This Volume originates from the lectures delivered at the CLXXI Course of the “Enrico Fermi” School, which was held in Varenna from July 1 to July 11, 2008. The purpose of the Course was to give an overview of the manifestations of quantum coherence in different solid-state systems including semiconductor confined systems, magnetic systems, crystals and superconductors. Besides being of paramount importance in fundamental physics, the study of quantum coherence furnishes the starting point for important applications like quantum computing or secure data transmission. Quantum coherence has been studied in photon systems in quantum optics as well as in atomic systems after the demonstration of Bose-Einstein condensation. Effects analogous to the ones predicted and observed in atoms and photons have been predicted and observed in different solid-state systems during the last few years. Some examples are polariton condensation and superfluidity in semiconductor quantum wells, magnon condensation in magnetic systems, entanglement in confined semiconductor systems, and in ionic crystals. We notice that the coherent effects discussed during the Course mainly involve elementary excitations in solids like polaritons, excitons, magnons, macroscopic quantities like superconductor currents, and electron spins. Therefore, several new aspects of the physics of quasi-particles are understood and discussed in this context. Finally, due to the variety of systems in which quantum coherence may be observed, solid-state systems are the natural candidates for applications that rely on coherence like e.g. quantum computers.

The basic theoretical tools relevant to the field of quantum coherence have been introduced by Serge Haroche who lectured on quantum coherence in quantum optical system and by Sandro Stringari in his lecture on Bose-Einstein condensation in atomic systems. The theory of polariton condensation was the subject of the lectures by Vincenzo Savona, whereas experiments on polariton condensation were presented and discussed in the lectures by Yoshisha Yamamoto and Benoît Deveaud-Plédran (unfortunately, the latter encurred in an accident and the lecture was delivered by Maxime Richard). The lecture by Sergej Demokritov delt with condensation of magnons. The lecture by Cristiano Ciuti was devoted to parametric effects and superfluidity in low-dimensional polariton systems (polaritonics), whereas Wolfgang Langbein discussed experiments of coherent effects in quantum dot excitons. A link between quantum optics and polariton physics was presented in the lecture by Raffaello Girlanda, whereas Atac Imamoglu lectured on quantum optics in mesoscopic systems, and Keiichi Edamatsu discussed the emission of entangled photons from quantum dots. The topic of manipulation of excitons into a cooperative state was developed in the lecture by Matoko Kuwata-Gonokami, whereas Giuseppe La Rocca devoted his contribution to the self-transparency in semiconductors. The lecture of Daniel Loss was devoted to the physics of spin q-bits in quantum dots, and Michael Mehring discussed spin entanglement in fullerenes. Finally, Michel Devoret showed the insurgence of quantum coherence in Josephson circuits, and Marcus Arndt lectured on experimens on coherence and decoherence with clusters and molecules.

The Course was attended by a large number of students from all over the world, who followed the lectures with great interest and assiduity. They had the opportunity to present their research work in two poster sessions, which were very successful. Thanks to the enthusiasm of the lecturers and of the participants, we found again the friendly and exciting atmosphere we enjoyed years ago as students in the Villa Monastero. We take the occasion to thank warmly everybody. However, the Course could have never been successful without the precious help of the team of the Società Italiana di Fisica including Barbara Alzani, Ramona Brigatti, Marta Pigazzini, Laura Strolin, Marcella Missiroli and Angela Di Giuseppe. We also mention in particular the support of the President of the Società Italiana di Fisica Luisa Cifarelli. Finally, we kindly acknowledge the financial support of the Società Italiana di Fisica and the Ecole Polytechnique Fédérale de Lausanne.

This volume is dedicated to the memory of Franco Bassani, the former President of the Società Italiana di Fisica and our long-time friend. With his great enthusiasm, he gave us an important support during the preparation of this Course. He was not able to join us in Varenna and passed away in the fall of 2008.

A. Quattropani, B. Deveaud-Plédran and P. Schwendimann