0198506961.pdf

176 Doppler-free laser spectroscopy

Determine the line width of the peaks and the fre-

quency shift between the even isotopes from the

scan. The line width arises from residual Doppler

broadening. Calculate the collimation angle of the

atomic beam.

Comment. This line has a normal mass shift of

180 MHz between the two even isotopes. There are

smaller contributions to the isotope shift from the

specific mass and volume effects.

(8.4)Hyperfine structure in laser spectroscopy
What is the physical origin of the interaction that
leads to hyperfine structure in atoms?
Show that hyperfine splittings obey an interval rule
whichcanbeexpressedas

∆EF,F− 1 =AnljF,

i.e. the splitting of two sub-levels is proportional to

the total angular momentum quantum numberF

of the sub-level with the largerF.

The naturally-occurring isotope of caesium (^133 Cs)

has a nuclear spin ofI=7/2. Draw a diagram

showing the hyperfine sub-levels, labelled by the ap-

propriate quantum number(s), that arise from the

62 S 1 / 2 and 6^2 P 3 / 2 levels in caesium, and the al-

lowed electric dipole transitions between them.

Explain the principle of Doppler-free saturation

spectroscopy.

The figure shows the saturated absorption spectrum

obtained from the 6^2 S 1 / 2 –6^2 P 3 / 2 transition in a

vapour of atomic caesium, including the cross-over

resonances which occur midway betweenallpairs of

transitions whose frequency separation is less than

the Doppler width. The relative positions of the

saturated absorption peaks within each group are

given below in MHz.

Frequency

ab

cd

e f

A B

CD

E

F

8588.2 MHz

Probe beam intensity

AB C D E F

0 100.7 201.5 226.5 327.2 452.9

ab c d e f

0 75.8 151.5 176.5 252.2 353.0

Using these data and the information in the dia-

gram:

(a) determine the extent to which the interval rule

is obeyed in this case and deduce the hyper-

fine parameterAnljfor the 6^2 S 1 / 2 and 6^2 P 3 / 2

levels;

(b) estimate the temperature of the caesium

vapour. (The wavelength of the transition is

852 nm.)

(8.5)Hyperfine structure in laser spectroscopy

The energy separation between the two hyperfine

levels in thens configurations of hydrogen is given

by eqn 6.10, and forn= 1 this corresponds to

a hyperfine transition frequency of ∆fHFS(1s) =

1 .4GHz.

(a) Determine the separation of the hyperfine sub-

levels in the 2s^2 S 1 / 2 level of hydrogen, and

compare your answer to the value in the cap-

tion of Fig. 8.7.

(b) Show that the peaks presented in Fig. 8.11 have

an expected separation of 167 ∆fHFS(1s). Com-

pare the expected value with that in the figure

(e.g. by measurement with a ruler and using

the frequency scale given).