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126 The interaction of atoms with radiation 7.2 The EinsteinBcoefficients In the previous section we found the effect of an elec ...
7.3 Interaction with monochromatic radiation 127 The factor of 1/3 arises from averaging ofD·̂erad,wherêeradis a unit vector al ...
128 The interaction of atoms with radiation |c 2 (t)|^2 = Ω^2 W^2 sin^2 ( Wt 2 ) , (7.27) where W^2 =Ω^2 +(ω−ω 0 )^2. (7.28) At ...
7.3 Interaction with monochromatic radiation 129 Usingeqn7.5forΨ(t) gives this dipole moment of the atom as Dx(t)= ∫ ( c 1 e−iω^ ...
130 The interaction of atoms with radiation . ̃c 1 = . c 1 e−iδt/^2 − iδ 2 c 1 e−iδt/^2. (7.40) Multiplication by i and the use ...
7.3 Interaction with monochromatic radiation 131 that . R·R=0so|R|^2 is constant—it is straightforward^15 to show that^15 |R|=1f ...
132 The interaction of atoms with radiation energy−μ·Bis constant, and the magnetic moment precesses around the direction of the ...
7.4 Ramsey fringes 133 as expected from the Fourier transform relationship of the frequency and time domains. We shall now consi ...
134 The interaction of atoms with radiation Fig. 7.3 Ramsey fringes from an atomic fountain of caesium, showing the transition p ...
7.5 Radiative damping 135 than a derivation, but this approach does give useful physical insight. 7.5.1 The damping of a classic ...
136 The interaction of atoms with radiation The sum of the kinetic energy^12 m . x 2 and the potential energy^12 mω^20 x^2 gives ...
7.5 Radiative damping 137 7.5.2 The optical Bloch equations A two-level atom has an energy proportional to the excited-state pop ...
138 The interaction of atoms with radiation 7.6 The optical absorption cross-section Monochromatic radiation causes an atom to u ...
7.6 The optical absorption cross-section 139 This formula, known as Beer’s law (see Fox 2001), works well for ab- sorption of lo ...
140 The interaction of atoms with radiation area under this line shape function equals unity: ∫∞ −∞ gH(ω)dω=1. (7.78) The pre-fa ...
7.6 The optical absorption cross-section 141 circularly-polarized light must have the correct handedness and propa- gate along t ...
142 The interaction of atoms with radiation In a two-level atom the upper level can only decay to level 1 so Γ =A 21 , and for a ...
7.6 The optical absorption cross-section 143 We can also obtain eqn 7.82 directly from the steady-state value of w=(N 1 −N 2 )/N ...
144 The interaction of atoms with radiation 7.7 The a.c. Stark effect or light shift In addition to its effect on the population ...
7.8 Comment on semiclassical theory 145 (a) (b) (c) Fig. 7.9Eigenenergies of a two-level atom interacting with an external elect ...
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