The book « Condensats de
Bose-Einstein - La théorie, des fondements aux applications
» in short
Predicted by Albert Einstein in 1925 and realized in 1995 in atomic gases cooled to one millionth of a degree above absolute zero — earning Eric Cornell, Carl Wieman, and Wolfgang Ketterle the 2001 Nobel Prize in Physics — Bose-Einstein condensates constitute a highly exotic state of matter, a giant de Broglie wave, with a large number of particles in the same wave function. This gives them unique properties of spatial and temporal coherence, and opens up promising application prospects, particularly in high-precision quantum measurements.
Accessible from the master's level, this book, published in two volumes by EDP Sciences, methodically develops the theory from first principles, leaving no step untouched. It addresses in particular questions and applications generally absent from works on quantum fluids, inspired by quantum optics. It adopts a universally oriented formulation, freeing itself from the particularities of experimental implementations to highlight general concepts. Finally, it expands on analyses already published by the author or other researchers, and contains unpublished results, as well as a rich bibliography of 370 references.
Contents of volume 1 :
- Gross-Pitaevskii equation (or nonlinear Schrödinger equation) for the condensate mode, applications and inadequacies;
- Bogoliubov theory (includes quantum and thermal fluctuations omitted by Gross-Pitaevskii, also in the time-dependent case), first corrections to Gross-Pitaevskii, first applications;
- notion of 3D superfluidity, its subtleties, Leggett bound;
- condensate phase operator, its evolution equation (quantum version of the second Josephson relation);
- frequencies of the eigenmodes of the condensate beyond Gross-Pitaevskii (including at non-zero temperature), in-depth analytical study.
Contents of volume 2 :
- spin squeezing and Schrödinger cats (strongly entangled quantum states for metrology): multimode and non-zero temperature analysis, limiting factors;
- coherence time of the condensate in a perfectly isolated gas: phase interference versus phase diffusion, role of quantum ergodicity;
- grand-canonical Bogoliubov theory pushed to the next order (Wu order);
- quasi-condensates in low dimension: grand-canonical Bogoliubov method in modulus-phase representation; spatial coherence, pair density, BKT transition in 2D, particularities of 1D superfluidity.
For more details : see the table of contents of the book.
The paperback book, although intended as a whole, has been separated into two volumes for technical reasons, with multiple cross-references between them (there is, however, a complete digital version - in one volume, see the editor's page).