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8.4 Two-photon spectroscopy 163

(atoms in 2s^2 S 1 / 2 level) but it was not resolved by optical techniques
before the invention of Doppler-free laser spectroscopy.

8.4 Two-photon spectroscopy

Two-photon spectroscopy uses two counter-propagating laser beams, as
shown in Fig. 8.8. This arrangement has a superficial similarity to sat-
urated absorption spectroscopy experiments (Fig. 8.4) but these two
Doppler-free techniques differ fundamentally in principle. In two-photon
spectroscopy the simultaneous absorption of two photons drives the
atomic transition. If the atom absorbs one photon from each of the
counter-propagating beams then the Doppler shifts cancel in the rest
frame of the atom (Fig. 8.9(a)):

ω

(

1+

v

c

)

+ω

(

1 −

v

c

)

=2ω. (8.20)

Beam splitter

sends light

to calibration Detector

Lens Sample Mirror

Filter

Laser

Fig. 8.8A two-photon spectroscopy experiment. The lens focuses light from the
tunable laser into the sample and a curved mirror reflects this beam back on itself
to give two counter-propagating beams that overlap in the sample. For this exam-
ple, the photons spontaneously emitted after a two-photon absorption have different
wavelengths from the laser radiation and pass through a filter that blocks scattered
laser light. Usually, only one of the wavelengths corresponding to the allowed tran-
sitions at frequenciesω 1 iorωi 2 (in the cascade shown in Fig. 8.9(a)) reaches the
detector (a photomultiplier or photodiode). The beam splitter picks off some laser
light to allow measurement of its frequency by the methods discussed in Section 8.5.

(a)

(b)

Atom

2

1

Laboratory

frame:

Atom

frame:

Fig. 8.9(a) The atom has a compo-

nent of velocityvalong the axis of the

laser beams (the light has frequency

ω). The atoms sees an equal and op-

posite Doppler shift for each beam.

So these shifts cancel out in the sum

of the frequencies of the two counter-

propagating photons absorbed by the

atom (eqn 8.20). The sum of the fre-

quencies does not depend onvso reso-

nance occurs for all atoms when 2ω=

ω 12. (b) A two-photon transition be-

tween levels 1 and 2. The atom decays

in two steps that each emit a single pho-

ton with frequenciesωi 2 andω 1 i.