By Shore B.W.

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**Extra info for Coherent manipulations of atoms using laser light**

**Example text**

Secs. 3. g. a frequency chirp) along with variation of the intensity, and population transfer occurs without oscillations; cf. Sec. 5. For each of these classes I offer Hilbert-space pictures of the excitation. These are particular cases of the many two-state models which allow solution in terms of conventional special functions; cf. Appendix E. 1 Weak pulse: Perturbation theory The model of excitation by monochromatic light is an idealization that neglects any fluctuations in the phase or amplitude of the field, properties that affect the frequency content of the field.

2, 1, 5. There is initially no excitation. (after Fig. 2-2 of [2]) This behavior contrasts with that of coherent excitation, for which the relevant parameter is the time integral of the electric field amplitude; cf. Sec. 2. 5. This value is only approached if the stimulated rate is much larger than the spontaneous rate, B21 s(ν)I(t) A21 or, equivalently, n ¯ 1, as will occur for sufficiently high intensity I(t). Figure 12 illustrates the behavior. 4 Comments Such radiative rate equations, supplemented with additional rates for collision-induced population changes, have been adequate for the description of numerous environments in which the radiation is incoherent.

Mathematicians refer to the Bloch sphere, or the Poincar´e sphere, as Riemann spheres that provide a “compactification of the complex-number line”. Picturing changes 275 for describing general elliptical polarization of light, as shown in eqn. (12). As with that picture, points on opposite sides of the Bloch sphere represent orthogonal states. 1): 2c1 c∗1 = 2c2 c∗2 = 2c1 c∗2 = 2 cos2 (θ/2) = 1 + cos θ = 2P1 , 2 sin2 (θ/2) = 1 − cos θ = 2P2 , 2eiφ cos(θ/2) sin(θ/2) = eiφ sin θ. (45) Section 7 illustrates the usefulness of the Bloch sphere for presenting a simple visualization of various pulse effects.