Related papers: Theory of cold atoms: Bose-Einstein statistics
The aim of this Tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term {\it cold} implies that considered temperatures are low, such that quantum…
This paper is a short introduction to cold atom physics and Bose-Einstein condensation. Light forces on atoms are presented, together with laser cooling, and a few atom traps: the magneto-optical trap, dipole traps and magnetic traps. A…
The theoretical description of trapped weakly-interacting Bose-Einstein condensates is characterized by a large number of seemingly very different approaches which have been developed over the course of time by researchers with very…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular…
This article reviews recent investigations on the phenomenon of Bose-Einstein condensation of dilute gases. Since the experimental observation of quantum degeneracy in atomic gases, the research activity in the field of coherent…
The Bose-Einstein condensation of atoms can be conveniently formulated as a problem in thermal quantum field theory. There are many properties of the equilibrium system and its collective excitations that can be studied experimentally. The…
Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms ($^{87}Rb$, $^{23}Na$ and $^{7}Li$) have been cooled to the point of condensation (temperature of 100 nK) using laser cooling and trapping, followed by magnetic…
The critical temperature of Bose-Einstein condensation essentially depends on internal properties of the system as well as on the geometry of a trapping potential. The peculiarities of defining the phase transition temperature of…
This thesis describes the observation and study of Bose-Einstein condensation of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the 1S-2S transition. We condense over 10^9…
This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -- namely, the fraction of…
We outline the general features of the conventional mean-field theory for the description of Bose-Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with…
A survey is given of the present state of the art in studying Bose-Einstein condensation of dilute atomic gases. The bulk of attention is focused on the principal theoretical problems, though the related experiments are also mentioned. Both…
The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two…
We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, sometimes called bubble trap. In order to obtain the critical temperature for Bose-Einstein…
A simple picture describes the results of recent treatments of partially-condensed, dilute, trapped Bose gases at temperature T > 0. The condensate wavefunction is nearly identical to that of a T=0 condensate with the same number of…
We consider two characteristic temperatures for a Bose-Einstein condensate, that are related to certain properties of the condensate statistics. We calculate them for an ideal gas confined in power-law traps and show that they approach the…
We have observed Bose-Einstein condensation of an atomic gas in the (quasi-)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion…
To investigate the phenomenon of Bose-Einstein condensation in perfect crystals a hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system is employed, the hierarchy being obtained…
In the last 25 years, much progress has been made producing and controlling Bose-Einstein condensates (BECs) and degenerate Fermi gases. The advances in trapping, cooling and tuning the interparticle interactions in these cold atom systems…