Home > The Quantum World of Ultra-Cold Atoms and Light
The Quantum World of Ultra-Cold Atoms and Light
Crispin Gardiner and Peter Zoller
» The Authors
» The Quantum World Trilogy
» Book 1: Foundations of Quantum Optics
» Book 2: The Physics of Quantum Optical Devices
» Book 3: Ultra-ColdAtoms
» The eBooks
» Modifying the Files
» PDF Readers
» References
The Authors

Crispin Gardiner is an Honorary Professor of Physics at the University of Otago, New Zealand.

Peter Zoller is a Professor of Physics at the University of Innsbruck, Austria and a Research Director at IQOQI, the Institute for Quantum Optics and Quantum Information of Austrian Academy of Sciences in Innsbruck.

Both of the authors are major figures in the fields of quantum optics and ultra cold atoms. They have collaborated on numerous scientific papers, as well as being the authors of Quantum Noise, a widely used reference on the application of quantum stochastic methods to quantum Optics. In addition, Crispin Gardiner is the author of Stochastic Methods, the standard reference on the scientific applications of classical stochastic processes.
The Quantum World Trilogy

Quantum optics has always been the science of atoms and light. Traditionally, the main interest was in the quantum mechanics of the light. With the advances in laser cooling of the 1980s, culminating in the creation of the first Bose-Einstein condensate in 1995, the collective properties of the atoms became to occupy a dominant role. Quantum optics and condensed matter physics of became strongly interdependent. At the same time, quantum-optical control over individual atoms became increasingly comprehensive and precise, giving rise to the prospect of quantum devices, such as the ion trap quantum computer.

We decided to write three books, a trilogy, in which the fields of quantum optics, quantum-controlled cold atoms and the physics of large ensembles of cold atoms, including Bose-Einstein condensates, quantum degenerate Fermi gases, and cold atoms trapped in optical lattices are covered in a systematic and consistent manner. The three books in the trilogy will present the theoretical techniques needed to describe the devices based on quantum science. There is a strong emphasis on the construction of quantum devices using the toolbox provided by the precise control now available.

The books are intended as textbooks for graduate students. Book I, Foundations of Quantum Optics is quite short, and presents the most basic aspects of the kind of quantum optical formalism needed for both of the subsequent books.
Book 1: Foundations of Quantum Optics

Foundations of Quantum Optics—Book I of the trilogy The Quantum World of Ultra-Cold Atoms and Light—provides an introductory text on the theoretical techniques of quantum optics, containing the elements of what one needs to teach, learn, and think about quantum optics. There is a particular emphasis on the classical and quantum stochastic methods which have come to dominate the field.

Special attention is given to the use of phase-space techniques, by which some quantum systems can be mapped to classical stochastic systems. It finishes with a simple formulation of the foundations and the practical application of quantum measurement theory
Book 2: The Physics of Quantum-Optical Devices

The Physics of Quantum-Optical Devices—Book II of the trilogy The Quantum World of Ultra-Cold Atoms and Light—provides a comprehensive treatment of theoretical quantum optics. It covers applications to the optical manipulation of the quantum states of atoms, laser cooling, continuous measurement, quantum computers and quantum processors, superconducting systems and quantum networks.

The subject is consistently formulated in terms of quantum stochastic techniques, and a systematic and thorough development of these techniques is a central part of the book. There is also a compact overview of the ideas of quantum information theory.

The main aim of the book is to present the theoretical techniques necessary for the understanding of quantum optical devices, with special attention to those devices used in quantum information processing and quantum simulation. Although these techniques were developed originally for the optical regime, they are also applicable to electromagnetic radiation from the microwave realm to the ultra-violet, and for atomic systems, Josephson junction systems, quantum dots and nano-mechanical systems.
Book 3: Ultra-Cold Atoms

Ultra-Cold Atoms — Book III of the trilogy The Quantum World of Ultra-Cold Atoms and Light — covers the field of ultra-cold atoms from the point of view of atomic physics. It is a surprising fact that the methods of quantum optics, with their orientation based on a modular paradigm, have nevertheless proved themselves capable of describing the apparently non-modular systems which appear in this field. Hence, like the other books in the trilogy, it makes extensive use of the quantum stochastic paradigm.

The book covers five main areas

  • The physics of cold collisions, binding of atoms into molecules, and Feshbach resonances,
  • Bose-Einstein condensation, at zero temperature, and at finite temperature,
  • Quantum kinetic theory,
  • Ultra-cold Fermions,
  • Atoms in optical lattices.

The treatment of the field emphasizes the description of systems of ultra-cold atoms as they are produced in the laboratory nowadays, using the techniques laser cooling and trapping. These methods involve very specific quantum states of atoms, and a range of trapping potentials, ranging from harmonic potentials, both magnetic and optical, to the optical lattice potentials produced by intricate arrangements laser fields.
The eBooks

Design and Production: In designing the eBook versions, we settled on a fully hyperlinked pdf format, as the format which gives the best control over quality of layout, especially in mathematics. This fully hyperlinked pdf eBook format, enables cross referencing both within each eBook, and between the different eBooks. It was produced using LaTeX, enhanced by

  • The packages fourier.sty and eucal.sty (for calligraphic capitals).
  • The package psfrag.sty toproduce text labels for the figures.
  • The package hyperref.sty to produce all of the hyperlinking.
  • The final pdf files produced from PostScript files using the ps2pdf program.
Modifying the Files

CAUTION: Only make modifications to a COPY of an eBook file! Modifying the file°™including making annotations, highlighting, etc requires the software to rewrite the file, and with unsuitable sofware this can result in damage to the hyperlinks.

If you make annotations and find that hyperlinks are damaged, you can download the original version of the ebook again from the website where you made the purchase.

If you have purchased the ebook from the Publisher directly, you can download the original version of the ebook from the following link: https://www.worldscientific.com/worldscibooks/10.1142/p983#t=toc.

Login credentials will be required for the download. Please login with the same username as you have used when you purchase this ebook. For enquiries, please email sales@wspc.com.sg
PDF Readers

There is software for reading pdf files on almost every computer and tablet platform. It is not possible to test all such software.

Adobe Acrobat products and Goodreader do not appear to damage the hyperlinks when annotations are made, whereas Apple Preview definitely does damage hyperlinks when annotations are made, and also under some other circumstances.

We have tested the following configurations, and all of them appear to support the hyperlinks within the books, and the hyperlinks from one book to another.

Mac OS XApple Preview Provides a very nice reading experience, but damages hyperlinks when saving, and therefore should not be used for making annotations.
Adobe Acrobat ReaderNot as beautiful, and somewhat slower than Preview. Does not damage hyperlinks
SkimProvides a very good appearance, and does not damage hyperlinks. Skim is freeware, available from https://skim-app.sourceforge.net.

Windows Adobe Acrobat Reader Does not damage hyperlinks
Adobe Acrobat Professional    Does not damage hyperlinks

Linux Adobe Acrobat ReaderDoes not damage hyperlinks

IOS on iPad    GoodreaderProbably the only IOS pdf viewer which supports all of the hyperlinking, both internal and external. Very nice annotation features, and saving the annotated file does appear to preserve the hyperlinking, both internal and external.

AndroidAdobe Acrobat ReaderDoes not damage hyperlinks

Unfortunately Acrobat Reader for iOS does not provide a back button. So, while all links function correctly, getting back to the original place is difficult.


  • Crispin Gardiner: Stochastic Methods: A handbook for the Natural and Social Sciences, 4th ed. Springer 2009
  • C W Gardiner and P Zoller: Quantum Noise; A Handbook of Quantum Stochastic Methods with Applications to Quantum Optics, 3rd ed. Springer 2004

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