The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics.The topics covered are 1.Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including "Feshbach resonances" and hybrid condensates; 4. Elementary excitations in the Bogoliubov approximation and beyond; and 5. Splitt traps, interference phenomena and condensate arrays.
The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics.The topics covered are 1.Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including "Feshbach resonances" and hybrid condensates; 4. Elementary excitations in the Bogoliubov approximation and beyond; and 5. Splitt traps, interference phenomena and condensate arrays.
Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of the most active areas in contemporary physics. This book explains phenomena in ultracold gases from basic principles, without assuming a detailed knowledge of atomic, condensed matter, and nuclear physics. This new edition has been revised and updated, and includes new chapters on optical lattices, low dimensions, and strongly-interacting Fermi systems. This book provides a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problems are included at the end of each chapter.
Since an atomic Bose-Einstein condensate, predicted by Einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold Bose and Fermi gases has become one of the most active areas in contemporary physics. This book explains phenomena in ultracold gases from basic principles, without assuming a detailed knowledge of atomic, condensed matter, and nuclear physics. This new edition has been revised and updated, and includes new chapters on optical lattices, low dimensions, and strongly-interacting Fermi systems. This book provides a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problems are included at the end of each chapter.
Topics in the Theory of the Ultracold Dilute Alkali Gases (A J Leggett) Statistical Mechanics of Bosonic Systems (J Oitmaa) Condensate Oscillations, Kinetic Equations and Two-Fluid Hydrodynamics in a Bose Gas (A Griffin) Finite Temperature Effects in Bose-Einstein Condensates (K Burnett) The Theory of Atom Lasers (R J Ballagh & C M Savage) Vortices and Solitons in Bose-Condensates (P D Drummond) Cooling, Trapping and Manipulation of Neutral Atoms and Bose-Einstein Condensates by Electromagnetic Fields (K Helmerson & W D Phillips) Experimental Aspects of Bose-Einstein Condensation (A C Wilson & C R McKenzie).
Since the dramatic discovery of Bose–Einstein condensation (BEC) in trapped atomic gases in 1995 (Anderson et al. , 1995), there has been an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first phase of this research was discussed in the influential review article by Dalfovo et al. (1999) and in the proceedings of the 1998 Varenna Summer School on BEC (Inguscio et al. , 1999). More recently, this research has been well documented in two monographs, by Pethick and Smith (2008, second edition) and by Pitaevskii and Stringari (2003). Most of this research, both experimental and theoretical, has concentrated on the case of low temperatures (well below the BEC transition temperature, T BEC ), where one is effectively dealing with a pure Bose condensate. The total fraction of noncondensate atoms in such experiments can be as small as 10% of the total number of atoms and, equally importantly, this low-density cloud of thermally excited atoms is spread over a much larger spatial region compared with the high-density condensate, which is localized at the centre of the trapping potential. Thus most studies of Bose-condensed gases at low temperatures have concentrated entirely on the condensate degree of freedom and its response to various perturbations. This region is well described by the famous Gross–Pitaevskii (GP) equation of motion for the condensate order parameter Φ( r , t ). As shown by research since 1995, this pure condensate domain is very rich in physics. The main goal of the present book, in contrast, is to describe the dynamics of dilute trapped atomic gases at finite temperatures such that the noncondensate atoms also play an important role.
The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.
The main topic of these lectures is the physics of quantum degenerate atomic Fermi gases both under uniform confinement and in harmonic traps. To begin with, a general introduction on ideal Fermi gases is proposed. This "academic" limit is relevant in experiments where ultracold fermionic atoms are all polarized in a single spin state: the low atom momenta together with the fermionic nature of the atoms forbid atomic s-wave scattering and the atoms can be considered as free. Interactions are then introduced for the case of a gas with two spin components. Interactions can be tuned via Feshbach resonances and control the microscopic features of the superfluid phase, ranging from the BCS limit (formation of Cooper pairs) to the BEC limit (Bose-Einstein condensation of dimers). Various theoretical approaches for the description of the BCS-BEC crossover and their predictions in comparison with the experimental results are discussed.