Editorial

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 22; no. 3; pp. 307 - 310
• Main Authors: Eschner Jürgen, Gatti, Alessandra, Maître Agnès, Morigi Giovanna
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.01.2003
• Subjects: Angular momentum; Arrays; Atom optics; Atomic physics; Atomic structure; Bosons; Cross-sections; Crystallization; Data processing; Detectors; Electromagnetic fields; Electromagnetism; Electrons; Image processing; Imaging techniques; Information retrieval; Investigations; Laser cooling; Lasers; Light; Noise measurement; Optics; Photons; Physics; Quantum dots; Quantum theory; Room temperature; Sensitivity; Spatial resolution; Vortices
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2003-99999-x

From simple interference fringes, over molecular wave packets, to nonlinear optical patterns - the fundamental interaction between light and matter leads to the formation of structures in many areas of atomic and optical physics. Sophisticated technology in experimental quantum optics, as well as modern computational tools available to theorists, have led to spectacular achievements in the investigation of quantum structures.This special issue is dedicated to recent developments in this area. It presents a selection of examples where quantum dynamics, fluctuations, and coherence generate structures in time or in space or where such structures are observed experimentally. The examples range from coherence phenomena in condensed matter, over atoms in optical structures, entanglement in light and matter, to quantum patterns in nonlinear optics and quantum imaging.The combination of such seemingly diverse subjects formed the basis of a successful European TMR network, "Quantum Structures" (visit http://cnqo.phys.strath.ac.uk/~gianluca/QSTRUCT/). This special issue partly re.ects the results and collaborations of the network, going however well beyond its scope by including contributions from a global community and from many related topics which were not addressed directly in the network.The aim of this issue is to present side by side these di.erent topics, all of which are loosely summarized under quantum structures, to highlight their common aspects, their di.erences, and the progress which resulted from the mutual exchange of results, methods, and knowledge. To guide the reader, we have organized the articles into subsections which follow a rough division into structures in material systems and structures in optical .elds. Nevertheless, in the following introduction we point out connections between the contributions which go beyond these usual criteria, thus highlighting the truly interdisciplinary nature of quantum structures.Much of the progress in atom optics has been generated by the application of concepts from wave optics to matter waves. An example is the contribution by Franke-Arnold et al. The authors investigate the coherence properties of two trapped cold atoms using concepts developed in wave optics. Nevertheless, novel features appear in this system due to the quantum statistics - as atoms may be bosons or fermions - and due to interactions. Matter waves find a spectacular manifestation in Bose-Einstein condensates (BECs) of cold dilute atomic gases. Several concepts of wave optics, like the laser, have been discussed in relation to BECs, and the .eld of atom optics with BECs is rapidly developing. The similarity between the theoretical description of a weakly interacting BEC with that of a non-linear optical system has motivated a series of experiments that led to the observation of, e.g., solitons, vortices and vortex crystallization in matter waves. In this context, the paper by Josopait et al. describes the dynamics of a Bose-Einstein condensate containing a vortex. The vortex stability is discussed as a function of the interparticle interaction, which can be tuned using Feshbach resonances, and the dynamics of the BEC reflected by an atomic mirror is investigated.Non-linear optics merges with atomic physics also in a relatively new research area which aims at quantum non-linear optics with cold atomic gases. Labeyrie et al. use a dense, laser-cooled atomic gas as a non-linear medium for light propagation, and discuss the conditions for observing optical patterns in the transmitted beam.Pattern formation in non-linear optical media is one of the numerous forms of self-organization that these systems display, including also turbulence and optical solitons. With respects to other physical systems, where these phenomena are commonly observed, optical systems are however special: at optical frequencies thermal .uctuations are negligible and do not hide the presence of quantum .uctuations, even at room temperature. Remarkably, the interplay between non-linearity and quantum noise leads to novel phenomena, including optical patterns driven by quantum noise, quantum images, non-classical spatio-temporal correlations, and spatial quantum entanglement. Quantum images are an example of spatial structures dominated by quantum noise, where the structure is absent at a classical level and only proper correlation functions of quantum fluctuations reveal the presence of a regular spatial order. Hoyuelos et al. describe an example of such an image, which is formed in the cross section of the light emitted by an optical parametric oscillator, close to but below the threshold for a square pattern formation. The optical parametric oscillator is also studied in the paper by Rabbiosi et al. which describes the onset of a spatial structure consisting of arrays of localized peaks (cavity solitons) in the transverse cross section of the signal beam. This represents an example of a "disorder to order" transition mediated by quantum noise, where the ordered arrays of solitons are selected among the many possible stable states, only thanks to the presence of quantum noise.As the study of the dynamics of quantum .uctuations in spatially extended systems is a nontraditional subject in quantum optics, alternative techniques of theoretical analysis are needed. The paper by Zambrini et al. proposes an approach based on the use of phase-space representations, in particular of the Q-function with its associated nonlinear Langevin equations. This method provides a full description of the transition from a quantum image to a classical structure through a modulation instability. The Q-representation is also used in a different physical system, the dynamics of the electrons in a driven Helium atom, in the paper by Schlagheck and Buchleitner. Here the authors investigate the quantum manifestations of order and disorder in the motion of the electrons, identifying correspondences between features of the classical phase space and the quantum dynamics.In optical patterns the structure and stability are critically determined by the type of non-linearity of the medium where light propagates, and by the cavity geometry. In atom optics, spatial atomic patterns can be created by light potentials, in particular by arrangements of suitably polarized laser beams which form an optical lattice. The atoms experience mechanical forces arising from the gradient of the light potential. Depending on the tuning of the lasers with respect to the driven atomic transition, these light forces can have a strong or negligible dissipative component, leading to incoherent or coherent motional dynamics. Atomic motion in optical lattices is experimentally investigated in the contributions by Carminati et al. and Jersblad et al. The first article investigates motion-induced resonances in a three-dimensional optical lattice which are observed through pumpprobe laser spectroscopy. The latter contribution studies the effect of the lattice geometry on the atomic steady-state by measuring velocity distributions. The creation of more complex light structures is the subject of the paper by Ellmann et al., where the realization of a double optical lattice is discussed. Such lattices may open up the possibility of coherent manipulation of the atoms in the individual potential wells.An alternative way to structure atoms spatially is discussed by Grabowski and Pfau: here, a regular arrangement of magnetic and magneto-optical traps for ultracold atoms above a surface is described and experimentally observed, where the lattice con.guration is determined by the direction of currents in wire segments beneath the surface. In a different physical systems, semiconductor quantum dots, Jacak et al. study the coupling of arti.cial atoms with the collective excitations of the bulk material in which they are embedded, and investigate coherent and incoherent effects due to this interaction.The presence of correlations at the quantum level leads naturally to the issue of entanglement. This is an exclusive feature of the quantum world, which represents a valuable resource for quantum information processing and for high-precision measurements. The de.nition and criteria for measuring entanglement have been traditionally formulated within the Hilbert-space formalism (the quantum state formalism). However, quantum structures are intrinsically multi-mode systems, for which the Hilbert-space approach is often unpractical and cumbersome. More appealing are the "classical looking" phase space descriptions, where it is hence of great importance to reformulate concepts such as entanglement or Bell inequalities. The paper by Santos addresses the general problem of characterizing the entanglement properties of an electromagnetic field in the language of Q-representation. Entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum provides new degrees of freedom and could play an important role in the field of quantum information, since such non-classical states enable the possibility of multichannel communications. The paper by Barbosa discusses quantum states of twin photons produced by parametric down-conversion and entangled in polarization and orbital angular momentum.The issue of entanglement is intrinsically connected to decoherence, and to the transition from the quantum to the classical world. In particular, massive systems are characterized by strong interactions with the environment, and at room temperature they usually exhibit classical behaviour. In this context, the paper by Karlsson discusses the decay of quantum correlations of protons and positive muons in condensed matter, a system characterized by strong coupling to the environment, and proposes experiments where such quantum correlations could be measured. Mancini et al. investigate macroscopic manifestations of quantum features, presenting a proposal for entangling the macroscopic osci