Bose-Einstein condensate properties

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Eiquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Abstract. Scientific interest in ultracold hydrogen arises from its properties as a Bose-Einstein condensate, its unique roles as a testing ground for atomic theory and a target for ultra high resolution spectroscopy. We describe major developments since the last hydrogen meeting. 

As the temperature is lowered further, the quantum statistical effects dominate the properties of the system, and a transition to the Bose-Einstein condensed phase is manifested. The Bose-Einstein transition temperature T ° in the infinite, noninteracting, uniform boson system is... 

How can one characterize threshold size effects for superfluidity/Bose-Einstein condensation in small boson systems— for example, what is the minimal size of a (" He) cluster for the attainment of these properties ... 

It is of considerable interest to use the electron bubble as a probe for elementary excitations in finite boson quantum systems—that is, ( He)jy clusters [99, 128, 208, 209, 243-245]. These clusters are definitely liquid down to 0 K [46 9] and, on the basis of quantum path integral simulations [65, 155], were theoretically predicted (see Chapter II) to undergo a rounded-off superfluid phase transition already at surprising small cluster sizes [i.e., Amin = 8-70 (Table VI)], where the threshold size for superfluidity and/or Bose-Einstein condensation can be property-dependent (Section II.D). The size of the ( He)jy clusters employed in the experiments of Toennies and co-workers [242-246] and of Northby and coworkers [208, 209] (i.e., N lO -lO ) are considerably larger than Amin- In this large cluster size domain the X point temperature depression is small [199], that is, (Tx — 2 X 10 — 2 X 10 for V = lO -lO. Thus for the current... 

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. 

Bose-Einstein condensates display unusual properties and are considered a new phase of matter. The atoms get packed together so closely that their wavefunctions become correlated like those of photons in... 

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 functions (x a) with a = 312,512 appear in the study of Bose-Einstein condensation of ideal quantum particles [21] that obey Bose-Einstein statistics. Their mathematical properties were studied by Truesdell [22] in detail, so that it is called the Truesdell functions. Their radius of convergence is given by x = 1. Both the functions O (x 3/2) and d> (x 5/2) remain at a finite value at x = 1, but diverge as soon as x exceeds unity. 

The phenomenon of a significant fraction of bosons falling into the ground state is called Bose-Einstein condensation. Bose-Einstein condensation is important in determining the properties of superfluid liquid " He (whose atoms are bosons), but the interatomic interactions in the liquid make theoretical analysis difficult. 

Boesten HMJM, Vogels JM, Tempelaaxs JGC, Verhaar BJ. (1996) Properties of cold collisions of atoms and of atoms in relation to Bose-Einstein condensation. Phys. Rev. A 54 R3726-R3729. 

The expressions considered above are valid for the phase transition to the Bose-Einstein condensate in an ideal gas of noninteracting atomic species. In any real atomic gas, atomic interactions alter the properties of the transition to the BEC. 

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