Condensate in confining potential

This subject is directly related to Chapter 1 of this book and will be briefly summarised here although it has already been treated in an appendix of [E-11].

Spin polarised hydrogen H↓ is listed in the right hand column of Table 1.1 as a system predicted to show Bose-type superfluidity. Bose–Einstein condensation was observed, somewhat unexpectedly, in spin polarised alkaline gases Li↓, Na↓, and Rb↓, with quite an ingenious method using laser light, prior to observation in H↓ gas (see [H-1] – [H-3]). It is unquestionable that the macroscopic wave function appears although superfluidity has yet to be observed. See [H-4] for works on H↓, and related systems preceding this breakthrough.

In a typical experiment the magneto-optical trap, which we can approximate by an anisotropic 3-dimensional harmonic oscillator potential, is used to provide the confining potential for atoms. Its spatial scale is given by R ∼ (ħ/mω)½ ∼ 10−3m, where m is the mass of the atom while ω is the frequency of the harmonic oscillator. There are N ∼ 106 atoms trapped in a volume ∼ R3, for which the Bose–Einstein condensation temperature TBE given by Eq. (1.3) is of the order of 10−7 K for Rb atoms. It should be added that evaporation cooling, which has been used to cool H↓ gas, is required in addition to laser cooling to reach this temperature.