Ebook: Nano Optics and Atomics: Transport of Light and Mater Waves

Many fundamental processes in physics involve transport. For a variety of physical systems, e.g. electrons, light, cold atoms and sound, transport mechanisms eventually reduce to different manifestations of wave transport. In the last decades, pushed by the spectacular progresses in the control and engineering of matter at the nano-scale, new regimes of wave transport became of strong interest. Indeed, fascinating effects emerge when transport is studied at the “nano” level, when atoms behave like waves and light propagation in nano-engineered structures acquires intriguing behaviors. This book collects contributions from speakers and lecturers of the CLXXIII International School of Physics “Enrico Fermi” which was held in Varenna (Italy) from June 23rd to July 3rd 2009. Different aspects of wave transport were covered during the school, from electrons to light propagation, from sound to ultracold atoms. Considering the ubiquitous nature of wave transport phenomena, the school was characterized by a strongly interdisciplinary approach, with speakers, lecturers and students from different communities meeting and sharing their knowledge and the often complementary points of view and approaches.

Among the different media in which waves can travel, periodic and disordered structures surely deserve particular attention. Interference of waves in periodic structures results in the formation of energy bands, which are responsible for the conduction properties of electrons in solids. Periodic structures can be realized also for light and ultra-cold atoms, in the form of photonic crystals or optical lattices, respectively, which allow the observation of effects which have been originally predicted in the context of solid-state physics. The most recent advances in the physics of ultra-cold atoms in optical lattices are discussed in the contribution by I. Bloch concerning quantum simulation of condensed-matter physics. Optical lattices also allow the production of low-dimensional atomic systems, as discussed in the paper by Z. Hadzibabic and J. Dalibard devoted to the investigation of transport and superfluidity in 2D bosonic quantum gases.

Disordered structures also show fascinating phenomena. Multiple scattering in random media results in the localization of waves predicted by P. W. Anderson fifty years ago for electrons moving in disordered crystals, and reviewed in this book in the opening article by P. Woefle. Also in this case, a phenomenon originally predicted for electrons in crystals has been observed both for propagation of classical waves — light and sound — in disordered media and very recently for ultracold atoms expanding in disordered optical potentials. Transport of sound waves in different media, including Anderson localization in disordered structures, is discussed in the contributions by J. Page.

At the border between periodic and disordered media, quasicrystals are topological structures showing long-range order and absence of periodicity, which results in intriguing properties that are described in the contribution by P. J. Steinhardt. Optical quasicrystals can be realized for ultra-cold atoms and used to study Anderson localization of matter waves, as discussed in the article by L. Fallani and M. Inguscio.

Knowledge of transport properties in complex systems is important not only for fundamental studies, but also for applications. Understanding the propagation of light is extremely important for engineering new devices, as metamaterials and plasmonic materials, and for applications in the field of energy, biology and medicine. In this perspective, the article by R. C. Mesquita and A. G. Yodh covers the application of diffuse optics to medical imaging. Extending these concepts beyond the field of optics, in two different contributions to this book, M. Fink and coworkers discuss multi-wave imaging for medical applications and present theory and applications of time-reversal focusing.

The success of the Summer School was not only determined by the high quality of the lectures, but also by the enthusiasm of the students and observers who attended the Course. Their active participation resulted in the success of the two poster sessions (the most interesting posters have been upgraded to invited presentations) and of the final discussion session on future research perspectives. We would like to warmly thank all the speakers, lecturers, participants and express our gratitude to the organizing team, in particular Barbara Alzani of the Italian Physical Society for her passion and dedication in the Course organization, as well as Ramona Brigatti and Marta Pigazzini for their enthusiasm and assistance in Varenna. We also acknowledge financial support from the Italian Physical Society through its president Luisa Cifarelli, and from the European network Intercan.

Finally, the Summer School hosted a celebration in memoriam of Franco Bassani (1929-2008), former president of the Italian Physical Society. On this occasion, friends and colleagues Lucio Andreani, Luisa Cifarelli, Massimo Inguscio and Erio Tosatti presented several portraits of his scientific and personal life. Franco Bassani was an excellent scientist and an outstanding man. We dedicate this book to his memory.

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

The basic concepts of the theory of Anderson localization are reviewed in the example of electrons in disordered solids. The lectures are organized in three sections. In the first, the phenomenon of localization of quantum particles or classical waves is introduced on a qualitative level. The regimes of strong and weak localization are discussed. Sample to sample fluctuations are considered for one-dimensional and quasi–one-dimensional systems. In sect. 2 the scaling theory of the Anderson localization transition is presented. The renormalization group theory is introduced and results and consequences are presented. The classification of the Anderson transitions into universality classes is described. Basic concepts of the fractal structure of the wave functions at the critical point are reviewed. In sect. 3 the self-consistent theory of Anderson localization is presented. The effect of the electron-electron interaction in destroying the phase coherence is briefly discussed.

Photonic crystals, periodic arrangements of two or more dielectric materials, have been studied for more than two decades as a means of controlling and manipulating the flow of light. These lectures describe recent progress in designing non-periodic photonic solids. The aim is to find arrangements of dielectric materials that produce substantial complete photonic band gaps that block light in all directions and for all polarizations over a range of frequencies. Methods are described for constructing quasicrystalline examples with a wide range of rotational symmetries and a special class of isotropic, disordered photonic band gap materials.

The material in this paper is different from the mainstream topics in this summer's International School of Physics “Enrico Fermi”. It should become apparent, however, that the roots of these biomedical optics research problems share common features with much of the light scattering and transport research taught in the Varenna summer school. Here, our intention is to provide an informal review that establishes the roots of diffuse optics, and then demonstrates how diffuse optics is finding application in medicine. This paper will have two main themes. After a brief motivation of the problem, the first theme will provide a coherent discussion about light transport in turbid media. The second theme is oriented towards problems in biomedicine. As such, a short discussion of hemodynamics will be followed by representative current work from our lab, particularly with breast and brain.

Ultrasonic experiments are well suited to the investigation of classical wave transport through strongly scattering media, and are playing a role that is often complementary to investigations using light or microwaves. Advantages of ultrasonic techniques are their ability to readily detect the wave field (not just the intensity), to perform experiments resolved in both time and space, and to control the properties of the medium being investigated over a wide range of scattering contrasts. This first paper reviews what has been learned from ultrasonic experiments over the last 15 years about the ballistic and diffusive propagation of classical waves through strongly scattering disordered media. These results are compared with studies of ordered media (phononic crystals), where band gaps and super-resolution focusing have been observed.

Some fifty years after Anderson localization was first proposed, there is currently a resurgence of interest in this phenomenon, which has remained one of the most challenging and fascinating aspects of wave transport in random media. This paper summarizes recent progress in demonstrating the localization of ultrasound in a “mesoglass” made by assembling aluminum beads into a disordered three-dimensional elastic network. In this system, the disorder is sufficiently strong that interference leads to trapping of the waves at intermediate frequencies, as demonstrated by studying three different fundamental aspects of Anderson localization: time-dependent transmission, transverse confinement of the waves, and the statistics of the non-Gaussian intensity fluctuations. Additional ultrasonic experiments have been performed to reveal the multifractal character of the wave functions near the Anderson transition. This is the first time that so many different aspects of localization have been studied simultaneously, providing very convincing evidence for the localization of ultrasonic waves in the presence of disorder in three dimensions, and enabling new aspects of Anderson localization to be studied experimentally.

Mesoscopic wave physics underpins many of the new developments in ultrasonic spectroscopy for probing the physical properties of complex heterogeneous materials. In this paper, two examples of recent progress are summarized. The first is Diffusing Acoustic Wave Spectroscopy (DAWS), which is a powerful approach for investigating the dynamics of strongly scattering media, one example being velocity fluctuations in fluidized suspensions of particles. Recent advances in using phase statistics to probe the particle dynamics are shown to give increased sensitivity in some situations; this work has also led to new insights into the meaning of phase for multiply scattered waves. The second topic is the spectroscopy of soft food biomaterials, illustrated by experimental studies of ultrasonic velocity and attenuation in bread dough. Since wheat flour dough contains one of the strongest scatterers of ultrasonic waves (bubbles) dispersed in a viscoelastic matrix that is also very dissipative, appropriate ultrasonic techniques provide an excellent means for investigating its structure and dynamics. In addition to fundamental studies, unraveling the contributions of bubbles and matrix to dough properties is relevant to the baking industry, because the bubbles ultimately grow into the voids that determine the structural integrity of bread — an important quality attribute. The interpretation of ultrasonic experiments on bread dough over three decades in frequency is giving new insights into this complex material, as well as providing the basis for new non-destructive methods of evaluating both dough processing behaviour and the breadmaking potential of different flours.

Interactions between waves can be turned into profit to break diffraction limits and invent new kinds of medical images. It consists in productively combining two very different waves — one to provide contrast, another to provide spatial resolution — in order to build a new kind of image. Contrary to multimodality medical imaging that remains the superposition of two different images limited by their respective contrast/resolution couples, MultiWave imaging overcomes this limitation by providing a unique image of the most interesting contrast with the most interesting resolution. MultiWave imaging can benefit from three different potential interactions among waves that will be described in this paper.

Time reversal mirrors refocus an incident-wave field to the position of the original source, regardless of the complexity of the propagation medium. TRMs have now been implemented in a variety of physical scenarios from GHz Microwaves to MHz Ultrasonics and to hundreds of Hz in ocean acoustics. Common to this broad range of scales is a remarkable robustness exemplified by observations at all scales that the more complex the medium (random or chaotic), the sharper the focus. A TRM acts as an antenna that uses complex environments to appear wider than it is, resulting, for a broad-band pulse, in a refocusing quality that does not depend on the TRM aperture. Moreover, when the complex environment is located in the near field of the source, time reversal focusing opens completely new approaches to super-resolution. We will shown that, for a broad-band source located inside a random metamaterial, a TRM located in the far field radiates a time-reversed wave that interacts with the random medium to regenerate not only the propagating but also the evanescent waves required to refocus below the diffraction limit.

In this paper we illustrate the physics of ultracold atoms in bichromatic optical lattices. The properties of biperiodic systems are presented in detail, with a particular focus on the localization transition for incommensurate lattices. We then present recent work on the experimental investigation of these systems.

We review several experimental aspects of ultracold bosonic and fermionic quantum gases in optical lattices. After introducing optical lattices, we use the superfluid-Mott insulator transition of ultracold bosonic quantum gases, to highlight the physics of strongly correlated quantum systems. We discuss the coherence properties and recent measurements of the shell structure in the Mott insulating phase. Subsequently, dynamical interaction effects in the collapse and revival of the matter wave field of a BEC are analyzed, followed by a discussion on interacting fermions, superexchange-mediated spin-spin interactions and quantum noise correlation interferometry in optical lattices.

We give in this lecture an introduction to the physics of two-dimensional (2d) Bose gases. We first discuss the properties of uniform, infinite 2d Bose fluids at non-zero temperature T. We explain why thermal fluctuations are strong enough to destroy the fully ordered state associated with Bose-Einstein condensation, but are not strong enough to suppress superfluidity in an interacting system at low T. We present the basics of the Berezinskii-Kosterlitz-Thouless theory, which provides the general framework for understanding 2d superfluidity. We then turn to experimentally relevant finite-size systems, in which the presence of residual “quasi–long-range” order at low temperatures leads to an interesting interplay between superfluidity and condensation. Finally we summarize the recent progress in theoretical understanding and experimental investigation of ultracold atomic gases confined to a quasi-2d geometry.