A Prediction of the Bose-Einstein Condensate

Wolfgang Ketterle

The field of atomic quantum gases has seen rapid and sometimes surprising developments since its beginnings in 1995. In this chapter, I summarize, highlight, and comment on selected topics. Introduction Bose-Einstein condensation (BEC) in atomic gases was first observed in 1995, and has changed the face of atomic physics. It is for atoms or matter waves what the laser is for photons: a macroscopically occupied quantum state. It was regarded as an elusive goal until it was discovered in 1995. Although BEC was immediately viewed as a major accomplishment, its impact has far exceeded expectations. Now, twenty years on, there is no question that the field remains exciting. It is impossible to give a review over the developments during those twenty years. Instead, in this chapter, I want to illustrate how often predictions or expectations changed in the pursuit of Bose-Einstein condensation. There were many surprises, and some advances and breakthroughs happened although they were predicted to be impossible. A lesson we can learn from this is that we should always carefully read the fine print when something is proven or assumed impossible, and try to figure out if the assumptions can be circumvented! Since the early history of Bose-Einstein condensation provides several examples for such “impossibility theorems,” I digress into those earlier developments in the first part of this chapter. Early Theoretical Questions Validity of the Prediction of Bose-Einstein Condensation Einstein predicted Bose-Einstein condensation in 1924 in the second of two papers where he generalized Bose's treatment from photons to massive particles [1]. Using statistical arguments introduced by Bose, he found that below a critical temperature, bosonic particles condense in the lowest energy state of the system. In contrast, at very low temperature photons can simply disappear. However, for about a decade, this prediction was not taken at face value. Einstein himself wrote to Ehrenfest, “From a certain temperature on, the molecules ‘condense’ without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it?” [2]. In 1927, George E. Uhlenbeck concluded that the predicted BEC phase transition was an artifact of the replacement of the summation over states by an integral and wrote that no “splitting into two phases” would occur [3].

Russell James Donnelly

Matteo Fadel

Stefano Mancini, Vladimir I. Man’ko

The spectrum of light scattered from a Bose–Einstein condensate is studied in the limit of particle-number conservation. To this end, a description in terms of deformed bosons is invoked and this leads to a deviation from the usual predict spectrum’s shape as soon as the number of particles decreases. PACS number(s): 03.65.Fd (Algebraic methods), 03.75.Fi (Bose condensation), 42.50.Ct (Quantum statistical description of interaction of light and matter) 1 The recent achievements of Bose–Einstein condensate (BEC) with a gas of atoms confined by a magnetic trap [1] has stimulated renewed interest in the question as to what signatures Bose–Einstein condensation imprints in the spectrum of light scattered from atoms in such a condensate [2, 3]. As well known, to deal with the dynamics of BEC gas the Bogolubov approximation in quantum many-body theory [4] is an efficient approach, in which the creation

Jian Zhang

Vortices in Bose-Einstein condensates (BEC) and recent experimental and theoretic progress in chromium condensation are reviewed It is shownthat the structure of vortex lattices in these condensates will be significantly affected by the dipolar interactions, and particularly that an exotic anisotropic structure of vortex lattice is predicted to exist.

Eric Cornell, Carl Wieman