Summary 1099 .4 A note about coldatoms
We have seen that quantum statistics are needed at high densities and low temper-
atures. In recent years, scientistshavedevelopedsome entirely new methodsfor
coolingcomparativelysmall(albeit macroscopic) numbers ofgaseous atoms, usually
alkali metal atoms such as sodium or rubidium.
Space (andpossiblythe author’s expertise?) precludes adetaileddiscussion of
this excitingfield, excitingenoughtogenerate the 1998 Nobelprizefor three ofits
inventors. The techniques involve the clever use of laser beams to slow down a group
ofthe atoms. Typicallysixbeams aredirectedto the groupfrom allsides, operating
at a specialtunedfrequencysuchthat atoms movingtowardsthebeam are slowed,
but those moving towards it are not; this trick (charmingly called ‘optical molasses’)
dependsonthe energy levelstructure ofthe atoms andexploits the Doppler shift
of the movingatoms. Usingsuch techniques, typicallybillions of atoms are slowed
down so that their translational kinetic energy corresponds to the microkelvin regime.
But the storydoesn’t endthere. The atoms can alsobe confinedwithinalimited
volume usingamagnetic field trap, a zero field ‘bottle’, exploitingthe magnetic
moment of the atoms. Finally, the hotter atoms in the trap can be ‘evaporated’ by
loweringtheedges ofthis trap,leavingan arrayofeven colder atoms (corresponding
to several nanokelvin). And these atoms can be observed opticallyor byother means.
The bottom line is that under these unusual conditions, quantum coherence and,
inthe case ofbosonic atoms, Bose–Einstein condensationisobserved.Thesimple
theoryof this chapter fits the observed facts verywell, since thesegroups of cold
atoms are sufficiently dilute that they are indeed examples of the weakly-interacting
particles on whichour statisticsisbased.
9 .5 Summary
Thischapterdiscusses the properties ofanidealBose–Einsteingas together with
applications to systems of interest.
Quantum statistics rather than MB statistics are appropriate forgases at high
density and low temperature.
Thefriendlynature ofbosonsleads to a Bose–Einstein condensation under these
conditions. The condensation implies coherent behaviour of all theparticles
involved.
3 .TheidealBEgasbelowTTTBcanbevisualisedon a two-fluidmodelofsuperfluid
and normal fluid.
Thispictureis usefulin considering the properties ofliquid^4 He, whichshowsa
superfluidtransition.
Interactions between atoms are strong in the liquid, so that the ideal gas model
does not applyindetail.
The idealgas model does applywell to assemblies of cold bosonic atoms.