels in a spectral window close to the edge of the semicircle. M. Smoluchowski Institute of Physics Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland e-mail: [email protected]

Karol Życzkowski (invited speaker), p. 14 Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland e-mail: [email protected]

50 3 INVITED TALKS PARTICIPANTS AND AUTHORS

Andrzej L. Sobolewski (co-author), p. 38 Fidelity in chaotic and random systems Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland Heinerich Kohler e-mail: [email protected] Instituto de Ciencia de Materiales de Madrid, CSIC, Spain Bartłomiej Spisak (poster), p. 41 Fidelity is the overlap of a wave function, propagated by a Hamil- Dept. of Applied Informatics and Computational Physics, AGH University tonian in time, with the same initial wave function, propagated by a per- of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland turbed wave function. Its behavior depends crucially on the choice of the e-mail: [email protected] initial wave function. In the talk we review two cases: If the initial state is random a simple analytic relation with parametric spectral correlations can be established. Filip Studniˇcka (contributed talk), p. 21 The latter can easier be measured, since no knowledge of the wave func- University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove, tion is required. On the other hand, if the initial state is an eigenstate of Czech Republic the unperturbed system we find unexpected features like non-ergodicity. e-mail: fi[email protected] In this case fluctuations become important and the full fidelity distribution (FFD) becomes a non-trivial function. We calculated the FFD in the Jacek Szczepkowski long time limit and for small perturbations. Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

Jerzy Szonert, p. 30, 32 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

Biniyam Taddese (co-author), p. 22 Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA

Gregor Tanner (invited speaker), p. 11 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK e-mail: [email protected]

4 49 PARTICIPANTS AND AUTHORS INVITED TALKS

Achim Richter (invited speaker), p. 8 Institut fuer Kernphysik, Technische Universitaet, Darmstadt, Schlossgartenstr. 9, Chaos in the brain D-64289 Darmstadt Jan Kˇríž e-mail: [email protected] University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove, Michał Rode (poster), p. 38 Czech Republic Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, We describe several links between EEG data processing and quantum 02-668 Warsaw, Poland mechanics. Then we show examples of exploitation of methods commonly e-mail: [email protected] used in quantum chaos for EEG data analysis. Adam Sawicki (contributed talk), p. 20 Center for Theoretical Physics Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland; Dept. of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK e-mail: [email protected]

Dima Shepelyansky (invited speaker), p. 9 Laboratoire de Physique Théorique, UMR 5152 du CNRS, IRSAMC, Université Paul Sabatier, 118, Route de Narbonne, F-31062 Toulouse Cedex 4, France e-mail: [email protected]

Leszek Sirko, p. 18, 24 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

Marek Smaczyński, p. 14 Atomic Optics Department, Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland e-mail: log [email protected]

Uzy Smilansky (invited speaker), p. 10 Dept. of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot, 76100 IL, Israel e-mail: [email protected]

48 5 INVITED TALKS PARTICIPANTS AND AUTHORS

Agn`es Maurel (invited speaker), p. 7 Magnetic Schr¨odinger operators on graphs: spectra, Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France inverse problems and applications e-mail: [email protected]

Pavel Kurasov Dmitrii Maksimov (co-author), p. 11 Mathematical Institute, Stockholm University, 106 91 Stockholm, Sweden School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK Magnetic Schrodinger¨ operators on metric graphs as models for elec- e-mail: [email protected] tron transport in nanowires will be discussed. It will be shown how the inverse spectral problem can be solved in the case of several cycles. New Jan Mostowski families of isospectral graphs and trees will be discussed. The results Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, will be applied to model quantum transport in nanosystems. Theoretic 02-668 Warsaw, Poland and experimental observations will be compared. e-mail: [email protected]

Arkadiusz Orłowski (poster), p. 36, 37 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

Edward Ott (co-author), p. 1, 22 Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA e-mail: [email protected]

Ewa Paul-Kwiek (co-author), p. 30, 32 Institute of Physics, Pomeranian University in Słupsk, ul. Arciszewskiego 22b, 76-200 Słupsk, Poland e-mail: [email protected]

Zdzisław Pawlicki Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

Adam Prządka (poster), p. 40 Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France e-mail: [email protected]

6 47 PARTICIPANTS AND AUTHORS INVITED TALKS

Krzysztof Kowalski, p. 30, 32 Institute of Physics Polish Academy of Sciences, Al. Lotników 32/46, Experimental study of waves propagation 02-668 Warsaw, Poland using Fourier Transform Profilometry e-mail: [email protected] Agnès Maurel Jan Kˇríž (invited speaker), p. 5 Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France University of Hradec Králové, Faculty of Education, Department of Physics, Rokitanského 62, 500 03 Hradec Králové, Czech Republic We have developed recently an optical method able to quantitatively e-mail: [email protected] measure the field of surface elevation with very good spatial and temporal resolutions. This allows for the study of several problems of wave Pavel Kurasov (invited speaker), p. 6 propagation in complex medium, either in the context of water waves or Mathematical Institute, Stockholm University, 106 91 Stockholm, Sweden surface waves. We will present recent results concerning resonances of e-mail: [email protected] water waves near floating object, wave turbulence in the context of water waves and bending waves and Time Reversal water waves. Marek Kuś, p. 14 [1] P. Cobelli, V. Pagneux, A. Maurel, P. Petitjeans, Experimental study on Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, water-wave trapped modes, J. Fluid Mech. 666, 445 (2011). 02-668 Warsaw, Poland [2] P. Cobelli, P. Petitjeans, A. Maurel, V. Pagneux, N. Mordant, Space-time e-mail: [email protected] resolved wave turbulence in a vibrating plate, Phys. Rev. Lett. 103, 204301 (2009). Michał Ławniczak (contributed talk), p. 18, 24 [3] P. Cobelli, V. Pagneux, A. Maurel, P. Petitjeans, Experimental observation of trapped modes in water wave channel, Europhys. Letters 88, 20006 (2009). Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

Mateusz Łącki (poster), p. 35 Atomic Optics Division, Jagiellonian University, Reymonta 4, PL-30-059 Cracow, Poland e-mail: [email protected]

Paweł Masiak Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

46 7 INVITED TALKS PARTICIPANTS AND AUTHORS

Orestis Georgiou (poster), p. 28, 29 Simulating graphene with a microwave photonic School of Mathematical Sciences, University of Bristol, Howard House, crystal Queens Ave, Bristol BS8 1SN, UK e-mail: [email protected] Achim Richter Institut fuer Kernphysik, Technische Universitaet Darmstadt, Martin Holthaus (co-author), p. 37 D-64289 Darmstadt, Germany, and the European Centre for Theoretical Studies Condensed Matter Theory Group, Institut für Physik, Carl von Ossietzky in Nuclear Physics and Related Areas, I-38100 Villazzano (Trento), Italy Universität, D-26111 Oldenburg, Germany e-mail: [email protected] We have measured recently reflection and transmission spectra of a microwave photonic crystal consisting of 874 metallic cylinders arranged Oleh Hul, p. 18, 24 in form of a triangular lattice [1]. A cusp structure has been observed close to the expected Dirac frequency and related to the local density of Institute of Physics Polish, Academy of Sciences, Al. Lotników 32/46, states in the photonic crystal, providing clear evidence for the existence 02-668 Warsaw, Poland of a Dirac point which is a characteristic of relativistic massless fermions. e-mail: [email protected] Dirac points are also a peculiar property of the electronic band structure of Graphene [2] whose properties can thus be described by the relativistic Maciej Janowicz (contributed talk), p. 17, 36, 37 Dirac equation [3–5]. It will be shown how several features of Graphene Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, (dispersion relation, so-called edge states, pseudodiffusive transmission 02-668 Warsaw, Poland at the Dirac point) are modeled in photonic crystals. Furthermore, as e-mail: [email protected] a direct extension of the present work, the experimental investigation of properties of the eigenvalues and eigenfunctions of a superconducting Felix Jörder (poster), p. 34 Dirac billiard is discussed. The photonic crystal will thereby be placed in a closed resonator box [6,7]. Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany Supported by the DFG within the SFB 634. e-mail: [email protected] [1] S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, F. Schaefer, Phys. Rev. B 82, 014301 (2010). Heinerich Kohler (invited speaker), p. 4 [2] A.K. Geim, K.S. Novoselov, Nature Mater. 6, 183 (2007). Dept. of Theory and Simulation of Materials, Instituto de Ciencias de Materiales [3] P.R. Wallace, Phys. Rev. 71, 622 (1947). de Madrid, Sor Juana Ines de la Cruz 3, Cantoblanco, 28049 Madrid, Spain [4] G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984). e-mail: [email protected] [5] C.W.J Beenakker, Rev. Mod. Phys. 80, 1337 (2008). [6] M.V. Berry, R.J. Mondragon, Proc. R. Soc. Lond. A412, 53 (1987). Katarzyna Kowalczyk [7] J. Wurm, A. Rycerz, I. Adagideli, M. Wimmer, K. Richter, H.U Baranger, Dept. of Physics, Warsaw University, Hoża St. 69, Warsaw, Poland Phys. Rev. Lett. 102, 056806 (2009). e-mail: kejta [email protected]

8 45 PARTICIPANTS AND AUTHORS INVITED TALKS

Lock Yue Chew (contributed talk), p. 15 Division of Physics and Applied Physics, Nanyang Technological University, Wigner crystal in snaked nanochannels 21 Nanyang Link, SPMS-PAP-04-04, Singapore e-mail: [email protected] Dima Shepelyansky Laboratoire de Physique Theorique UMR 5152 du CNRS, IRSAMC Universite Felix Eckert (poster), p. 27 Paul Sabatier 118, Route de Narbonne, F-31062 Toulouse Cedex 4, France Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany We study properties of Wigner crystal in snaked nanochannels and e-mail: [email protected] show that they are characterized by conducting sliding phase at low charge densities and insulating pinned phase emerging above a certain critical charge density. The transition between these phases has a devil’s staircase Matthew Frazier (co-author), p. 22 structure typical for the Aubry transition in dynamical maps and the Fren- Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA kel–Kontorova model. We discuss implications of this phenomenon for e-mail: [email protected] charge density waves in quasi-one-dimensional organic conductors and for supercapacitors in nanopore materials. Yan V. Fyodorov (invited speaker), p. 3 Mathematical Physics, School of Mathematical Sciences, University of Nottingham, NG72RD Nottingham, UK e-mail: [email protected]

Sanka Gateva-Kostova (co-author), p. 30, 32 Institute of Electronics, BAS, Blvd. Tzarigradsko Shaussee 72, 1784 Soﬁa, Bulgaria e-mail: [email protected]

Stefano Giani (co-author), p. 11 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK e-mail: [email protected]

Małgorzata Głódź (poster), p. 30, 32 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland e-mail: [email protected]

44 9 INVITED TALKS PARTICIPANTS AND AUTHORS

Steven M. Anlage (invited speaker), p. 1, 22 Stationary scattering from a nonlinear network Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA e-mail: [email protected] Uzy Smilansky Department of Physics of Complex Systems, The Weizmann Institute of Science, Thomas Antonsen (co-author), p. 1, 22 Rehovot, 76100 IL, Israel Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA e-mail: [email protected] Transmission through a complex network of nonlinear one-dimensional leads will be discussed by extending the stationary scattering theory Szymon Bauch (poster), p. 18, 24 on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, number of sharp resonances that dominate scattering. The latter reso- 02-668 Warsaw, Poland nances are then shown to be extremely sensitive to the nonlinearity and e-mail: [email protected] display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks. Tobias Binninger (poster), p. 26 Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hauriweg 10, 79110 Freiburg, Germany e-mail: [email protected]

Agata Borkowska, p. 18 Dept. of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland e-mail: [email protected]

Andreas Buchleitner (invited speaker), p. 2 Quantum optics and statistics, Institute of Physics, Albert-Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany e-mail: [email protected]

David Chappell (co-author), p. 11 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK e-mail: [email protected]

10 43 POSTERS INVITED TALKS

Localisation in semiconductor Fibonacci superlattice Wave intensity distributions in complex structures

Maciej Wołoszyn Gregor Tanner, David Chappell, Stefano Giani, Dmitrii Maksimov Dept. of Applied Informatics and Computational Physics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland School of Mathematical Sciences, University of Nottingham, NG7 2RD Nottingham, UK A finite semiconductor superlattice generated by the Fibonacci se- quence and the electronic states formed within it are studied in the limit of The vibro-acoustic response of mechanical structures can in general weak electric field. Effect of the electric field on the energy spectrum and be well approximated in terms of linear wave equations. Standard numer- the density of states is discussed in terms of the anticrossings originating ical solution methods comprise the finite or boundary element method in the system. (FEM, BEM) in the low frequency regime and Statistical Energy Analy- It is shown that the generalized dimension calculated as a function sis (SEA) in the high-frequency limit. Major computational challenges are of electric field has maxima in the vicinity of anticrossings, and that at posed by the so-called mid-frequency problem – that is, composite struc- the same values of the electric field the minimal values of the inverse tures where the local wave length may vary by orders of magnitude across participation ratio are observed. the components. Recently, a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures improving on standard SEA has been proposed in [1]. The technique interpolates between SEA and ray tracing containing both these methods as limiting cases. The method has its origin in studying solutions of wave equation with an underlying chaotic ray-dynamics =- often referred to as wave chaos. Within the new theory – Dynamical Energy Analysis (DEA) – SEA is identified as a low resolution ray tracing algorithm and typical SEA assumptions can be quantified in terms of the properties of the ray dynamics. We have furthermore developed a hybrid SEA/FEM method based on random wave model assumptions for the short-wavelength components. This makes it possible to tackle mid-frequency problems under certain constraints on the geometry of the structure. Extensions of the technique towards a DEA/FEM hybrid method will be discussed. DEA and SEA/FEM calculations for a range of multi-component model systems will be presented. The results are compared with both SEA results and FEM as well as BEM calculations. DEA emerges as a numerically efficient method for calculating mean wave intensities with a high de- gree of spatial resolution and capturing long range correlations in the ray dynamics. [1] G. Tanner, Journal of Sound and Vibration 320, 1023 (2009).

42 11 INVITED TALKS POSTERS

3D Anderson localization of ultrasound and cold Phase space approach to the eﬀect of weak magnetic atoms ﬁeld on the 2kF backscattering mechanism

Bart van Tiggelen Bartłomiej Spisak LPMMC CNRS/UJF, Maison des Magisteres, BP 166 38042, Grenoble, France Dept. of Applied Informatics and Computational Physics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland Anderson localization is a phenomenon that was introduced more than 50 ago by its creator P.W. Anderson to understand metal-insulator In structurally disordered systems the conduction electrons may be transitions in condensed matter. The huge impact it has had in condensed prone to weak localisation which is caused by coherent multiple scatter- matter physics cannot be underestimated, recognized by the Nobel Prize ings in the backward direction. This effect is regarded as a precursor of in 1977. Yet, the experimental study of Anderson localization turned the Anderson localisation. out very hard. Arguably, only when it was realized in the early eight- The weak localisation of the conduction electrons in three dimen- ies that Anderson localization of classical waves such as light and sound sional structurally disordered systems is considered in the limit of weak should exist, a new experimental activity started. In this presentation I will magnetic field within the framework of the generalised kinetic equation present a recent observation of Anderson localization with elastic waves in for the Wigner distribution function and the effective medium approxi- “mesoglass” structure. I will describe how this “unrecognizable monster” mation. The results of calculations are compared with the experimental (a quote from Anderson himself) has revealed itself in our experiments: in data of magnetoresistance measurements for amorphous CaxAl1 x metal- the dynamics of the wave propagation, in the fluctuations of the speckles, lic glass. − in the confinement and the structure of the wave packet. I will men- tion how we describe, model and analyse these features theoretically: by modified transport theory, random matrices, multi-fractal analyses. THE theory does not exist; The best theories probably make the most severe approximations... The last revolution stems from cold atoms. Very con- trolled experiments can now be carried out with cold atoms expanding in disordered light speckle. These coherent matter waves have been seen to localize in low dimensions. We present some theoretical predictions on 3D cold atom localization. Work done in close collaboration with John Page (University of Manitoba), Sergey Skipetrov (LPMMC), Nicolas Cherroret (LPMMC), Sanli Faez, Ad Lagendijk (Amsterdam), Anna Minguzzi (LPMMC), Boris Shapiro (Technion) and Afifa Yedjour (LPMMC/Oran). For more information see http://www.andersonlocalization.com/. For recent re- views see: A. Lagendijk, B.A. van Tiggelen, D.S. Wiersma, Fifty years of An- derson localization, Physics Today 62 (8), 24 (2009), A. Aspect, M. Inguscio, Anderson localization of ultracold atoms, Physics Today 62 (8), 30 (2009).

12 41 POSTERS INVITED TALKS

Experimental time-reversal of water wave Extraction of information from dynamics for strongly correlated systems Adam Prządka Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France Jakub Zakrzewski M. Smoluchowski Institute of Physics, Jagiellonian University, The phenomena of the time-reversal of acoustic and optical waves ul. Reymonta 4, PL-30-059 Cracow, Poland were deeply studied in the recent years. The extension of this phenomenon to the surface water waves is presented. The optical method of Fourier A spectacular progress has been reached in ultra cold atomic systems Transform Profilometry (FTP) is used to measure the surface elevation in recently. In particular, the observation of a quantum phase transition from time and space. The experiments in the capillary-gravity regime show that superfluid phase to Mott insulator, as well as emergence of a Bose glass after the time-reversion of the waves (although attenuated), the successful for disordered system, has served as a stimulus for an immense activity temporal and spatial refocalisation can be observed (with half of the in the field. We show that, in a strict quantum mechanical sense, the adia- wavelength spatial limit). batic dynamics across the superfluid-insulator transition is far from being obvious. The nonadiabatic behavior is amplified for disordered systems. Still, analysis of the dynamically created wave-packet reveals that while excited states contribute significantly to the obtained dynamical state, their character, at least in some of the experiments, seems to be quite similar to that of the ground state. The consequences of the results for quantum simulator implementation are pointed out.

40 13 INVITED TALKS POSTERS

Level spacing distribution revisited Our study shows how the substituent eﬀect exerts the inﬂuence on the energetical landscape of the excited state and may be used in practice 1 2 3 to search for materials of desired energetical and optical properties. Karol Życzkowski , Tomasz Tkocz , Marek Smaczyński , Marek Kuś1 [1] H. Mori, E. Miyoshi, Bull. Chem. Soc. Jpn. 80, 1335 (2007). 1 Center for Theoretical Physics, Polish Academy of Sciences, [2] M. Sauer, Proc. Natl. Acad. Sci. U.S.A. 102, 9433 (2005). [3] F.M. Raymo, Adv. Mater. , 401 (2002). al. Lotników 32/46, 02-668 Warszawa, Poland 14 [4] P. Zhao, C.F. Fang, C.J. Xia, Y.M. Wang, D.S. Liu, S. Xie, J. Appl. Phys. 2Dept. of Physics, Warsaw University, Hoża 69, 00-681 Warsaw, Poland Lett. 93, 013113 (2008). 3 Atomic Optics Department, Institute of Physics, Jagiellonian University, [5] P. Zhao, C.F. Fang, C.J. Xia, D.S. Liu, S. Xie, J. Chem. Phys. Lett. 453, 62 Reymonta 4, 30-059 Cracow, Poland (2008). [6] P. Zhao, Z. Zhang, P.J. Wang, D.S. Liu, Physica B 404, 3462 (2009). Spectral properties of quantized chaotic systems can be described [7] D. Dulic, S.J. van der Molen, T. Kudernac, H.T. Jonkman, J.D. de Jong, by the theory of random matrices. The distribution of the largest eigen- T.N. Bowden, J. van Esch, B.L. Feringa, B.J. van Wees, Phys. Rev. Lett. 91, value of a random hermitian matrix is described by the Tracy–Widom 207402 (2003). Law. An analogous problem of characterizing the extremal gaps between [8] C. Benesch, M.F. Rode, M. Cizek, R. Hartle, O. Rubio-Pons, M. Thoss, neighbouring eigenphases of random unitary matrices are analyzed. The A.L. Sobolewski, J. Phys. Chem. C 113, 10315 (2009). spectral statistics are also investigated in the case of random unitary ma- [9] V. Bermudez, N. Capron, T. Gase, F.G. Gatti, F. Kajzar, D.A. Leigh, F. Zer- trices with a tensor product structure, which represent evolution operators betto, S.W. Zhang, Nature 406, 608 (2000). for non-interacting quantum composite systems. [10] A.L. Sobolewski, Phys. Chem. Chem. Phys. 10, 1243 (2008). [11] L. Lapinski, M.J. Nowak, J. Nowacki, M.F. Rode, A.L. Sobolewski, Chem. Phys. Chem. 10, 2290 (2009). [12] M.F. Rode, A.L. Sobolewski, sent for review to J. Phys. Chem. A.

14 39 POSTERS CONTRIBUTED TALKS

Effect of chemical substituents on energetical The quantum signature of chaos landscape of a molecular switch: an ab initio study through the dynamics of entanglement classically regular and chaotic systems M.F. Rode, A.L. Sobolewski Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Lock Yue Chew 02-668 Warsaw, Poland Division of Physics and Applied Physics, Nanyang Technological University, PO Box: 21 Nanyang Link, SPMS-PAP-04-04, Singapore The search for optically switchable molecules is nowadays an important and popular issue [1–3] Optical molecular switches enable the Quantum entanglement is an important resource in quantum infor- storage of information on a molecular level and route signals in molecu- mation processing. The capability of preparing quantum states that are lar electronic logic circuits [2,4–7]. They are considered as the controllers highly entangled is especially significant in applications such as quantum of current flow when linked to conjugated polymer chains [8]. In order to teleportation and superdense coding [1]. An approach to prepare such serve as a molecular switch, a molecular system must posses at least two states is to examine the time evolution of quantum states generated by stable forms which may be switched by an external electric filed, electron Hamiltonians of two-coupled oscillator systems. In this talk, I will present transfer, chemical reaction or optical excitation [9]. our recent investigation on the dynamics of entangled states which are In our investigation we are searching for optical molecular switches generated by systems that are classically regular, mixed, and chaotic [2-3]. which operate on the Excited State Intramolecular Proton Transfer For systems that are classically regular, we found periodic entanglement (ESIPT) phenomenon [8,10–12]. The switching process involves the lon- which has twice the frequency of the corresponding classical motion. Such grange transfer of a proton which is picked up by a “molecular crane”; at frequency doubling continues to hold true in the entanglement dynamics the donor site due to optical excitation, and delivered to the acceptor site of for a second model that exhibits a two-frequency orbit in the classical the system by rotation of the crane. The reversibility of the switch is guar- domain. Surprisingly, we found that a periodic classical trajectory can anteed by the ESIPT mechanism conditions, which are: (i) photochromism give rise to a quasi-periodic entanglement dynamics upon quantization. of the system and (ii) a barrierless access on the potential-energy surface For a system that is chaotic, we have reaffirmed existing results that the (PES) of the S1 state to the S1–S0 conical intersection (CI) which is entanglement production rate is higher when the classical system is more common for both photochromic forms. chaotic, i.e., the system possesses a more positive Lyapunov exponent [4]. In our theoretical study we have chosen 7-hydroxy-quinoline 7HQ When the system contains a mixed phase space, the entanglement dynam- as a skeleton of the switch, as it may posses two isomeric forms due the ics is found to be insensitive to the choice of the initial conditions in the presence of two distinguishing hydrogen-donor/acceptor centers: O and N regular or the chaotic classical regime. In fact, we have demonstrated atoms, being able to donate the hydrogen atom to the crane [11,12]. We complete dependence of the dynamical pattern of entanglement on the have investigated several potential crane molecules such as carbaldehyde, global classical dynamical domain without being influenced by the lo- pyridine and oxazine being attached at the position 8′ of the 7HQ skele- cal classical behavior in all the three classical regimes for the first time. ton and searched for appropriate side groups which, substituted at the While such global dependence is not necessary for all coupled oscillator given position, would improve the energetical landscape of the molecular systems, the nonlocal models that we have investigated have the advantage system. of generating an encoding subspace [5] that is stable against any errors in the preparation of the initial separable coherent states. Such a feature

38 15 CONTRIBUTED TALKS POSTERS will be physically significant in the design of robust quantum information Coherence in chaotic coupled logistic map lattices processing protocols. 1 1 2 [1] M. Christandl, N. Schuch and A. Winter, Highly entangled states with almost Maciej Janowicz , Arkadiusz Orłowski , Martin Holthaus 1 no secrecy, Phys. Rev. Lett. 104, 240405 (2010). Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, [2] N. N. Chung and L. Y. Chew, Dependence of entanglement dynamics on the 02-668 Warsaw, Poland global classical dynamical regime, Phys. Rev. A , 016204 (2009). 2 80 Condensed Matter Theory Group, Institut für Physik, Carl von Ossietzky [3] N. N. Chung and L. Y. Chew, Two-step approach to the dynamics of coupled Universität, D-26111 Oldenburg, Germany anharmonic oscillator systems, Phys. Rev. A 80, 012103 (2009). [4] S.-H. Zhang and Q.-L. Jie, Quantum-classical correspondence in entangle- Waves generated by systems of diffusively coupled logistic maps ment production: entropy and classical tori, Phys. Rev. A 77, 012312 (2009). have been employed in numerical simulations to perform an analogue of [5] E. Ciancio and P. Zanardi, Coupling bosonic modes with a qubit: entangle- the two-slit diffraction experiment. Interference patterns with high visi- ment dynamics at zero and a finite temperature, Phys. Lett. A360, 49 (2006). bility of the fringes emerge naturally, differing significantly from the sum of the two diffraction patterns obtained with only one open slit, provided the nonlinearity is sufficiently strong. Moreover, the appropriately defined coherence matrix exhibits off-diagonal long-range order, and admits fac- torization. Thus, nonlinear diffusive systems can possess features which are characteristics of genuinely coherent fields.

16 37 POSTERS CONTRIBUTED TALKS

Transient pattern formation and condensate-like Quantum properties of coupled generalized logistic behavior in coupled map lattices based on logistic map lattices map Maciej Janowicz Maciej Janowicz, Arkadiusz Orłowski Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland 02-668 Warsaw, Poland Properties of quantized versions of coupled system of minimal non- Pattern formation in two-dimensional coupled map lattices based on singular symplectic generalizations of logistic maps have been investi- the logistic mapping has been investigated as dependent on the coupling gated. It is shown that the behavior of such systems resembles that of constant, the diﬀusion constant, and initial conditions. Three additional Bose–Einstein condensates. In particular, the oﬀ-diagonal long range or- quantitative measures of the coupled map lattices behavior: reduced den- der and dominant eigenvalues of the reduced density matrices have been sity matrix, reduced wave function, and an analog of particle number found. are introduced. It is found that the standard CMLs seem to approach the states which resemble the condensed states of systems of Bose particles.

36 17 CONTRIBUTED TALKS POSTERS

Investigation of Wigner reaction matrix, cross- Spinor Bose–Hubbard model with disorder – phase and velocity correlators for microwave networks diagram and phase transitions

Michał Ławniczak1, Szymon Bauch1, Oleh Hul1, Mateusz Łącki 2,1 1 Agata Borkowska , Leszek Sirko Atomic Optics Division, Jagiellonian University, Kraków, Poland 1 Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland Spinor Bose–Hubbard model describes behavior of ultracold Bose 2Department of Chemistry, Warsaw University of Technology, Noakowskiego 3, gas on optical lattice. Description of general (and quite rich) phase di- 00-664 Warsaw, Poland agram as well as phase transitions in presence of disorder is presented using various theoretical and numerical methods. Quantum graphs are excellent examples of quantum chaotic systems [1]. Experimentally, quantum graphs are simulated by microwave networks consisting of joints and microwave cables [2,3]. This is possible due to an equivalency of the one-dimensional Schrödinger equation describing a quantum system and the telegraph equation describing an ideal microwave network. We present the results of the experimental studies of the distribution of the reﬂection coeﬃcient P(R) and the distributions of the imaginary P(ν) and the real P(u) parts of the Wigner reaction matrix K for irregu- lar fully connected microwave networks which simulate quantum graphs with broken time reversal symmetry. Quantum graphs with broken time reversal symmetry are simulated by microwave networks consisting microwave circulators. The measurements were performed as a function of absorption which was varied by using microwave attenuators. We present also our investigations of the cross-correlation function c12(ν) [4,5]. For the systems with time reversal symmetry c12(ν) = 1. In the case of the systems with broken time reversal symmetry c12(ν) < 1. We show that the direct processes are responsible for the increase of the cross-correlation function c12(ν). Furthemore, we present the results of the experimental studies of the autocorrelation functions of level velocities of the pentagonal microwave networks. This work was partially supported by the Ministry of Science and Higher Educa- tion grant no. N N202 130239.

18 35 POSTERS CONTRIBUTED TALKS

Complex dilation for time-dependent phenomena [1] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997). in driven helium [2] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, L. Sirko, Phys. Rev. E 69, 056205 (2004). Felix Jörder [3] M. Ławniczak, O. Hul, S. Bauch, P. Seba, L. Sirko, Phys. Rev. E 77, 056210 Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, (2008). Hermann-Herder-Str. 3, Freiburg, Germany [4] M. Ławniczak, S. Bauch, O. Hul, L. Sirko, Phys. Scr. T135, 014050 (2009). [5] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A. Richter, F. Schäfer, The electromagnetically driven helium atom defines a paradigmatic H.A. Weidenmüller, Phys. Rev E 81, 036205 (2010). scenario of a fragmenting quantum system, characterized by high spectral densities and decay channels into multiple continua. A powerful tool to access the spectral structure underlying the field-induced excitation and fragmentation process is provided by complex dilation of the Hamiltonian, which uncovers the pole structure of the resolvent operator.We summarize the current status of applications of complex dilation techniques in this specific physical context, and discuss novel perspective, such as the impact of the interelectronic repulsion on dynamical localization effects in the excitation process.

34 19 CONTRIBUTED TALKS POSTERS

Scattering from isospectral graphs

Adam Sawicki Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland; Department of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK

In 1966 Marc Kac asked “Can one hear the shape of a drum?”. The answer was given only in 1992, when Gordon et al. found a pair of drums with the same spectrum. The study of isospectrality and inverse problems is obviously not limited to drums and treats various objects such as molecules, quantum dots and graphs. In 2005 Okada et al. conjectured that isospectral drums can be distinguished by their scattering poles (resonances). We prove that this is not the case for isospectral quantum graphs, i.e., isospectral quantum graphs share the same resonance distribution. This is a joint work with Rami Band and Uzy Smilansky (Weizmann Institute).

count for the m m absorption transitions to the non-coupled m states, → ′ ′ and to the pairs of m′ states with incomplete coupling, we have com- plemented the results of the 5-level model with the ones of its reduced forms [1]. Satisfactory agreement of the positions of respective modeled and experimental spectral peaks was achieved. [1] E. Paul-Kwiek et al., Proc. of SPIE 7747, 77470I-1 (2011).

20 33 POSTERS CONTRIBUTED TALKS

The influence of Zeeman D2 transitions on probe Analysis of biomedical signals using differential absorption spectra in a multilevel Lambda scheme geometry invariants for cold 85Rb atoms Filip Studniˇcka E. Paul-Kwiek1, M. Głódź2, K. Kowalski2, J. Szonert2, 3 University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove, S. Gateva Czech Republic 1 Institute of Physics, Pomer. University in Słupsk, ul. Arciszewskiego 22b, 76-200 Słupsk, Poland Tensometers and accelerometers were placed on a bed to measure 2Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, human haemodynamics and movement activity. It is shown that n signals n 02-668 Warsaw, Poland from those devices can be described as a 1D manifolds in R . Those 3Institute of Electronics, BAS, 1784 Sofia, Boul. Tsarigradsko Shosse 72, signals are analysed using classical and affine differential geometry in- Bulgaria variants to investigate e.g. the propagation of pulse wave in aorta and heart and breathing activity. Matlab script which can monitor movement We have observed complex spectral features in probe absorption in activity of the person lying on the bed has been finished. This script can a multilevel Lambda-scheme of the D2 transitions in 85Rb atoms cooled distinguish between the movement of the person itself or movement of and trapped in MOT. The related physical phenomena are: partially sup- the person caused by someone else (e.g. turning of the person etc.). It pressed EIT and Autler–Townes effect, under conditions of Lambda ex- will be used in the medical industry in less than one year. citation of Zeeman substates by two linearly polarized-light beams, one strong and the other weak. The strong beam provided 5S1/2 (F = 2) 5P3/2 (F′) coupling. For a series of coupling beam frequencies (spanned↔ from much below C1 to much above C3, the resonant frequencies marked on the Figure), absorption spectra were observed of the weak probe-beam (P), whose frequency was scanned in the vicinity of the 5S1/2 (F = 3) 5P3/2 (F′) resonances. T and R arrows are for trapping and repumping→ MOT beams, respectively. Their intensity was maintained at possibly low levels in order to minimize their influence on the experiment. Our adopted explanation relies on the fact that, in general, across the pumped and probed region, the MOT magnetic field vector has various directions (which define the directions of quantization axis), therefore one can expect that with linear laser beam polarizations both σ and π-type transitions can actually take place. Our formalism is essentially based on master equations describing the evolution of the density operator for the case of a 5-level atom interacting with two laser fields (atomic levels involved are numbered 1 – 5 in the Figure). In order to indirectly ac- | i | i

32 21 POSTERS POSTERS

Nonlinear time-reversed electromagnetics in wave chaotic systems

Matthew Frazier, Biniyam Taddese, Edward Ott, Thomas Antonsen, Steven M. Anlage Physics Department, University of Maryland, College Park, MD 20742-4111, USA

The quantum mechanical concepts of Loschmidt Echo and Fidelity measure the effect of perturbations on a quantum wave system. In previous work, we extended these concepts to classical waves, such as acoustic and electromagnetic waves, to realize a new sensor paradigm [1,2]. The sensor makes explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to sensitively and remotely measure the presence of small perturbations to the system. The loss of fidelity is measured through a classical wave-analog of the Loschmidt echo by employing a single-channel time-reversal mirror to rebroadcast a probe sona signal into the perturbed system [3]. The operation of the time-reversal mirror itself benefits from the wave chaotic scattering in the system. We also introduced the use of exponential amplification of the probe sona signal Basing on our experimental procedure and by using a simple three- to partially overcome the effects of propagation losses [1]. In addition, level model, we have still demonstrated [2] that, despite the complex na- time windowing of the sona signal, along with the exponential amplifi- ture of interactions in MOT, within a range of MOT parameters it is cation, was demonstrated to be effective at varying the spatial range of justified to characterise MOT with an approximate value of an effective sensitivity to perturbations [2]. Now, we take this work in a different di- Rabi frequency Ω0eff , by using the formula Ω0eff = √BP, which is analo- rection by considering the case in which there is an object with a classical gous to the one used for in interaction of a single atom with local light nonlinear response inside a wave chaotic electromagnetic system. After field. √B is a mean experimentally determined scaling factor, and P is being stimulated, the nonlinear object creates a new frequency-translated the total trapping laser power. The value of √B and applicability limits of sona signal, which is gathered and recorded by the time-reversal mirror. the method have to be verified with each new implementation of MOT. We demonstrate that when the time-reversed nonlinear sona is sent back [1] J.H. Marquardt et al., J. Opt. Soc. Am. B 13, 1384 (1996). into the system, it creates a time-reversed pulse that collapses back onto [2] M. Głódź et al., Opt. Commun. (2011), in press. the nonlinear object. This constitutes a new modality for directed wave propagation in strongly scattering and wave chaotic media. Work funded by the IC Post-Doc program, ONR MURI grant N000140710734, the ONR/Maryland AppEl Center Task A2 (contract No. N000140911190), and the AFOSR under grant FA95501010106.

22 31 POSTERS POSTERS

Pump-probe spectroscopy on operating Rb MOT [1] B.T. Taddese et al., Appl. Phys. Lett. 95, 114103 (2009). in 5s–5p–5d cascade [2] B.T. Taddese et al., J. Appl. Phys. 108, 1 (2010). [3] S.M. Anlage et al., Acta Physica Polonica A 112, 569 (2007). M. Głódź1, K. Kowalski1, J. Szonert1, E. Paul-Kwiek2, S. Gateva3 2 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland 2Institute of Physics, Pomer. University in Słupsk, ul. Arciszewskiego 22b, 76-200 Słupsk, Poland 3Institute of Electronics, BAS, 1784 Soﬁa, Boul. Tsarigradsko Shosse 72, Bulgaria

A pump-probe experiment was performed on an operating 85Rb mag- neto-optical trap (MOT). The 5S1/2 (F = 3) 5P3/2 (F′ = 4) transition was driven by the red-detuned trapping beam→ (pump). Absorption of a weak beam (probe), tuned across the second-step hyperfine (hf) transitions 5P3/2 (F′ = 4) 5D5/2 (F′′ = 3, 4, 5) was registered for various pump-beam powers →P and with various pump-beam detunings ∆ from the (F = 3) (F′ = 4) resonance. An example of a series of P-dependent spectra→ is presented in Fig. 1 for ∆ = 18 MHz. All three resonances corresponding to the second-step hfs transitio− ns are split due to Autler–Townes effect in the first step. The distance between A–T peaks (marked by arrows) corresponding to the dominating (F′ = 4) (F′′ = 5) transition was analyzed as a function of the experimental pa→rameters ∆ and P. In the figure the spectra are presented with the most pronounced A–T peaks in the pair being aligned. The conditions of cold atoms vary throughout the MOT cloud. For example, the detuning from resonance varies with magnetic field gradi- ent, the electric field of six overlapping beams vary macroscopically and in microscopic scale. The microscopic changes in space (and in time) are due to beam interference pattern and are affected by fluctuations of various origin. Therefore the possibility of defining a single value of a mean effective Rabi frequency, characterizing an average interaction of the ensemble of MOT atoms with trapping beams, is being challenged (e.g. [1]).

30 23 POSTERS POSTERS

Experimental investigation of the enhancement Transmission and reflection in the stadium billiard: factor and cross-correlation functions for graphs time-dependent asymmetric transport with and without time reversal symmetry Orestis Georgiou Michał Ławniczak, Szymon Bauch, Oleh Hul, Leszek Sirko School of Mathematical Sciences, University of Bristol, Howard House, Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, Queens Ave, Bristol BS8 1SN, UK 02-668 Warszawa, Poland The survival probability of the open stadium billiard with one hole on Quantum graphs are widely used to investigate properties of quantum its boundary is well known to decay asymptotically as a power law. We chaos [1]. Experimentally, quantum graphs are simulated by microwave investigate the transmission and reflection survival probabilities for the graphs (networks) consisting of joints and microwave cables [2,3]. This is case of two holes placed asymmetrically. Classically, these distributions possible due to an equivalency of the one-dimensional Schrödinger equa- are shown to lose their algebraic decay tails depending on the choice of tion describing a quantum system and the telegraph equation describing injecting hole therefore exhibiting asymmetric transport. The mechanism an ideal microwave network. behind this is explained while exact expressions are given and confirmed We present the results of experimental studies of the enhancement numerically. factor [4,5] WS,β: pvar(S aa)var(S bb) W = S,β var(S ab) and cross-correlation function c12(ν) ∆ ∆ S 12(ν + ν)S 21∗ (ν + ν) ∆ν c12(ν) = h i p S (ν + ∆ν) 2 ∆ S (ν + ∆ν) 2 ∆ h| 12 | i νh| 21 | i ν for fully connected, hexagon microwave graphs. Lengths of the 15 bonds of each realization of the graphs were chosen to be incommensurable in order to avoid a degeneracy of the eigenfrequencies. The vector network analyzer (Agilent E8364B) was used to measure the scattering matrix S of the microwave graphs with time reversal symmetry (TRS), which statistical properties of eigenfrequencies can be described by Gaussian Orthogonal Ensemble (GOE), as well as of the graphs with broken time reversal symmetry described by Gaussian Uni- tary Ensemble (GUE). To simulate the graphs with broken TRS we used microwave circulators. The measurements were performed as a function of absorption, which was varied by using microwave attenuators.

24 29 POSTERS POSTERS

Sticky and non-sticky open mushrooms [1] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1999). [2] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, L. Sirko, Phys. Orestis Georgiou Rev. E 69, 056205 (2004). School of Mathematical Sciences, University of Bristol, Howard House, [3] M. Ławniczak, O. Hul, S. Bauch, P. Seba, L. Sirko, Phys. Rev. E 77, 056210 Queens Ave, Bristol BS8 1SN, UK (2008). [4] D.V. Savin, Y.V. Fyodorov, H.-J. Sommers, Acta Phys. Pol. A 109, 53 (2006). We investigate mushroom billiards, a class of dynamical systems [5] M. Ławniczak, S. Bauch, O. Hul, L. Sirko, Phys. Rev. E, accepted for publi- with sharply divided phase space. For typical values of the control pa- cation (2010). rameter of the system, an in finite number of marginally unstable periodic orbits (MUPOs) exist making the system sticky in the sense that unstable orbits approach regular regions in phase space and thus exhibit regular be- haviour for long periods of time. The problem of finding these MUPOs is expressed as the well known problem of finding optimal rational approximations of a real number, subject to some system-specific constraints. By introducing a generalized mushroom and using properties of continued fractions, we describe a zero measure set of control parameter values for which all MUPOs are destroyed and therefore the system is less sticky. The open mushroom (billiard with a hole) is also considered in order to quantify the stickiness exhibited and exact leading order expressions for the algebraic decay of the survival probability function are calculated.

28 25 POSTERS POSTERS

Coherent backscattering of light by a cloud of cold Weak localization in non-linear media atoms Felix Eckert Tobias Binninger Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hermann-Herder-Str. 3, Freiburg, Germany Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg, Hauriweg 10, 79110 Freiburg, Germany When waves propagate through samples with randomly located scat- We theoretically study coherent backscattering of intense laser light tering centers, it is well known that on average the transmission through in a cloud of cold atoms in the framework of the recently proposed pump– the sample is reduced with respect to the classical expectation. If the probe approach. Within this approach, valid for all atoms being in the wavelength of the incident wave is much smaller than the mean free path far field of each other, the atomic radiation is described classically and this effect, arising from constructive interference within loops formed represents a probe field, while the laser field represents a pump field. by counter propagating wave amplitudes, is called weak localization and We show that a generalization of the pumpprobe approach, developed amounts to a small reduction of the diffusion coefficient. previously for double scattering, to the case of many atoms leads to the However, the interplay of weak localization and non-linearity is to single atom Optical Bloch Equations under a polychromatic stochastic date not fully understood. The enhancement of intensity in the back scat- driving field. We discuss a method of solution of the resulting equations tering direction, which is another manifestation of weak localization, was as well as the connection of these solutions with the spectrum, intensity, shown to be very sensitive to even weak non-linearities [1]. The con- and enhancement factor of the coherently backscattered light. structive interference in the back scattering direction in the linear case can even turn into destructive interference in the non-linear case. The prediction of the transport equation arising from diagrammatic theory within the diffusion approximation does not show this cross-over to destructive interference, since it neglects the contributions of propagation over distances smaller or of the order of the mean free path. Therefore, we first concentrate on the linear case and determine the leading corrections to the scattering and the transport mean free path for propagation in a white-noise Gaussian potential, including also the contribution of short loops beyond the diffusion approximation. In the future, we will include non-linearity into these calculations in order to clarify whether the transition to destructive coherent back scattering goes along with a weak anti-localization effect induced by the nonlinearity. [1] T. Wellens, Applied Physics B: Lasers and Optics 95, 189 (2009).

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