7.8 Comment on semiclassical theory 145(a) (b) (c)Fig. 7.9Eigenenergies of a two-level atom interacting with an external electric field. (a) and (b) show the a.c. Stark effect
for negative and positive frequency detunings respectively, as a function of the Rabi frequency. (c) The d.c. Stark effect as a
function of the applied field strength.
This equation is also valid for negative frequency detuningδ<0when
the light shift of this state decreases its energy. The dependence of
the light shift on the sign ofδhas important consequences for dipole-
force traps for atoms, as described in Chapter 9. Figure 7.9 summarises
the light shift and shows the d.c. Stark shift for comparison, and the
eigenstates of the perturbation are discussed in Appendix A.
7.8 Comment on semiclassical theory
This chapter’s treatment of the interaction of radiation with atoms is
semiclassical—the energy of the atoms is quantised but the radiation is
not (sinceE 0 cosωtis a classical electric field). It is individual two-level
atoms that absorb energy in lumps ofωfrom the radiation; neverthe-
less, the quantityI/ωis commonly referred to as the flux of photons.
In addition to transitions between two bound quantum states of the
atom, this semiclassical theory can also describe photo-ionization where
light excites an electron from a bound state to an unbound state above
the ionization limit. In such a transition the atom suddenly becomes an
ion (plus a free electron) at a given time, like a quantum jump between
bound states. The average of many such jumps corresponds to the rate
predicted semiclassically.^54 Photo-ionization of individual atoms closely
(^54) Similarly, in radioactivity the indi-
vidual nuclei decay randomly but a
large sample exhibits a smooth expo-
nential decay.
resembles the photoelectric effect that occurs at the surface of a metal
with work function Φ illuminated by light of frequencyω.Thesur-