Bose-Einstein condensation of atomic gases

In an ideal atomic gas at a temperature T, the characteristic size of the atomic wave packet is governed by the de Broglie wavelength 

For example, when atoms are cooled down to a temperature of T = 1 mK, quantum-statistical effects can manifest themselves at a density of n = 2x 10 cm. At a temperature of T = 1 /xK, quantum-statistical effects become important at a density of n = 7 X 10 cm , and at an extremely low temperature of T = 1 nK these effects become manifest at a very low density of n = 2 x 10 cm . 

If the atoms in the gas have an integer spin, that is, if they are bosonic atoms, they are distributed among the quantum states in accordance with the Bose-Einstein distribution 

at T Tc the number of atoms in the groimd state is comparable to the total number of atoms in the gas. 

It should be noted that in real experimental situations an atomic gas is always confined in a potential well with a certain wall steepness. In such practical situations, the value of the critical temperature % depends on the shape of the potential well. The steeper the potential well, the higher the critical temperature. 

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Dalfovo F, Giorgini S, Pitaevskii LP, Stringari S. (1999) Theory of bose-einstein condensation in trapped gases. Rev. Mod. Phys. 71 463 512. Anglin JR, Ketterle W. (2002) Bose-einstein condensation of atomic gases. Nature 416 211-218. 

Inguscio, M., Stringari, S., and Wieman, C.E., Eds., Bose Einstein Condensation in Atomic Gases, lOS Press, Amsterdam, 1999 Proceedings of the International School of Physics Enrico Eermi, Course CXL, Vareima, 7-17 July 1998. 

Observation of Bose Einstein condensation in atomic gases... 

For achieving a Bose-Einstein condensate in dilute gases of alkali atoms, Eric A. Cornell and Carl E. Wieman ivere awarded the 2001 Nobel Prize in Physics. Sharing the prize with Cornell and Wieman was Wolfgang Ketterle for his fundamental studies of condensates. 

The development of techniques for cooling and trapping of atoms has led to great advances in physics, which have already been recognized by two Nobel prizes. In 1997 the prize was jointly awarded to Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips for their developments of methods to cool and trap atoms with laser light [1-3]. In 2001, Eric A. Cornell, Wolfgang Ketterle, and Carl E. Wieman jointly received the Nobel prize for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates [4,5]. 

The cooling of atoms to ultracold temperatures has resulted in spectacular discoveries. The realization and study of new states of matter like Bose Einstein Condensates/ degenerate Fermi gases and (Bardeen,... 

W. Ketterle, M.R. Andrews, K.B. Davies, D.S. Durfee, D.M. Korn, M.-O. Mewes, N. J. van Druten Bose-Einstein condensation of ultra<-cold atomic gases. Phys. Scr. T66, 31 (1996)... 

Courteille, P. W., Bagnato, V. S., and Yukalov, V. I. (2001). Bose-Einstein condensations of trapped atomic gases. Laser Physics, 11, 659 800. 

Concurrently, the world of ultracold systems has expanded its boundaries during the last decade to encompass ultracold, three-dimensional, large hnite systems [e.g., ( He)jy clusters (N = 2-10" ), and ( He)jy clusters (N = 25-10 )] in the temperature range of T = 0.1-2.2 K [6-11, 50-78], finite optical molasses in laser irradiated ultracold atomic gases in the temperature range of 10-100 pK [79], as well as finite Bose-Einstein condensates in the temperature range of 10-100 nK [14, 80],... 

Rubidium gas has become important in the study of an exotic state of matter called a Bose-Einstein condensate. This state, first predicted in 1924 by Indian physicist Satyendra Nath Bose, was not observed until 1995. Many laboratories now produce these cooled clouds of atoms, mostly using gases of alkali elements, which have appropriate spin and magnetic properties. 

What happens to a gas when cooled to nearly absolute zero More than seventy years ago, Albert Einstein, extending work by the Indian physicist Satyendra Nath Bose, predicted that at extremely low temperatures gaseous atoms of certain elements would "merge" or "condense" to form a single entity and a new form of matter. Unlike ordinary gases, liquids, and solids, this super-cooled substance, which was named the Bose-Einstein condensate (BECj, would contain no individual atoms because the original atoms would overlap one another, leaving no space in between. 

As we noted in the introduction, spectroscopic evidence is available for small no-pair dimers and trimers [4a,b,c, 5a,b,c,d, 6a,b, 7] and therefore the elucidation of NPFM bonding is not a mere academic exercise. An additional potential interest in this kind of clusters is their relationship to Bose-Einstein condensates, in which the quantum states of all atoms are identical, and to Fermi gases of fermionic isotopes of alkali metals, (e.g., K with atomic mass 40) in magnetic fields [6, 19]. 

The realization of Bose-Einstein condensates (BEC) and quantum degenerate Fermi gases with cold atoms has been one of the highlights of experimental atomic physics during the last decade [1]. In view of recent progress in the experimental work on the production of cold molecules we expect a similarly spectacular... 

The trapping of cold neutral atoms is a powerful tool in experimental atomic physics that has made it possible to conduct many fundamental experiments, such as Bose Einstein condensation and the production of Fermi-degenerate quantmn gases. It is therefore one of the most vivid demonstrations of the capabilities inherent in the laser control of atoms. 

The methods of trapping cold atoms, considered in Chapter 5 and the present chapter in a very brief and retrospective fashion, have become a very powerful tool in experimental physics. They have led to the development of atom optics, the observation and investigation of dilute quantum gases (Bose-Einstein condensation, atom lasers, Fermi-degenerate quantum gases, and ultracold molecules), and probably many other discoveries in the physics of ultracold atoms. These will be discussed in Chapters 7 and 8. But it would be expedient to consider at the end of this chapter a few examples of applications that lie beyond the mainstream, but are of physical interest. 

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