7.9 Conclusions 147feature for all broadening mechanisms.^57 In particular, this means that^57 Both for mechanisms that are homo-
geneous like radiative broadening, e.g.
collisionsas shown in Loudon (2000),
and also for inhomogeneous mecha-
nisms such as Doppler broadening (Ex-
ercise 7.9).
the steady-state populations for an atom illuminated by monochromatic
(laser) radiation can be related to the case of illumination by broad-
band radiation and the rate equations that Einstein wrote down. The
theory of the interaction between radiation and matter can also be de-
veloped by working ‘backwards’ from the rate equations in Einstein’s
treatment of broadband radiation to find the rate equations for the case
of monochromatic radiation by making ‘reasonable’ assumptions about
the atomic line shape, etc. This approach avoids perturbation theory
and is commonly adopted in laser physics; however, it gives no informa-
tion about coherent phenomena (Rabi oscillations, etc.).^5858 Using time-dependent perturbation
theory to describe the underlying be-
haviour of the two-level atom and find-
ing the rate equations from them gives
a clear understanding of the conditions
under which these rate equations for
the populations are valid.
Section 7.6 introduced the concept of an absorption cross-section and
its use in the calculation of the absorption of radiation propagating
through a gas with a certain number density of atoms.^59 The discussion
(^59) The inverse of absorption is gain; this
is a critical parameter in laser systems
that is calculated in terms of an opti-
cal cross-section in a very similar way
to absorption. The gain also exhibits
saturation.
of the cross-section provides a link between two different perspectives
on the interaction of radiation with matter, namely (a) the effect of
the radiation on the individual atoms, and (b) the effect of the atomic
gas (medium) on the radiation, e.g. absorption.^60 The saturation of ab-
(^60) An important objective of this chap-
ter was to show that both of these view-
points embody the same physics.
sorption as characterised by the saturation intensity forms the basis for
a method of Doppler-free spectroscopy described in Chapter 8. From
viewpoint (a), saturation arises because there is a maximum rate at
which an atom can scatter radiation and this result for individual atoms
is important in the discussion of radiation forces in Chapter 9. The for-
malism developed in this chapter allowed a straightforward derivation of
the a.c. Stark effect on the atomic energy levels; this light shift is used in
some of the methods of trapping and cooling atoms with laser radiation
(also described in Chapter 9).
Further reading
Loudon’s book on quantum optics gives more rigorous derivations of
many formulae in this chapter.^61 Further properties of the optical Bloch^61 I have used similar notation, except
Γ for the full width at half maximum
(FWHM), whereas Loudon uses the
half widthγ=Γ/2.
equations are discussed by Cohen-Tannoudjiet al. (1992) and Barnett
and Radmore (1997). The treatment of the optical absorption cross-
section of a gas closely resembles the calculation of the gain cross-section
for a laser and further details can be found in books on laser physics in-
cluding detailed discussion of broadening mechanisms, e.g. Davis (1996)
and Corney (2000).