9.10 Conclusions 213temperature is the same in both cases.^8080 These caesium atoms have a veloc-
ity spread of about 3vr 10 mm s−^1.
These atoms could be used directly if
the measurement time is 0.3 s, but there
would be a large loss of atoms in a
higher fountain withT=1s.
In an atomic fountain the scheme for detecting that a microwave tran-
sition has occurred is very different to that in an atomic beam (Sec-
tion 6.4). The ground configuration of caesium hasJ=1/2 (like all
alkalis) and the two hyperfine levels areF= 3 and 4 (for the only sta-
ble isotope that has nuclear spinI =7/2). If the atoms start in the
lower levelF= 3 then the microwave radiation transfers a fraction of
the atoms to theF = 4 level. This fraction is determined when the
atoms fall through a laser beam that detects atoms in theF= 4 level,
by exciting a transition from this level and monitoring the fluorescence,
see Fig. 9.16. (Atoms in theF = 3 level pass through undetected.^81 )^81 To normalise the signal the atoms in
theF= 3 level are detected with a sec-
ond probe laser beam (not shown in the
figure).
Figure 7.3 shows a plot of the transition probability between the hyper-
fine levels as a function of the microwave frequency—so-called Ramsey
fringes. The narrow line width means that the frequency of the mi-
crowave source used to drive the transition can be set very precisely
to the caesium hyperfine frequency. Such an apparatus maintains the
frequency of the microwave source stable to better than 1 part in 10^15 ,
or 32 ns per year. Many causes of perturbations that might give fre-
quency shifts are small because of the atoms’ low atomic velocity, but
the Zeeman effect of magnetic fields remains a limitation. Experiments
use theF=3,MF=0toF=4,MF= 0 transition because states with
MF= 0 have no first-order Zeeman shift. Nowadays, such caesium foun-
tain frequency standards play an important role in guiding the ensemble
of clocks in national standards laboratories around the world that give
agreed Universal Time.^82
(^82) The important uses of such clocks
weregiveninSection6.4.2andup-to-
date information can be found on the
web sites of national standards labora-
tories.
9.10 Conclusions
The techniques that have been developed to reduce the temperature of
atoms from 1000 K to well below 1μK have had an enormous impact
on atomic physics. Laser cooling has made it possible to manipulate
neutral atoms in completely new ways and to trap them by magnetic and
dipole forces. Some important applications of atom trapping have been
mentioned, such as the great improvement in precision measurements,
and others are given in later chapters, e.g. Bose–Einstein condensation
and the laser cooling of trapped ions.
The important principles of radiation forces have been discussed,
namely: the way in which the scattering force dissipates the energy
of atoms and cools them to the Doppler cooling limit; the trapping of
atoms by the dipole force in various configurations including optical lat-
tices; and sub-Doppler cooling by the Sisyphus mechanism and sub-recoil
cooling. This chapter greatly simplifies the real story of laser cooling for
the sake of a clear presentation; the bookLaser cooling and trapping of
atomsby Metcalf and van der Straten (1999) gives a more comprehen-
sive description of the important contributions made by many people
and many references to other material—see also the review by Wieman