6.4 Measurement of hyperfine structure 119wherevbeamis the typical velocity in the beam andlis the length of
the interaction region. Therefore the atomic beams used as primary
standards are made as long as possible. An interaction over a region
2 m long gives a line width of ∆f= 100 Hz.^40 Thus the quality factor is
(^40) Caesium atoms have velocities of
vCs=(3kBT/MCs)^1 /^2 = 210 m s−^1 at
T= 360 K.
f/∆f∼ 108 ; however, the centre frequency of the line can be determined
to a small fraction of the line width.^41 As a result of many years of
(^41) In a normal experiment it is hard to
measure the centre of a line with an un-
certainty of better than one-hundredth
of the line width, i.e. a precision of only
careful work at standards laboratories, atomic clocks have uncertainties 1in10^10 in this case.
of less than 1 part in 10^14. This illustrates the incredible precision of
radio-frequency and microwave techniques, but the use of slow atoms
gives even higher precision, as we shall see in Chapter 10.^42 There is
(^42) The hydrogen maser achieves a long
interaction time by confining the atoms
in a glass bulb forτ∼ 0 .1s to give a
line width of order 10 Hz—the atoms
bounce off the walls of the bulb with-
out losing coherence. Thus masers can
be more precise than atomic clocks but
this does not mean that they are more
accurate, i.e. the frequency of a given
maser can be measured to more dec-
imal places than that of an atomic-
beam clock, but the maser frequency
is shifted slightly from the hyperfine
frequency of hydrogen by the effect of
collisions with the walls. This shift
leads to a frequency difference between
masers that depends on how they were
made. In contrast, caesium atomic
clocks measure the unperturbed hyper-
fine frequency of the atoms. (The use
of cold atoms improves the performance
of both masers and atomic clocks—the
above remarks apply to uncooled sys-
tems.)
a great need for accurate timekeeping for the synchronisation of global
telecommunications networks, and for navigation both on Earth through
the global positioning system (GPS) and for satellites in deep space.
The atomic-beam technique has been described here because it fur-
nishes a good example of the Zeeman effect on hyperfine structure, and
it was also historically important in the development of atomic physics.
The first atomic-beam experiments were carried out by Isador Rabi and
he made numerous important discoveries. Using atomic hydrogen he
showed that the proton has a magnetic moment of 2. 8 μN,whichwas
about three times greater than expected for a point-like particle (cf. the
electron withμB, i.e. one unit of the relevant magnetic moment). This
was the first evidence that the proton has internal structure. Other
important techniques of radio-frequency spectroscopy such as optical
pumping are described elsewhere, see Thorneet al. (1999) and Corney
(2000).
Further reading
Further details of hyperfine structure and isotope shift including the
electric quadrupole interaction can be found in Woodgate (1980). The
discussion of magnetic resonance techniques in condensed matter (Blun-
dell 2001) gives a useful complement to this chapter.
The classic reference on atomic beams isMolecular beams(Ramsey
1956). Further information on primary clocks can be found on the web
sites of the National Physical Laboratory (for the UK), the National
Institute of Standards and Technology (NIST, in the US), and similar
sites for other countries. The two volumes by Vannier and Auduoin
(1989) give a comprehensive treatment of atomic clocks and frequency
standards.