Download 5th Workshop on Quantum Chaos and Localisation Phenomena

5th Workshop
on Quantum Chaos
and Localisation Phenomena
May 20–22, 2011, Warsaw, Poland
organised by Institute of Physics Polish Academy of Sciences,
Center for Theoretical Physics Polish Academy of Sciences,
and Pro Physica Foundation
Organising Committee
PROGRAMME
Szymon Bauch ([email protected])
Oleh Hul ([email protected])
Marek Kuś ([email protected])
Michał Ławniczak ([email protected])
Leszek Sirko – chairman ([email protected])
Sunday, May 22
9:00–9:35
9:35–10:10
10:10–10:45
Objectives
To assess achievements and to formulate directions of new research
on quantum chaos and localisation
To bring together prominent experimental and theoretical physicists
who share a common interest in quantum chaos and localisation
phenomena
10:45–11:20
11:20–11:50
11:50–12:25
12:25–13:00
13:00–13:35
Scope
Presentations will focus on the following topics:
Quantum chaos and nonlinear classical systems
Quantum and microwave billiards
Quantum and microwave graphs
Atoms in strong electromagnetic fields – experiment and theory
Chaos vs. coherent effects in multiple scattering
Anderson localisation
Random lasers
Quantum chaos and quantum computing
Entanglement and noise
13:35–14:30
14:30–14:50
14:50–15:10
15:10–15:30
15:30–15:40
INVITED TALKS
Uzy Smilansky (Rehovot, Israel)
Stationary scattering from a nonlinear network
Yan V. Fyodorov (Nottingham, UK)
Level curvature distribution at the spectral edge of random
Hermitian matrices
Pavel Kurasov (Stockholm, Sweden)
Magnetic Schrödinger operators on graphs: spectra,
inverse problems and applications
Karol Życzkowski (Warsaw, Poland)
Level spacing distribution revisited
coffee break
Andreas Buchleitner (Freiburg, Germany)
Transport, disorder, and entanglement
Jan Kříž (Hradec Králové, Czech Republic)
Chaos in the brain
Agnès Maurel (Paris, France)
Experimental study of waves propagation using Fourier
Transform Profilometry
lunch break
CONTRIBUTED TALKS
Filip Studnička (Hradec Králové, Czech Republic)
Analysis of biomedical signals using differential
geometry invariants
Michał Ławniczak (Warsaw, Poland)
Investigation of Wigner reaction matrix, cross- and velocity
correlators for microwave networks
Maciej Janowicz (Warsaw, Poland)
Quantum properties of coupled generalized logistic map
lattices
Closing remarks
PROGRAMME
Friday, May 20
19:00–21:00
Welcome party
INVITED TALKS
Fading statistics in communications – a random
matrix approach
Saturday, May 21
9:00–9:10
9:10–9:45
9:45–10:20
10:20–10:55
10:55–11:30
Leszek Sirko (Warsaw, Poland)
Opening
INVITED TALKS
Achim Richter (Darmstadt, Germany)
Simulating graphene with a microwave photonic crystal
Steven M. Anlage (College Park, USA)
Fading statistics in communications – a random matrix
approach
Jakub Zakrzewski (Cracow, Poland)
Extraction of information from dynamics for strongly
correlated systems
Heinerich Kohler (Madrid, Spain)
Fidelity in chaotic and random systems
11:30–12:00
coffee break
12:00–12:35
Dima Shepelyansky (Toulouse, France)
Wigner crystal in snaked nanochannels
Bart van Tiggelen (Grenoble, France)
3D Anderson localization of ultrasound and cold atoms
Gregor Tanner (Nottingham, UK)
Wave intensity distributions in complex structures
12:35–13:10
13:10–13:45
13:45–14:45
lunch break
14:45–16:00
POSTER SESSION
16:00–16:20
16:20–16:40
16:40
CONTRIBUTED TALKS
Lock Yue Chew (Singapore)
The quantum signature of chaos through the dynamics
of entanglement
Adam Sawicki (Warsaw, Poland and Bristol, UK)
Scattering from isospectral graphs
Jen-Hao Yeh, Thomas Antonsen, Edward Ott, Steven M. Anlage
Physics Department, University of Maryland, College Park, MD 20742-4111,
USA
Fading is the observation of variations in signal strength measured at
a receiver due to time-dependent variations in the propagation of waves
from the source, or due to multi-path scattering and interference. It is
well known that the quantitative statistical theory of wave chaos – random
matrix theory (RMT) – can be successfully applied to predict statistical
properties of many quantities, such as the scattering matrix, of a wave
chaotic system. Here we start from the statistical model of the scattering matrix [1] to establish a general fading model. The model provides
a first-principles understanding of the most common statistical model used
in the communications field, namely Rayleigh fading, and shows that the
statistical properties are governed by a single quantity related to the loss
or de-phasing parameter of RMT. We also combine the RMT fading
model with our random coupling model (RCM) that takes into account
system-specific features such as direct and short orbits [2–4], to build
a more general fading model that includes Rician fading. In the high
loss-parameter limit, our model agrees with the Rayleigh/Rice models,
however it shows significant deviations from the Rayleigh/Rice distribution 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
over a wide range of loss parameter values.
Work funded by the ONR/Maryland AppEl Center Task A2 (contract No.
N000140911190), the AFOSR under grant FA95500710049.
[1]
[2]
[3]
[4]
P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. B 55, 4695 (1997).
James A. Hart, T.M. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009).
Jen-Hao Yeh et al., Phys. Rev. E 81, 025201(R) (2010).
Jen-Hao Yeh et al., Phys. Rev. E 82, 041114 (2010).
Warsaw tour and conference dinner
1
INVITED TALKS
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 efficiency of large biomolecular units may stem from quantum coherence
phenomena, despite strong environment coupling. We explain such efficiency, 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
NOTES
PARTICIPANTS AND AUTHORS
Bart van Tiggelen (invited speaker), p. 12
CNRS/Laboratoire de Physique et Modelisation des Milieux Condeses, Universite
Joseph Fourier, Maison des Magisteres, BP 166, F-38042 Grenoble Cedex 9,
France
e-mail: [email protected]
INVITED TALKS
Level curvature distribution at the spectral edge
of random Hermitian matrices
Yan V. Fyodorov
Mathematical Physics, School of Mathematical Sciences,
University of Nottingham, NG72RD Nottingham, UK
Tomasz Tkocz (co-author), p. 14
Dept. of Physics, Warsaw University, Hoża 69, 00-681 Warsaw, Poland
Maciej Wołoszyn (poster), p. 42
Dept. of Applied Informatics and Computational Physics, AGH University
of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland
e-mail: [email protected]
Jen-Hao Yeh (co-author), p. 1
Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
e-mail: [email protected]
Jakub Zakrzewski (invited speaker), p. 13
M. Smoluchowski Institute of Physics Jagiellonian University, ul. Reymonta 4,
PL-30-059 Cracow, Poland
e-mail: [email protected]
Level curvature is a measure of sensitivity of eigenvalues of a disordered/chaotic system to perturbations. In the bulk of the spectrum Random
Matrix Theory predicts the probability distributions of level curvatures
to be given by Zakrzewski–Delande expressions. Motivated by growing
interest in statistics of extreme (maximal or minimal) eigenvalues of disordered systems of various nature, it is natural to ask about the associated
level curvatures. I show how calculating the distribution for the curvatures of extreme eigenvalues in GUE ensemble can be reduced to studying asymptotics of orthogonal polynomials appearing in a recent work by
Nadal and Majumdar. The corresponding asymptotic analysis being yet
outstanding, I instead will discuss solution of a related, but somewhat
simpler problem of calculating the level curvature distribution averaged
over all the levels in a spectral window close to the edge of the semicircle.
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]
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3
INVITED TALKS
Fidelity in chaotic and random systems
Heinerich Kohler
PARTICIPANTS AND AUTHORS
Andrzej L. Sobolewski (co-author), p. 38
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
Instituto de Ciencia de Materiales de Madrid, CSIC, Spain
Fidelity is the overlap of a wave function, propagated by a Hamiltonian in time, with the same initial wave function, propagated by a perturbed wave function. Its behavior depends crucially on the choice of the
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.
The latter can easier be measured, since no knowledge of the wave function is required. On the other hand, if the initial state is an eigenstate of
the unperturbed system we find unexpected features like non-ergodicity.
In this case fluctuations become important and the full fidelity distribution (FFD) becomes a non-trivial function. We calculated the FFD in the
long time limit and for small perturbations.
Bartłomiej Spisak (poster), p. 41
Dept. of Applied Informatics and Computational Physics, AGH University
of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland
e-mail: [email protected]
Filip Studnička (contributed talk), p. 21
University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove,
Czech Republic
e-mail: fi[email protected]
Jacek Szczepkowski
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]
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PARTICIPANTS AND AUTHORS
Achim Richter (invited speaker), p. 8
Institut fuer Kernphysik, Technische Universitaet, Darmstadt, Schlossgartenstr. 9,
D-64289 Darmstadt
e-mail: [email protected]
Michał Rode (poster), p. 38
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
INVITED TALKS
Chaos in the brain
Jan Kříž
University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove,
Czech Republic
We describe several links between EEG data processing and quantum
mechanics. Then we show examples of exploitation of methods commonly
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
Magnetic Schrödinger operators on graphs: spectra,
inverse problems and applications
PARTICIPANTS AND AUTHORS
Agnès Maurel (invited speaker), p. 7
Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France
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
e-mail: [email protected]
Magnetic Schrödinger operators on metric graphs as models for electron 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
families of isospectral graphs and trees will be discussed. The results
will be applied to model quantum transport in nanosystems. Theoretic
and experimental observations will be compared.
Jan Mostowski
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
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]
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PARTICIPANTS AND AUTHORS
Krzysztof Kowalski, p. 30, 32
Institute of Physics Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
INVITED TALKS
Experimental study of waves propagation
using Fourier Transform Profilometry
Agnès Maurel
Jan Kříž (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
e-mail: [email protected]
Pavel Kurasov (invited speaker), p. 6
Mathematical Institute, Stockholm University, 106 91 Stockholm, Sweden
e-mail: [email protected]
Marek Kuś, p. 14
Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
Michał Ławniczak (contributed talk), p. 18, 24
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
We have developed recently an optical method able to quantitatively
measure the field of surface elevation with very good spatial and temporal resolutions. This allows for the study of several problems of wave
propagation in complex medium, either in the context of water waves or
surface waves. We will present recent results concerning resonances of
water waves near floating object, wave turbulence in the context of water
waves and bending waves and Time Reversal water waves.
[1] P. Cobelli, V. Pagneux, A. Maurel, P. Petitjeans, Experimental study on
water-wave trapped modes, J. Fluid Mech. 666, 445 (2011).
[2] P. Cobelli, P. Petitjeans, A. Maurel, V. Pagneux, N. Mordant, Space-time
resolved wave turbulence in a vibrating plate, Phys. Rev. Lett. 103, 204301
(2009).
[3] P. Cobelli, V. Pagneux, A. Maurel, P. Petitjeans, Experimental observation of
trapped modes in water wave channel, Europhys. Letters 88, 20006 (2009).
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]
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INVITED TALKS
Simulating graphene with a microwave photonic
crystal
PARTICIPANTS AND AUTHORS
Orestis Georgiou (poster), p. 28, 29
School of Mathematical Sciences, University of Bristol, Howard House,
Queens Ave, Bristol BS8 1SN, UK
e-mail: [email protected]
Achim Richter
Institut fuer Kernphysik, Technische Universitaet Darmstadt,
D-64289 Darmstadt, Germany, and the European Centre for Theoretical Studies
in Nuclear Physics and Related Areas, I-38100 Villazzano (Trento), Italy
We have measured recently reflection and transmission spectra of
a microwave photonic crystal consisting of 874 metallic cylinders arranged
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
states in the photonic crystal, providing clear evidence for the existence
of a Dirac point which is a characteristic of relativistic massless fermions.
Dirac points are also a peculiar property of the electronic band structure
of Graphene [2] whose properties can thus be described by the relativistic
Dirac equation [3–5]. It will be shown how several features of Graphene
(dispersion relation, so-called edge states, pseudodiffusive transmission
at the Dirac point) are modeled in photonic crystals. Furthermore, as
a direct extension of the present work, the experimental investigation of
properties of the eigenvalues and eigenfunctions of a superconducting
Dirac billiard is discussed. The photonic crystal will thereby be placed in
a closed resonator box [6,7].
Supported by the DFG within the SFB 634.
[1] S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, F. Schaefer,
Phys. Rev. B 82, 014301 (2010).
[2] A.K. Geim, K.S. Novoselov, Nature Mater. 6, 183 (2007).
[3] P.R. Wallace, Phys. Rev. 71, 622 (1947).
[4] G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984).
[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).
[7] J. Wurm, A. Rycerz, I. Adagideli, M. Wimmer, K. Richter, H.U Baranger,
Phys. Rev. Lett. 102, 056806 (2009).
8
Martin Holthaus (co-author), p. 37
Condensed Matter Theory Group, Institut für Physik, Carl von Ossietzky
Universität, D-26111 Oldenburg, Germany
e-mail: [email protected]
Oleh Hul, p. 18, 24
Institute of Physics Polish, Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
Maciej Janowicz (contributed talk), p. 17, 36, 37
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
Felix Jörder (poster), p. 34
Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg,
Hermann-Herder-Str. 3, 79104 Freiburg, Germany
e-mail: [email protected]
Heinerich Kohler (invited speaker), p. 4
Dept. of Theory and Simulation of Materials, Instituto de Ciencias de Materiales
de Madrid, Sor Juana Ines de la Cruz 3, Cantoblanco, 28049 Madrid, Spain
e-mail: [email protected]
Katarzyna Kowalczyk
Dept. of Physics, Warsaw University, Hoża St. 69, Warsaw, Poland
e-mail: kejta [email protected]
45
PARTICIPANTS AND AUTHORS
Lock Yue Chew (contributed talk), p. 15
Division of Physics and Applied Physics, Nanyang Technological University,
21 Nanyang Link, SPMS-PAP-04-04, Singapore
e-mail: [email protected]
INVITED TALKS
Wigner crystal in snaked nanochannels
Dima Shepelyansky
Laboratoire de Physique Theorique UMR 5152 du CNRS, IRSAMC Universite
Paul Sabatier 118, Route de Narbonne, F-31062 Toulouse Cedex 4, France
Felix Eckert (poster), p. 27
Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg,
Hermann-Herder-Str. 3, 79104 Freiburg, Germany
e-mail: [email protected]
Matthew Frazier (co-author), p. 22
Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
e-mail: [email protected]
Yan V. Fyodorov (invited speaker), p. 3
We study properties of Wigner crystal in snaked nanochannels and
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
structure typical for the Aubry transition in dynamical maps and the Frenkel–Kontorova model. We discuss implications of this phenomenon for
charge density waves in quasi-one-dimensional organic conductors and
for supercapacitors in nanopore materials.
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]
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9
INVITED TALKS
Stationary scattering from a nonlinear network
Uzy Smilansky
Department of Physics of Complex Systems, The Weizmann Institute of Science,
Rehovot, 76100 IL, Israel
Transmission through a complex network of nonlinear one-dimensional leads will be discussed by extending the stationary scattering theory
on quantum graphs to the nonlinear regime.
We show that the existence of cycles inside the graph leads to a large
number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and
display multistability and hysteresis. This work provides a framework for
the study of light propagation in complex optical networks.
PARTICIPANTS AND AUTHORS
Steven M. Anlage (invited speaker), p. 1, 22
Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
e-mail: [email protected]
Thomas Antonsen (co-author), p. 1, 22
Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
e-mail: [email protected]
Szymon Bauch (poster), p. 18, 24
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
e-mail: [email protected]
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]
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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
A finite semiconductor superlattice generated by the Fibonacci sequence and the electronic states formed within it are studied in the limit of
weak electric field. Effect of the electric field on the energy spectrum and
the density of states is discussed in terms of the anticrossings originating
in the system.
It is shown that the generalized dimension calculated as a function
of electric field has maxima in the vicinity of anticrossings, and that at
the same values of the electric field the minimal values of the inverse
participation ratio are observed.
School of Mathematical Sciences, University of Nottingham,
NG7 2RD Nottingham, UK
The vibro-acoustic response of mechanical structures can in general
be well approximated in terms of linear wave equations. Standard numerical solution methods comprise the finite or boundary element method
(FEM, BEM) in the low frequency regime and Statistical Energy Analysis (SEA) in the high-frequency limit. Major computational challenges are
posed by the so-called mid-frequency problem – that is, composite structures where the local wave length may vary by orders of magnitude across
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 degree of spatial resolution and capturing long range correlations in the ray
dynamics.
[1] G. Tanner, Journal of Sound and Vibration 320, 1023 (2009).
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INVITED TALKS
POSTERS
3D Anderson localization of ultrasound and cold
atoms
Phase space approach to the effect of weak magnetic
field on the 2k F 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
transitions in condensed matter. The huge impact it has had in condensed
matter physics cannot be underestimated, recognized by the Nobel Prize
in 1977. Yet, the experimental study of Anderson localization turned
out very hard. Arguably, only when it was realized in the early eighties that Anderson localization of classical waves such as light and sound
should exist, a new experimental activity started. In this presentation I will
present a recent observation of Anderson localization with elastic waves in
“mesoglass” structure. I will describe how this “unrecognizable monster”
(a quote from Anderson himself) has revealed itself in our experiments: in
the dynamics of the wave propagation, in the fluctuations of the speckles,
in the confinement and the structure of the wave packet. I will mention 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 controlled 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.
In structurally disordered systems the conduction electrons may be
prone to weak localisation which is caused by coherent multiple scatterings in the backward direction. This effect is regarded as a precursor of
the Anderson localisation.
The weak localisation of the conduction electrons in three dimensional structurally disordered systems is considered in the limit of weak
magnetic field within the framework of the generalised kinetic equation
for the Wigner distribution function and the effective medium approximation. The results of calculations are compared with the experimental
data of magnetoresistance measurements for amorphous Ca x Al1−x metallic glass.
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 reviews see: A. Lagendijk, B.A. van Tiggelen, D.S. Wiersma, Fifty years of Anderson 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
Experimental time-reversal of water wave
Adam Prządka
Institut Langevin, ESPCI, ParisTech, 10, rue Vauquelin, Paris 75005, France
The phenomena of the time-reversal of acoustic and optical waves
were deeply studied in the recent years. The extension of this phenomenon
to the surface water waves is presented. The optical method of Fourier
Transform Profilometry (FTP) is used to measure the surface elevation in
time and space. The experiments in the capillary-gravity regime show that
after the time-reversion of the waves (although attenuated), the successful
temporal and spatial refocalisation can be observed (with half of the
wavelength spatial limit).
40
INVITED TALKS
Extraction of information from dynamics for strongly
correlated systems
Jakub Zakrzewski
M. Smoluchowski Institute of Physics, Jagiellonian University,
ul. Reymonta 4, PL-30-059 Cracow, Poland
A spectacular progress has been reached in ultra cold atomic systems
recently. In particular, the observation of a quantum phase transition from
superfluid phase to Mott insulator, as well as emergence of a Bose glass
for disordered system, has served as a stimulus for an immense activity
in the field. We show that, in a strict quantum mechanical sense, the adiabatic 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.
13
INVITED TALKS
Level spacing distribution revisited
Karol Życzkowski1 , Tomasz Tkocz2 , Marek Smaczyński3 ,
Marek Kuś1
1
Center for Theoretical Physics, Polish Academy of Sciences,
al. Lotników 32/46, 02-668 Warszawa, Poland
2
Dept. of Physics, Warsaw University, Hoża 69, 00-681 Warsaw, Poland
3
Atomic Optics Department, Institute of Physics, Jagiellonian University,
Reymonta 4, 30-059 Cracow, Poland
Spectral properties of quantized chaotic systems can be described
by the theory of random matrices. The distribution of the largest eigenvalue of a random hermitian matrix is described by the Tracy–Widom
Law. An analogous problem of characterizing the extremal gaps between
neighbouring eigenphases of random unitary matrices are analyzed. The
spectral statistics are also investigated in the case of random unitary matrices with a tensor product structure, which represent evolution operators
for non-interacting quantum composite systems.
POSTERS
Our study shows how the substituent effect exerts the influence on
the energetical landscape of the excited state and may be used in practice
to search for materials of desired energetical and optical properties.
[1]
[2]
[3]
[4]
[5]
[6]
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[9]
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[12]
14
H. Mori, E. Miyoshi, Bull. Chem. Soc. Jpn. 80, 1335 (2007).
M. Sauer, Proc. Natl. Acad. Sci. U.S.A. 102, 9433 (2005).
F.M. Raymo, Adv. Mater. 14, 401 (2002).
P. Zhao, C.F. Fang, C.J. Xia, Y.M. Wang, D.S. Liu, S. Xie, J. Appl. Phys.
Lett. 93, 013113 (2008).
P. Zhao, C.F. Fang, C.J. Xia, D.S. Liu, S. Xie, J. Chem. Phys. Lett. 453, 62
(2008).
P. Zhao, Z. Zhang, P.J. Wang, D.S. Liu, Physica B 404, 3462 (2009).
D. Dulic, S.J. van der Molen, T. Kudernac, H.T. Jonkman, J.D. de Jong,
T.N. Bowden, J. van Esch, B.L. Feringa, B.J. van Wees, Phys. Rev. Lett. 91,
207402 (2003).
C. Benesch, M.F. Rode, M. Cizek, R. Hartle, O. Rubio-Pons, M. Thoss,
A.L. Sobolewski, J. Phys. Chem. C 113, 10315 (2009).
V. Bermudez, N. Capron, T. Gase, F.G. Gatti, F. Kajzar, D.A. Leigh, F. Zerbetto, S.W. Zhang, Nature 406, 608 (2000).
A.L. Sobolewski, Phys. Chem. Chem. Phys. 10, 1243 (2008).
L. Lapinski, M.J. Nowak, J. Nowacki, M.F. Rode, A.L. Sobolewski, Chem.
Phys. Chem. 10, 2290 (2009).
M.F. Rode, A.L. Sobolewski, sent for review to J. Phys. Chem. A.
39
POSTERS
Effect of chemical substituents on energetical
landscape of a molecular switch: an ab initio study
M.F. Rode, A.L. Sobolewski
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
The search for optically switchable molecules is nowadays an important and popular issue [1–3] Optical molecular switches enable the
storage of information on a molecular level and route signals in molecular electronic logic circuits [2,4–7]. They are considered as the controllers
of current flow when linked to conjugated polymer chains [8]. In order to
serve as a molecular switch, a molecular system must posses at least two
stable forms which may be switched by an external electric filed, electron
transfer, chemical reaction or optical excitation [9].
In our investigation we are searching for optical molecular switches
which operate on the Excited State Intramolecular Proton Transfer
(ESIPT) phenomenon [8,10–12]. The switching process involves the longrange transfer of a proton which is picked up by a “molecular crane”; at
the donor site due to optical excitation, and delivered to the acceptor site of
the system by rotation of the crane. The reversibility of the switch is guaranteed by the ESIPT mechanism conditions, which are: (i) photochromism
of the system and (ii) a barrierless access on the potential-energy surface
(PES) of the S1 state to the S1 –S0 conical intersection (CI) which is
common for both photochromic forms.
In our theoretical study we have chosen 7-hydroxy-quinoline 7HQ
as a skeleton of the switch, as it may posses two isomeric forms due the
presence of two distinguishing hydrogen-donor/acceptor centers: O and N
atoms, being able to donate the hydrogen atom to the crane [11,12]. We
have investigated several potential crane molecules such as carbaldehyde,
pyridine and oxazine being attached at the position 8′ of the 7HQ skeleton and searched for appropriate side groups which, substituted at the
given position, would improve the energetical landscape of the molecular
system.
38
CONTRIBUTED TALKS
The quantum signature of chaos
through the dynamics of entanglement
classically regular and chaotic systems
Lock Yue Chew
Division of Physics and Applied Physics, Nanyang Technological University,
PO Box: 21 Nanyang Link, SPMS-PAP-04-04, Singapore
Quantum entanglement is an important resource in quantum information processing. The capability of preparing quantum states that are
highly entangled is especially significant in applications such as quantum
teleportation and superdense coding [1]. An approach to prepare such
states is to examine the time evolution of quantum states generated by
Hamiltonians of two-coupled oscillator systems. In this talk, I will present
our recent investigation on the dynamics of entangled states which are
generated by systems that are classically regular, mixed, and chaotic [2-3].
For systems that are classically regular, we found periodic entanglement
which has twice the frequency of the corresponding classical motion. Such
frequency doubling continues to hold true in the entanglement dynamics
for a second model that exhibits a two-frequency orbit in the classical
domain. Surprisingly, we found that a periodic classical trajectory can
give rise to a quasi-periodic entanglement dynamics upon quantization.
For a system that is chaotic, we have reaffirmed existing results that the
entanglement production rate is higher when the classical system is more
chaotic, i.e., the system possesses a more positive Lyapunov exponent [4].
When the system contains a mixed phase space, the entanglement dynamics is found to be insensitive to the choice of the initial conditions in the
regular or the chaotic classical regime. In fact, we have demonstrated
complete dependence of the dynamical pattern of entanglement on the
global classical dynamical domain without being influenced by the local classical behavior in all the three classical regimes for the first time.
While such global dependence is not necessary for all coupled oscillator
systems, the nonlocal models that we have investigated have the advantage
of generating an encoding subspace [5] that is stable against any errors
in the preparation of the initial separable coherent states. Such a feature
15
CONTRIBUTED TALKS
will be physically significant in the design of robust quantum information
processing protocols.
[1] M. Christandl, N. Schuch and A. Winter, Highly entangled states with almost
no secrecy, Phys. Rev. Lett. 104, 240405 (2010).
[2] N. N. Chung and L. Y. Chew, Dependence of entanglement dynamics on the
global classical dynamical regime, Phys. Rev. A 80, 016204 (2009).
[3] N. N. Chung and L. Y. Chew, Two-step approach to the dynamics of coupled
anharmonic oscillator systems, Phys. Rev. A 80, 012103 (2009).
[4] S.-H. Zhang and Q.-L. Jie, Quantum-classical correspondence in entanglement production: entropy and classical tori, Phys. Rev. A 77, 012312 (2009).
[5] E. Ciancio and P. Zanardi, Coupling bosonic modes with a qubit: entanglement dynamics at zero and a finite temperature, Phys. Lett. A360, 49 (2006).
16
POSTERS
Coherence in chaotic coupled logistic map lattices
Maciej Janowicz1 , Arkadiusz Orłowski1 , Martin Holthaus2
1
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
2
Condensed Matter Theory Group, Institut für Physik, Carl von Ossietzky
Universität, D-26111 Oldenburg, Germany
Waves generated by systems of diffusively coupled logistic maps
have been employed in numerical simulations to perform an analogue of
the two-slit diffraction experiment. Interference patterns with high visibility 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 factorization. Thus, nonlinear diffusive systems can possess features which
are characteristics of genuinely coherent fields.
37
POSTERS
Transient pattern formation and condensate-like
behavior in coupled map lattices based on logistic
map
Maciej Janowicz, Arkadiusz Orłowski
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
Pattern formation in two-dimensional coupled map lattices based on
the logistic mapping has been investigated as dependent on the coupling
constant, the diffusion constant, and initial conditions. Three additional
quantitative measures of the coupled map lattices behavior: reduced density matrix, reduced wave function, and an analog of particle number
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
CONTRIBUTED TALKS
Quantum properties of coupled generalized logistic
map lattices
Maciej Janowicz
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warszawa, Poland
Properties of quantized versions of coupled system of minimal nonsingular symplectic generalizations of logistic maps have been investigated. It is shown that the behavior of such systems resembles that of
Bose–Einstein condensates. In particular, the off-diagonal long range order and dominant eigenvalues of the reduced density matrices have been
found.
17
CONTRIBUTED TALKS
POSTERS
Investigation of Wigner reaction matrix, crossand velocity correlators for microwave networks
Spinor Bose–Hubbard model with disorder – phase
diagram and phase transitions
Michał Ławniczak1 , Szymon Bauch1 , Oleh Hul1 ,
Agata Borkowska2,1 , Leszek Sirko1
Mateusz Łącki
Atomic Optics Division, Jagiellonian University, Kraków, Poland
1
Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46,
02-668 Warsaw, Poland
2
Department of Chemistry, Warsaw University of Technology, Noakowskiego 3,
00-664 Warsaw, Poland
Spinor Bose–Hubbard model describes behavior of ultracold Bose
gas on optical lattice. Description of general (and quite rich) phase diagram 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 irregular 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 Education grant no. N N202 130239.
18
35
POSTERS
Complex dilation for time-dependent phenomena
in driven helium
Felix Jörder
Physikalisches Institut, Albert-Ludwigs-Universitaet Freiburg,
Hermann-Herder-Str. 3, Freiburg, Germany
The electromagnetically driven helium atom defines a paradigmatic
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
CONTRIBUTED TALKS
[1] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997).
[2] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, L. Sirko, Phys.
Rev. E 69, 056205 (2004).
[3] M. Ławniczak, O. Hul, S. Bauch, P. Seba, L. Sirko, Phys. Rev. E 77, 056210
(2008).
[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,
H.A. Weidenmüller, Phys. Rev E 81, 036205 (2010).
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 complemented 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
The influence of Zeeman D2 transitions on probe
absorption spectra in a multilevel Lambda scheme
for cold 85 Rb atoms
E. Paul-Kwiek1 , M. Głódź2 , K. Kowalski2 , J. Szonert2 ,
S. Gateva3
CONTRIBUTED TALKS
Analysis of biomedical signals using differential
geometry invariants
Filip Studnička
University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove,
Czech Republic
1
Institute of Physics, Pomer. University in Słupsk, ul. Arciszewskiego 22b,
76-200 Słupsk, Poland
2
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warsaw, Poland
3
Institute of Electronics, BAS, 1784 Sofia, Boul. Tsarigradsko Shosse 72,
Bulgaria
We have observed complex spectral features in probe absorption in
a multilevel Lambda-scheme of the D2 transitions in 85 Rb atoms cooled
and trapped in MOT. The related physical phenomena are: partially suppressed EIT and Autler–Townes effect, under conditions of Lambda excitation 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 |1i–|5i in the Figure). In order to indirectly ac32
Tensometers and accelerometers were placed on a bed to measure
human haemodynamics and movement activity. It is shown that n signals
from those devices can be described as a 1D manifolds in Rn . Those
signals are analysed using classical and affine differential geometry invariants to investigate e.g. the propagation of pulse wave in aorta and
heart and breathing activity. Matlab script which can monitor movement
activity of the person lying on the bed has been finished. This script can
distinguish between the movement of the person itself or movement of
the person caused by someone else (e.g. turning of the person etc.). It
will be used in the medical industry in less than one year.
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
to partially overcome the effects of propagation losses [1]. In addition,
time windowing of the sona signal, along with the exponential amplification, was demonstrated to be effective at varying the spatial range of
sensitivity to perturbations [2]. Now, we take this work in a different direction by considering the case in which there is an object with a classical
nonlinear response inside a wave chaotic electromagnetic system. After
being stimulated, the nonlinear object creates a new frequency-translated
sona signal, which is gathered and recorded by the time-reversal mirror.
We demonstrate that when the time-reversed nonlinear sona is sent back
into the system, it creates a time-reversed pulse that collapses back onto
the nonlinear object. This constitutes a new modality for directed wave
propagation in strongly scattering and wave chaotic media.
Basing on our experimental procedure and by using a simple threelevel model, we have still demonstrated [2] that, despite the complex nature of interactions in MOT, within a range of MOT parameters it is
justified to characterise MOT with an approximate√value of an effective
Rabi frequency Ω0eff , by using the formula Ω0eff = BP, which is analogous to
√ the one used for in interaction of a single atom with local light
scaling factor, and P is
field. B is a mean experimentally determined
√
the total trapping laser power. The value of B and applicability limits of
the method have to be verified with each new implementation of MOT.
[1] J.H. Marquardt et al., J. Opt. Soc. Am. B 13, 1384 (1996).
[2] M. Głódź et al., Opt. Commun. (2011), in press.
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
Pump-probe spectroscopy on operating Rb MOT
in 5s–5p–5d cascade
POSTERS
[1] B.T. Taddese et al., Appl. Phys. Lett. 95, 114103 (2009).
[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
2
Institute of Physics, Pomer. University in Słupsk, ul. Arciszewskiego 22b,
76-200 Słupsk, Poland
3
Institute of Electronics, BAS, 1784 Sofia, Boul. Tsarigradsko Shosse 72,
Bulgaria
A pump-probe experiment was performed on an operating 85 Rb magneto-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 transitions 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 parameters ∆
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 gradient, 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
factor and cross-correlation functions for graphs
with and without time reversal symmetry
Transmission and reflection in the stadium billiard:
time-dependent asymmetric transport
Michał Ławniczak, Szymon Bauch, Oleh Hul, Leszek Sirko
School of Mathematical Sciences, University of Bristol, Howard House,
Queens Ave, Bristol BS8 1SN, UK
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46,
02-668 Warszawa, Poland
Quantum graphs are widely used to investigate properties of quantum
chaos [1]. Experimentally, quantum graphs are simulated by microwave
graphs (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 experimental studies of the enhancement
factor [4,5] WS,β :
p
var(S aa )var(S bb )
WS,β =
var(S ab )
and cross-correlation function c12 (ν)
c12 (ν) = p
Orestis Georgiou
The survival probability of the open stadium billiard with one hole on
its boundary is well known to decay asymptotically as a power law. We
investigate the transmission and reflection survival probabilities for the
case of two holes placed asymmetrically. Classically, these distributions
are shown to lose their algebraic decay tails depending on the choice of
injecting hole therefore exhibiting asymmetric transport. The mechanism
behind this is explained while exact expressions are given and confirmed
numerically.
∗
hS 12 (ν + ∆ν)S 21
(ν + ∆ν)i∆ν
h|S 12 (ν + ∆ν)|2 i∆ν h|S 21 (ν + ∆ν)|2 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 Unitary 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
Sticky and non-sticky open mushrooms
Orestis Georgiou
School of Mathematical Sciences, University of Bristol, Howard House,
Queens Ave, Bristol BS8 1SN, UK
We investigate mushroom billiards, a class of dynamical systems
with sharply divided phase space. For typical values of the control parameter 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 behaviour 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
POSTERS
[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.
Rev. E 69, 056205 (2004).
[3] M. Ławniczak, O. Hul, S. Bauch, P. Seba, L. Sirko, Phys. Rev. E 77, 056210
(2008).
[4] D.V. Savin, Y.V. Fyodorov, H.-J. Sommers, Acta Phys. Pol. A 109, 53 (2006).
[5] M. Ławniczak, S. Bauch, O. Hul, L. Sirko, Phys. Rev. E, accepted for publication (2010).
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POSTERS
POSTERS
Coherent backscattering of light by a cloud of cold
atoms
Weak localization in non-linear media
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
We theoretically study coherent backscattering of intense laser light
in a cloud of cold atoms in the framework of the recently proposed pump–
probe approach. Within this approach, valid for all atoms being in the
far field of each other, the atomic radiation is described classically and
represents a probe field, while the laser field represents a pump field.
We show that a generalization of the pumpŽprobe approach, developed
previously for double scattering, to the case of many atoms leads to the
single atom Optical Bloch Equations under a polychromatic stochastic
driving field. We discuss a method of solution of the resulting equations
as well as the connection of these solutions with the spectrum, intensity,
and enhancement factor of the coherently backscattered light.
Felix Eckert
When waves propagate through samples with randomly located scattering centers, it is well known that on average the transmission through
the sample is reduced with respect to the classical expectation. If the
wavelength of the incident wave is much smaller than the mean free path
this effect, arising from constructive interference within loops formed
by counter propagating wave amplitudes, is called weak localization and
amounts to a small reduction of the diffusion coefficient.
However, the interplay of weak localization and non-linearity is to
date not fully understood. The enhancement of intensity in the back scattering direction, which is another manifestation of weak localization, was
shown to be very sensitive to even weak non-linearities [1]. The constructive 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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