Homogeneous, periodic, quasiperiodic, irregular and disordered spatial structures have been at the heart of scientific interest and research for a long time and in many disciplines as diverse as chemistry, physics, biology and morphology. Some recent, spectacular achievements in experimental quantum optics have, however, made it possible to study quantum effects in a variety of spatial structures. The main aim of this Focus Issue is to present some of the most recent theoretical, numerical and experimental progresses in the area of Quantum Structures, i.e. spatial structures that display quantum features. A short background overview of Quantum Structures is provided at the beginning of this Focus Issue, in which individual authors' works are specifically commented. In brief, we can say that the articles can be catalogued into two main areas of research interest in Quantum Structures: quantum effects in spatial structures in nonlinear optics, and in atomic physics.
Homogeneous, periodic, quasiperiodic, irregular and disordered spatial structures have been at the heart of scientific interest and research for a long time and in many disciplines as diverse as chemistry, physics, biology and morphology. Some recent, spectacular achievements in experimental quantum optics have, however, made it possible to study quantum effects in a variety of spatial structures. The main aim of this Focus Issue is to present some of the most recent theoretical, numerical and experimental progresses in the area of Quantum Structures, i.e. spatial structures that display quantum features. A short background overview of Quantum Structures is provided at the beginning of this Focus Issue, in which individual authors' works are specifically commented. In brief, we can say that the articles can be catalogued into two main areas of research interest in Quantum Structures: quantum effects in spatial structures in nonlinear optics, and in atomic physics.
Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.
Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. This issue brings together the various researchers working in the border domain between atom optics and solid state physics and focuses on atomic motion in light fields in a regime that is dominated by quantum effects. The topics discussed in this issue include: • quantum effects of atomic motion in light fields; • quantum chaos in time dependent lattices; • tunnelling in stationary or time-dependent lattices; • Wannier-Stark ladder and Bloch oscillations; • atomic band structures; • many-body effects on transport in optical lattices; • effects of decoherence on quantum transport; • weak and dynamical localization. At this point we take the opportunity to express our gratitude to the authors of the papers of this issue and the reviewers for their efforts in preparing and ensuring the high quality of the state of the art presentation.
What is “complex”? A question which stimulates a panoply of often quite diverse associations and answers. While in condensed matter and also (macro-) molecular physics we are used to be forced into effective descriptions of large, multicomponent, interacting quantum systems, complexity is “(re-) constructed” in modern quantum optical experiments. In learning how “complexity” emerges from strongly coupling few degrees of freedom (or particles) we start to contemplate how to control complex systems, and learn to distinguish what is just complicated from what is truly complex. This special issue of Annalen der Physik collects expertise and perspectives on complex (quantum) systems from very diverse areas of research: disordered quantum systems, molecular dynamics and interactions, mesoscopic physics, quantum many body physics, open quantum systems, network and scattering theory, quantum information and control – which all share the same interest in getting a better grasp of complexity on the quantum level. Disorder physics with its long-standing history in the condensed matter context nowadays merges with the physics of ultracold atomic gases in highly controlled potential landscapes, and finds applications in “big data”. Mesoscopic transport theory finds novel playgrounds in graphene or in coupled quantum circuits. The coupling of electronic and nuclear degrees of freedom determines chemical reactions, as well as energy flow and directionality in large molecular complexes, with an intricate interplay of coherent and incoherent effects. Today's “femtochemistry” and “femtobiology” experiments reveal these ultrafast molecular pathways in detail and make the border between quantum and classical regimes directly observable. Indeed, this research area has become a test bed for quantum transport and control theory applied to realistic, truly complex, finite quantum systems. Given the generically highly structured spectral densities which underlie molecular systems, novel strategies are called for to characterize complex open quantum systems exhibiting structured, “active” environments. Well-controlled non- equilibrium many-particle quantum dynamics becomes accessible with ultracold quantum gases loaded into engineered potential landscapes, or in photonic circuitry. This challenges theory to develop novel tools for the efficient characterization of many-particle non-equilibrium dynamics and transport, and possibly for their control, e.g. through robust design principles. Furthermore, controlled many-body quantum systems allow for enhanced sensing, and give room for the creation of highly complex many-particle states. The latter may serve, e.g., as resources for quantum computation – which, in turn, may be used to characterize such states’ complexity. This collection of various contributions either on complex molecular structures which are ever better resolved, or on novel composite quantum systems or materials which are ever better controlled, provide a snapshot of current trends in the science of complex quantum systems. Our authors’ diverse specializations highlight the research field's interdisciplinary appeal, and the broad relevance of many of the unveiled structures – and of those phenomena which remain to be understood. We thus hope that this collection will inspire future work connecting concepts of complexity across disciplines. Irene Burghardt received her Ph.D. in chemistry in 1992 from the University of Lausanne. She carried out postdoctoral research at the Center for Nonlinear Phenomena and Complex Systems in Brussels in 1992–1995, followed by research fellowships at the Universities of Bonn and Heidelberg in 1996–1998. From 1999–2011, she held a CNRS research position at ENS Paris, and was appointed CNRS Research Director in 2007. In 2011, she moved to Goethe University Frankfurt where she holds a full professorship in Theoretical Chemistry. Her research addresses quantum molecular dynamics and nonequilibrium phenomena, with a focus on materials and biological systems. Andreas Buchleitner studied Physics at the Ludwig Maximilians University of Munich and received his diploma in 1989, upon research in experimental quantum optics. In 1993, he obtained his PhD, with theoretical research at Laboratoire de Spectroscopie Hertzienne (today Laboratoire Kastler Brossel) of Universite Pierre et Marie Curie and Ecole Normale Supérieure in Paris. Afterwards, he was a PostDoc at the Max Planck Institute for Quantum Optics, Garching, and a visiting researcher at the Queen's University of Belfast and at the Weizmann Institute of Science, Revohot. In 1999, he received his Habilitation from the Ludwig Maximilians University of Munich. From 1999 to 2007, he led the research group “Nonlinear Dynamics in Quantum Systems” at the Max Planck Institute for the Physics of Complex Systems in Dresden. Since 2007, he holds the Chair for “Quantum Optics and Statistics” at the Albert Ludwigs University of Freiburg. His main research interests are Quantum Chaos, Quantum Information and Quantum Transport. From October 2014 to 2015, he was a Senior Fellow, and Speaker of the Research Focus “Designed Quantum Transport in Complex Materials”, at the Freiburg Institute for Advanced Studies. He serves in different honorary capacities, e.g., for the German Physical Society and for the German National Academic Foundation.
From time to time in physics, single technical achievements have spawned an explosion of research activity and have led to the genesis of entirely new avenues of investigation. Precisely this occurred in the field of quantum gases - the topic of this Focus Issue - following the achievement of Bose-Einstein condensation in a dilute alkali gas in 1995. These experiments built on the foundational work on quantum fluids in dense systems, such as superfluid helium, and the technical achievements of laser cooling in atomic physics. Dilute quantum gases have already proved to be an incredibly fertile ground for exploring a wide range of macroscopic quantum phenomena. The rapid pace of experimental discovery and theoretical advance is evident and every year continues to bring significant achievements. A great advantage is that microscopic observations can be made directly and compared with the predictions of many-body theoretical formulations founded on interaction parameters which are completely determined - something which is not possible in their dense fluid counterparts. This Focus Issue brings together papers which cover many of the topical aspects of quantum gases: optical lattices, quantum degenerate fermions, quantum atom optics, molecular Bose-Einstein condensation, vorticity, and quantum fluctuations in systems of reduced dimensionality. One pervasive theme is the flexibility which arises from the ability to control the interactions, even dynamically if necessary. In quantum gases, this can be effected in two ways, either by changing the internal nature of the pairwise potentials by a Feshbach resonance, or by changing the nature of external potentials in which the atoms are confined and supported against gravity. The external potential may be used to spin gases to high vorticity, imprint on the system a periodic optical lattice potential, or even change the effective dimensionality. Optical lattices are particularly well represented in this Focus Issue. This is where there is the strongest connection with the physics of solids and strongly correlated fluids. Interest in optical lattices is partly due to the recent experimental demonstration that in these systems one can study the quantum phase transition from a Mott insulator, where the atoms are localized to individual sites of the optical potential, to a superfluid phase with long-range order. In contrast to a condensed matter system, the transition can be easily dynamically controlled since it is induced by simply varying the depth of the optical potential. Another area of focused interest is in fermionic gases where there is an ongoing effort, both experimentally and theoretically, to observe and characterize the high-temperature superfluid transition that should occur with enhanced pairwise interactions. If realized, this quantum system would allow experimental investigation of the crossover from Bose-Einstein condensation of dilute weakly-interacting composite bosons to the superconducting-like transition that occurs in a system of weakly interacting fermions. The topics of this Focus Issue represent well the building blocks of quantum gas studies which should allow the exploration of a wide range of macroscopic quantum phenomena in a highly controllable and clean system in which the effects of disorder may be completely absent. Given the recent progress, it will be intriguing to see where this field leads in the future. Focus on Quantum Gases Contents Anisotropic dissipation of superfluid flow in a periodically dressed Bose-Einstein condensate D M Stamper-Kurn Rapidly rotating Bose-Einstein condensates in anharmonic potentials G M Kavoulakis and Gordon Baym Feshbach resonances and collapsing Bose-Einstein condensates J N Milstein, C Menotti and M J Holland Three-body recombination of cold fermionic atoms H Suno, B D Esry and Chris H Greene Bogoliubov spectrum and Bragg spectroscopy of elongated Bose-Einstein condensates C Tozzo and F Dalfovo Quantum atom optics with Bose-Einstein condensates Klaus Mølmer Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms D Jaksch and P Zoller The Josephson frequency of resonantly coupled atomic and molecular condensates R A Duine and H T C Stoof Superfluid current disruption in a chain of weakly coupled Bose–Einstein condensates F S Cataliotti, L Fallani, F Ferlaino, C Fort, P Maddaloni and M Inguscio Bright matter wave solitons in Bose–Einstein condensates K E Strecker, G B Partridge, A G Truscott and R G Hulet Spin dynamics for bosons in an optical lattice Juan José García-Ripoll and Juan Ignacio Cirac Mean field ground state of a spin-1 condensate in a magnetic field Wenxian Zhang, Su Yi and Li You Atom resonant tunnelling through a moving barrier M L Chiofalo, M Artoni and G C La Rocca Local correlations in a strongly interacting one-dimensional Bose gas D M Gangardt and G V Shlyapnikov Shift of the molecular bound state threshold in dense ultracold Fermi gases with Feshbach resonance R Combescot Landau damping in trapped Bose condensed gases B Jackson and E Zaremba An exact reformulation of the Bose–Hubbard model in terms of a stochastic Gutzwiller ansatz Iacopo Carusotto and Yvan Castin Chemical potential standard for atomic Bose–Einstein condensates Sigmund Kohler and Fernando Sols The short-distance first-order correlation function of the interacting one-dimensional Bose gas Maxim Olshanii and Vanja Dunjko The relation between the Gross–Pitaevskii and Bogoliubov descriptions of a dilute Bose gas A J Leggett Superfluidity of Bose–Einstein condensate in an optical lattice: Landau–Zener tunnelling and dynamical instability B Wu and Q Niu Density-optimized efficiency for magneto-optical production of a stable molecular Bose–Einstein condensate Matt Mackie, Anssi Collin, Kalle-Antti Suominen and Juha Javanainen A two-atom picture of coherent atom–molecule quantum beats Bogdan Borca, D Blume and Chris H Greene Superfluid dynamics of a Bose–Einstein condensate in a periodic potential C Menotti, A Smerzi and A Trombettoni Phase diagram of two-component bosons on an optical lattice Ehud Altman, Walter Hofstetter, Eugene Demler and Mikhail D Lukin Murray J Holland University of Colorado at Boulder, USA
Peter Franken was a remarkable man. Immediately after the invention of the laser in 1960, he realized its potentialities for nonlinear effects. His revolutionary paper on second harmonic generation appeared in 1961. It started a revolution in optics, in spite of the fact that some picture editor had removed the spectral spot that was the proof of the effect. Within a few years the experimental field exploded and Bloembergen and collaborators had developed the theory of the new effects to a point that merited his textbook of 1965. Peter Franken turned 70 in 1998 and the traditional Festschrift was prepared. Unfortunately he passed away in 1999, and the book appeared as a dedication to his memory. And a very suitable one it is, because it covers many of the topics he initiated and much of the recent developments following from them. As a long-time friend and colleague, Professor Prokhorov writes the introduction. The book has reviews of topics in nonlinear optics, following their developments up to the late 1990s: Atomic time standards (Ramsay), Femtosecond phenomena at nonlinear optical boundaries (Bloembergen et al ), Nuclear excitation in plasmas (Sobelman) and Raman scattering (Powell and Basiev). Novel fields with strong connections to optics are presented: Quantum interference effects on optical dispersion (Scully et al ), Excitonic features in semiconductor cavities (Gibbs et al ), Nonlinear atom optics (Meystre et al ) and Laser-induced particle emission spectroscopy with atomic resolution (Letokhov). The field mentioned last has been developed by Professor Letokhov in recent years, and I do not know any other place where its methods and potentialities are presented in this detail. The book is a valuable source of information on recent progress in the topics included. It summarizes many important developments of contemporary laser physics. If one wants to get an overview of this research, the book is very valuable. The level of treatment varies a little, from purely descriptive to highly detailed; that is inevitable when many authors are involved. Reading the text requires a certain ability to discern and choose; hence it is no textbook for students. A mature and interested reader, however, can learn much from the book. The most recent developments will, no doubt, become dated, but so much material is central to the field of research that the main part of the text is of lasting value. Groups and individuals working in the area of laser physics will find the volume challenging and useful as a general reference. Here one can look up earlier material and find out its relevance to the most recent progress. Stig Stenholm