Magnetic trapping,

evaporative cooling and

Bose–Einstein

condensation

10

10.1 Principle of magnetic
trapping 218
10.2 Magnetic trapping 220
10.3 Evaporative cooling 224
10.4 Bose–Einstein
condensation 226
10.5 Bose–Einstein
condensation in
trapped atomic
vapours 228
10.6 A Bose–Einstein
condensate 234
10.7 Properties of
Bose-condensed gases 239
10.8 Conclusions 242

Exercises 243

Magnetic traps are used to confine the low-temperature atoms produced

by laser cooling. If the initial atomic density is sufficiently high, the

simple but extremely effective technique of evaporative cooling allows

experiments to reach quantum degeneracy where the occupation of the

quantum states approaches unity. This leads either to Bose–Einstein

condensation (BEC) or to Fermi degeneracy, depending on the spin of

the atoms. This chapter describes magnetic traps and evaporative cool-

ing, using straightforward electromagnetism and kinetic theory, before

giving an outline of some of the exciting new types of experiments that

have been made possible by these techniques. The emphasis is on pre-

senting the general principles and illustrating them with some relevant

examples rather than attempting to survey the whole field in a qualita-

tive way.

10.1 Principle of magnetic trapping

In their famous experiment, Otto Stern and Walter Gerlach used the

force on an atom as it passed through a strong inhomogeneous magnetic

field to separate the spin states in a thermal atomic beam. Magnetic

trapping uses exactly the same force, but for cold atoms the force pro-

duced by a system of magnetic field coils bends the trajectories right

around so that low-energy atoms remain within a small region close to

the centre of the trap. Thus the principle of magnetic trapping of atoms

has been known for many years but it only became widely used after the

(^1) There was early work on magnetic development of laser cooling. 1
trapping of ultra-cold neutrons whose
magnetic moment is only− 1. 9 μN,and
the nuclear magneton μN,whichis
much smaller than the Bohr magneton
μB.
A magnetic dipoleμin a field has energy
V=−μ·B. (10.1)
For an atom in the state|IJFMF〉this corresponds to a Zeeman energy
V=gFμBMFB. (10.2)