Quantum Computing With Bose-Einstein Condensates: A Literature Survey

Tim Byrnes

Vyacheslav I. Yukalov

Abstract Due to high current interest to Bose–Einstein condensation (BEC), the related topics, such as spontaneous gauge symmetry breaking, ergodic decomposition, and particle fluctuations, are intensively discussed in literature. These discussions, unfortunately, involve quite a number of controversies and confusions. The goal of the present brief survey is to clarify some of these confusions, concentrating on the principal points, such as the relationship between the conditions of BEC, the Bogolubov method of quasiaverages, spontaneous gauge symmetry breaking, ergodic decomposition, the presumed existence of nonthermodynamic particle fluctuations leading to the so-called ‘grand canonical catastrophe’, and the requirements for system stability.

Vyacheslav I. Yukalov

Due to high current interest to Bose-Einstein condensation, the related topics, such as spontaneous gauge symmetry breaking, ergodic decomposition, and particle fluctuations, are intensively discussed in literature. These discussions, unfortunately, involve quite a number of controversies and confusions. The goal of the present brief survey is to clarify some of these confusions, concentrating on the principal points, such as the relationship between the conditions of Bose-Einstein condensation, the Bogolubov method of quasiaverages, spontaneous gauge symmetry breaking, ergodic decomposition, the presumed existence of nonthermodynamic particle fluctuations leading to the so-called ``grand canonical catastrophe", and the requirements for system stability.

Matteo Fadel

Claude N. Cohen-Tannoudji

Meera M. Parish

This chapter presents the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-correlated pairs of fermions to the Bose-Einstein condensation (BEC) of diatomic molecules in the atomic Fermi gas. Our aim is to provide a pedagogical review of the BCS-BEC crossover, with an emphasis on the basic concepts, particularly those that are not generally known or are difficult to find in the literature. We shall not attempt to give an exhaustive survey of current research in the limited space here; where possible, we will direct the reader to more extensive reviews.