The International School of Physics “Enrico Fermi” on Atom Optics and Space Physics was organized by the Italian Physical Society in Villa Monastero, Varenna, Italy, during July 2-13, 2007, in collaboration with the Wilhelm und Else Heraeus-Stiftung. In the tradition of the Fermi Schools the main goal was to highlight within the physics community an advanced topic in a rapidly expanding area of research.

Wave optics with cold and ultracold atoms has experienced an enormous progress during the last few years, as recognized by the Nobel prizes for laser cooling in 1997, and for Bose-Einstein condensation in 2001. The high control in the production of ultracold atoms and molecules, and in the quantum engineering of the internal and external degrees of freedom of those systems has provided us with new tools for detailed investigations. Moreover, quantum optics of atom waves has reached a new level of refinement with the production of squeezed atomic samples and the non-linear generation of matter waves. Finally major breakthroughs with interferometers based on cold atoms demonstrated that atom optics has become a mature technology which produces matter wave sensors with unprecedented sensitivity for metrology and fundamental physics.

So far most atom optics experiments have been performed on Earth. Only a few have been made in free-fall, either in airplanes or in a drop tower, as to eliminate the influence of gravitation on the motion of the atoms. However, ultra-high precision experiments with atoms ask for ultra-low velocities to surpass the present limitations. In this regime experiments on Earth are limited by gravitation which is one of the main motivations for placing a cold atom interferometer in Space. This approach has to be viewed in the context of ongoing activities using state-of-the art cryogenic, superconducting or mechanical sensors to measure predictions of general relativity such as the Lense-Thirring effect or to test the Equivalence Principle. The Lense-Thirring effect is a manifestation of a “force” produced by the rotation of a massive object. It can also be thought of as the result of the “dragging of inertial frames”, a name proposed by Albert Einstein.

The goal of our School was to teach the rapidly moving field of atom optics and interferometry with all its intricate aspects ranging from fundamental physics to applications together with the theory of relativity. The breathtaking success in manipulating atoms using lasers has encouraged these two so far disjunct communities to move closer together and begin collaborations. However, further progress in this highly advanced branch of physics requires the training of young researchers with a combined expertise.

The general outline of the School can be characterized by a few topics. Starting points were the basic concepts of special and general relativity, including the formulations of rotation in relativity, the Sagnac effect and the basic elements of the Lense-Thirring effect and gravito-magnetism. Seminars on theoretical as well as experimental aspects of gravito-magnetism including lectures on the Gravity Probe B experiment completed this theme. The following lectures covered dark matter and dark energy, tests of general relativity in the Solar System including the Pioneer anomaly, and the gravitational decoherence modifying the response of a matter wave interferometer. Then detection of gravitational waves with resonant bar detectors, and with light interferometers on Earth and in Space was discussed.

A major issue of the School was the interface between cold atoms and relativity. After an introduction to atom optics and Bose-Einstein condensation, the theoretical foundations of cold atom interferometers, their use to test gravity, and their implementation in laboratory measurements of the rotation of the Earth and of Newton's gravitational constant were presented. Several lecturers reviewed the characteristics of gyroscopes and interferometers as sensors for inertial forces, starting from gyroscopes based on light waves and comparing their sensitivity to those based on matter waves. The scientific objectives and the technological developments of the atom interferometers associated with the space programs and ground projects were discussed. The presentation of a unifying theoretical approach towards space-time sensors based on optical or matter wave interferometers using optics in five dimensions and of new free-fall absolute gravimeters completed the theme of cold atoms and relativity.

The final topic of our School was the variation of fundamental constants, a subject that during the last years has attracted a lot of attention from different communities of physics. The underlying theories and the state of the art of light-based precision measurements of, for example, the time variation of the electron-proton mass ratio to put constraints on the variation of the fine structure constant were presented.

Unfortunately, a few of our lecturers are not represented in these Proceedings. For example, William D. Phillips (Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland, and University of Maryland, College Park, Maryland, USA) introduced the School to atom optics and Bose-Einstein condensation. He started with an overview of some laboratory experiments for fundamental physics in Space and convinced the audience that in the near future they will lead to real experiments in Space. In this way we can address some of the most penetrating questions of the physics of the 21st century. The principles of laser cooling and trapping of atoms, atom optics, Bose-Einstein condensation, manipulation of ultracold atoms, and atom interferometry were explained with his typical excitement and followed his famous intuitive approach. Emphasis was placed on modern tools of experimental quantum optics such as clocks using cold atoms or interferometers with ultracold coherent matter waves. They are instrumental in the context of fundamental physics as well as in tracking and navigation of satellites in deep-space exploration. The lectures by Phillips were based on his notes prepared for the 2006 Summer School and published in: K. Helmerson and W. D. Phillips: Cooling, trapping and manipulation of atoms and Bose-Einstein condensates: Applications to metrology, in Proceedings of the International School of Physics “Enrico Fermi”, Course CLXVI: Metrology and Fundamental Constants edited by T. W. Hänsch, S. Leschiutta and A.J. Wallard (IOS Press, Amsterdam and SIF, Bologna) 2007, pp. 211-262.

In his lectures Christof Wetterich (Institut für Theoretische Physik, Universität Heidelberg, Germany) covered quintessence, dark matter and dark energy. He focused on the evolution of the universe on the basis of a cosmological constant or quintessence, that is the presence of dynamical dark energy generated by a scalar field called cosmon. The principles of cosmodynamics and the consequence that “fundamental constants” are not really constant anymore were presented at an elementary level. These dramatic predictions require tests based on quantum metrology.

Ignazio Ciufolini (Dipartimento d'Ingegneria dell'Innovazione, Università di Lecce, Italy) reported on a more than twenty years lasting research effort to measure the Lense-Thirring effect through the modifications of the orbits of the LAGEOS and GRACE satellites induced by gravito-magnetism.

Christophe Salomon (Laboratoire Kastler Brossel, Ecole Normale Supérieure, Paris, France) summarized the subject of cold atom clocks on Earth and in Space to test the foundations of physics. Here he put special emphasis on the performance and limits of atomic fountains. Moreover, he presented the Ultra-stable Clocks in Space (ACES) Project approved by the European Space Agency to place ultrastable clocks inside the International Space Station. In this way a cold atom clock and a maser clock will be orbiting around the Earth and their time will be compared to clocks on the ground. The final goal of ACES is to test general relativity. The timetable of this project as well as the effort required to produce a reliable experimental apparatus was presented. The application of atomic clocks to prove or disprove that fundamental physical constants indeed vary with time was also discussed by Salomon.

The School was actively attended by more than 60 participants including students, lecturers and seminar speakers from all over the world. Several students presented their own research and a number of informal sessions with extremely lively discussions took place. An evening Round Table examined the future plans of the European and USA Space Agencies aimed at exploring the limits of fundamental physics in Space.

All activities were inspired by the breathtaking beauty of Lake Como, the Villa Monastero and its gardens, and by the rich scientific heritage of the Enrico Fermi International School. The success of the School is also due to the excellent organizational and administrative support provided by the staff of the Italian Physical Society and the generous monetary support of the Wilhelm und Else Heraeus-Stiftung.

During the completion of these proceedings we have been shocked and deeply saddened by the untimely death of Jürgen Ehlers one of the main lecturers of our School. Jürgen was a highly gifted teacher, an outstanding scientist, and a great friend to many of us. His lectures included in this volume are a living testimony to his deep insight into and love for relativity. Unfortunately his premature departure did not allow him to complete the proof reading of his article. We are most grateful to Endre Kajari for taking this task upon himself. He has done a wonderful job. Many thanks Endre!

Jürgen's participation through his crystal clear lectures, his penetrating questions and the numerous illuminating discussions was vital to the success of our School. For this reason we have decided to dedicate this volume to the memory of this great pioneer of relativity. A more detailed obituary of Jürgen Ehlers may be found in these proceedings. We are grateful to his widow Anita Ehlers and to his longterm collaborator Bernd Schmidt for their help and to Graham Allen as well as Elke Müller for providing us with the pictures of Jürgen shown in these Proceedings.

E. Arimondo, W. Ertmer, E. M. Rasel and W. P. Schleich