Title Page

Indice

R. Kaiser, D. S. Wiersma and L. Fallani - Preface

Gruppo fotografico dei partecipanti al Corso

P. Wolfle - Anderson localization

Basic notions of localization

Introductory remarks

Electrons and classical waves in disordered systems

Strong localization and Anderson transition

Weak localization

One-dimensional systems

Quasi-one-dimensional systems

Theory of localization: fundamental concepts

Thouless conductance

Scaling theory of the conductance

Renormalization group equation

Critical exponents

Dynamical scaling

Symmetry classes

Non-linear sigma-model

Fractal structure of critical wave functions

Anderson transition in the kicked rotor model

Theory of localization: diagrammatic approaches

Self-consistent theory of localization

Results of the self-consistent theory of localization

Destruction of localization by decoherence processes

Conclusion

P. J. Steinhardt - Photonic properties of non-crystalline solids

Some basics

Photonic band gaps in icosahedral quasicrystals

Dependence of band gap width on symmetry in 2D

Finding optimal complete band gaps for 2D photonic quasicrystals

Isotropic disordered photonic materials

Discussion

R. C. Mesquita and A. G. Yodh - Diffuse optics: Fundamentals and tissue applications

Introduction

Light transport tools

Absorption

Scattering

Dynamic light scattering

Multiple light scattering in tissues

Simple solutions of the photon diffusion equation

Diffuse Optical Spectroscopy (DOS): monitoring

Diffuse Optical Tomography (DOT): imaging

Diffuse Correlation Spectroscopy (DCS): blood flow

Background on tissue hemodynamics

Validation and clinical examples

Concluding remarks

J. H. Page - Ultrasonic wave transport in strongly scattering media

Introduction

Acoustic wave transport in random media

Ballistic propagation

Diffusive propagation

Wave transport in ordered media: phononic crystals in 2D and 3D

Conclusions

J. H. Page - Anderson localization of ultrasound in three dimensions

Introduction

Mesoglasses: porous elastic solids with very strong scattering

Time-dependent transmission

Transverse confinement

Statistical approach to localization

Conclusions

Appendix A. Schrodinger and Helmholtz equations in disordered media

J. H. Page - Ultrasonic spectroscopy of complex media

Introduction

Diffusing Acoustic Wave Spectroscopy

Probing food biomaterials with ultrasound

Conclusions

M. Fink and M. Tanter - MultiWave imaging

Introduction

Transcending classical diffraction limits

Wave-to-wave generation

Wave-to-wave tagging

Wave-to-wave imaging

Super-resolution in supersonic shear wave imaging

Clinical applications

Shear wave spectroscopy

Conclusion

Appendix A. Waves propagation in tissues

Appendix A.1. Electromagnetic waves

Appendix A.1.1. Low frequency

Appendix A.1.2. Microwaves

Appendix A.1.3. Optical waves

Appendix A.2. Mechanical waves

M. Fink, J. de Rosny, G. Lerosey and A. Tourin - Time reversal focusing and the diffraction limit

Introduction

Basic principles

An ideal time reversal experiment

Time reversal in free space

Time reversal through heterogeneous medium

An experimental point of view

Time reversal in complex media

One-channel time reversal in chaotic cavities

Time reversal in open systems: random media

Focusing microwaves below the diffraction limit

Conclusion

L. Fallani and M. Inguscio - Ultracold atoms in bichromatic lattices

Introduction

Optical lattices

Ultracold atoms

Light forces

Crystals made of light

Monochromatic lattices

Energy bands

Tight-binding model

Adding interactions

Mott insulators

Bichromatic lattices

Quasicrystals

General notations

Harper and Aubry-Andre model

Superlattices

Incommensurate lattices

Localization in bichromatic lattices

Localized states

Spectrum of the localized states

Further considerations

Anderson localization of matter waves in bichromatic lattices

Experimental setup

Absence of diffusion

Imaging the localized states

Effect of interactions

Strongly interacting atoms in bichromatic lattices

Towards a Bose glass

Noise correlations

Bragg spectroscopy

Concluding remarks

I. Bloch - Exploring strongly correlated ultracold bosonic and fermionic quantum gases in optical lattices

Introduction

Optical lattices

Optical dipole force

Optical lattice potentials

1D lattice potentials

2D lattice potentials

3D lattice potentials

Bose-Hubbard model of interacting bosons in optical lattices

Ground states of the Bose-Hubbard Hamiltonian

Double-well case

Multiple-well case

Superfluid-to-Mott-insulator transition

Multi-orbital quantum phase diffusion

Introduction

Theoretical model

Probing the energy scales via Fock state heterodyning

Experimental setup and results

Compressible and incompressible quantum phases of fermionic spin mixtures in optical lattices

Hubbard Hamiltonian in a trap

Experimental setup

Cloud compression

Entropy distribution

Controlled superexchange interactions

Theoretical model

Time-resolved observation of superexchange interactions

Quantum noise correlations

Time-of-flight versus noise correlations

Noise correlations in bosonic Mott and fermionic band insulators

Outlook

Z. Hadzibabic and J. Dalibard - Two-dimensional Bose fluids: An atomic physics perspective

Introduction

Absence of true long-range order in 2d

Outline of the paper

The infinite uniform 2d Bose gas at low temperature

The ideal 2d Bose gas

Interactions in a 2d Bose gas at low T

Suppression of density fluctuations and the low-energy Hamiltonian

Bogoliubov analysis

Algebraic decay of correlations

The Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2d Bose gas

The role of vortices and topological order

A simple physical picture

Results of the microscopic theory

The 2d Bose gas in a finite box

The ideal Bose gas

The interacting case

Width of the critical region and crossover

What comes first: BEC or BKT?

The case of anisotropic samples

The 2d Bose gas in a harmonic trap

The ideal case

LDA for an interacting gas

What comes first: BEC or BKT?

Width of the crossover

Achieving a quasi-2d gas with cold atoms

Experimental implementations

Interactions in a 2d atomic gas

Residual excitation of the z-degree of freedom

Probing 2d atomic gases

In situ density distribution

Two-dimensional Time-of-Flight expansion

Three-dimensional Time of Flight

Interference between independent planes

Interfering a single plane with itself

Conclusions and outlook

Elenco dei partecipanti