The Quantum Physics of Atomic Frequency Standards

The Quantum Physics of Atomic Frequency Standards: Recent Developments, Second Edition, covers advances in atomic frequency standards (atomic clocks) from the last several decades. It explains the use of various techniques, such as laser optical pumping, coherent population trapping, laser cooling, and electromagnetic and optical trapping, in the implementation of classical microwave and optical atomic frequency standards.

It provides an up-to-date, in-depth view of the vast improvements to atomic clocks that have occurred in the last 25 years. The improved stability and accuracy enable the verification of physical concepts used in fundamental theories, such as relativity, as well as the stability of fundamental constants intrinsic to those theories.

The book first discusses improvements to conventional atomic frequency standards, highlighting the main limitations of those frequency standards and the physical basis of the limitations. It then describes how advances in the theory and applications of atomic physics have opened new avenues in frequency standards. The authors go on to explore the research and development of new microwave and optical frequency standards before presenting the results in frequency stability and accuracy achieved with these new frequency standards. They also illustrate the application of atomic clocks in metrology, telecommunications, navigation, and other areas and give some insight into future work.

This new edition examines updated developments on the frequency standards, alongside content on the International System of Units (SI) and the role of atomic clocks on their base units. It also features new material on Coherent Population Trapping and new developments in the field of optical frequency standards.

• Describes the basic physics, including quantum mechanics, behind the operation of atomic clocks.








• Explores new frequency standards that provide better stability and accuracy than older, more conventional standards.








• Discusses the importance of the field in the general context of physics.

Jacques Vanier is retired from the National Research Council of Canada and as adjunct professor in the Physics Department at the University of Montreal. He is a fellow of the Royal Society of Canada, the American Physical Society, and the Institute of Electrical and Electronic Engineers. He has written more than 120 journal articles and proceedings papers and is the author of several books on masers, lasers, and atomic clocks. His main research work is oriented toward the understanding and application of quantum electronics phenomena.

Cipriana Tomescu is retired from The Institute of Physics, Bucharest, Romania, and as invited researcher in the Physics Department at the University of Montreal. She is the author of numerous articles in scientific journals and conference proceedings. Her research involves state-of-the-art atomic frequency standards and H masers.

This book constitutes an essential addition to the first two volumes of ?The Quantum Physics of Atomic Frequency Standards? (QAPAFS, 1989) written in the early 1980s, by C. Audoin and J. Vanier, the latter being also co-author of this work. QAPAFS has constituted and still constitutes THE reference for the so-called ?Time & Frequency? community. However, the evolution and progress in the domain have been quite spectacular during the following 25 years (1990-2015). This third book, published in 2015, fills the gap and describes in a very comprehensive manner the more recent achievements: use of laser cooling and other advanced effects based the atom-laser interactions, use of optical combs, extreme miniaturization, emerging new fields of applications, fundamental investigations in physics and metrology, etc. The second edition of the book (2025) includes important additional annexes, offering an overview on the latest developments, that occurred during the last ten years and discussing the main perspectives and challenges for the future.

- Gaetano Mileti, Professor of Physics, University of Neuchâtel, February 2025

This book is a successful attempt to cover the last thirty years of research in this amazing field of atomic frequency standards. 

After a resume of the main microwave atomic clocks, the book dedicates an entire chapter to the physics that played a significant role in the development of the most recent atomic frequency standards, including laser optical pumping, coherent population trapping (CPT) and laser cooling. Then, new conception microwave clocks are described, with particular emphasis for atomic fountains, their implementations and performances. The CPT approach is also extensively discussed, both in a hot vapor cell as well as in a laser-cooled ensemble. The last chapter is dedicated to optical clocks that were only briefly mentioned in the historical volumes. The main different techniques of implementing an optical frequency standard are discussed, including single ions and neutral atom lattice clocks.

This second edition includes some useful annexes, specifically, the last one is a resume of the SI redefinition which turns out to be quite interest. Definitely, it also addresses not only graduate students, but it can be a useful reference also to researchers working in the field of frequency metrology.

- Salvatore Micalizio, Istituto Nazionale di Ricerca Metrologica (INRIM), February 2025