Doppler-free laser

spectroscopy

8

8.1 Doppler broadening of

spectral lines 151

8.2 The crossed-beam

method 153

8.3 Saturated absorption

spectroscopy 155

8.4 Two-photon spectroscopy 163

8.5 Calibration in laser

spectroscopy 168

Further reading 175

Exercises 175

Doppler broadening is usually the dominant contribution to the observed
width of lines in atomic spectra, at room temperature. The techniques
of Doppler-free laser spectroscopy overcome this limitation to give much
higher resolution than, for example, a Fabry–Perot ́etalon analyzing the
light from a discharge lamp, as shown in Fig. 1.7(a). This chapter de-
scribes three examples that illustrate the principles of Doppler-free tech-
niques: the crossed-beam method, saturated absorption spectroscopy
and two-photon spectroscopy. To use these high resolution techniques
for precision measurements of atomic transition frequencies the laser fre-
quency must be determined accurately. Thus the calibration is a crucial
part of laser spectroscopy experiments, as discussed at the end of this
chapter. Since it is important to understand the problem before looking
at the solution, the chapter starts with an outline of Doppler broadening
of spectral lines in gases.

8.1 Doppler broadening of spectral lines

The relationship between the angular frequencyωof radiation in the
laboratory frame of reference and the angular frequency seen in a frame
of reference moving at velocityv, as shown in Fig. 8.1, is

ω′=ω−kv , (8.1)

where the wavevector of the radiation has magnitudek=ω/c=2π/λ.
It is the component of the velocity alongkthat leads to the Doppler
effect and here it has been assumed thatk·v=kv.^1

(^1) If necessary, this and other equations
in this chapter could be generalised by
replacingkvwith the scalar product
k·v.
Atom
Fig. 8.1The Doppler effect on the observed frequency of radiation. Radiation that
has an angular frequency ofωin the laboratory frame of reference has the frequencies
indicated in a reference frame moving with a speedv,e.g.therestframeofanatom.
Only the component of the velocity along the wavevectorkcontributes to the first-
order Doppler shift.