By Claude Cohen-Tannoudji

This e-book provides a entire assessment of the fantastic advances visible in atomic physics over the last 50 years. The authors clarify how such development was once attainable by means of highlighting connections among advancements that happened at various instances. They talk about the recent views and the recent examine fields that glance promising. The emphasis is positioned, now not on unique calculations, yet relatively on actual principles. Combining either theoretical and experimental concerns, the booklet might be of curiosity to quite a lot of scholars, academics and researchers in quantum and atomic physics.

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**Example text**

The integral over t′ is then proportional to the Fourier transform g(ω) of Ω(ta + t′ ) taken in ω0 − ωL . 43) where +∞ g(ω) = ′ Ω(ta + t′ ) ei ω t dt′ . 44) −∞ ′ Since Ω(ta + t′ ) ei ω t is maximum for t′ = 0 and has a width τ , g(ω) is maximum for ω = 0 and has a width on the order of 1/τ . 5in 26 ourbook Advances in atomic physics: an overview Ω(t) (a) τ ti ta tb Ω(t) T τ ti tf t (b) τ ta tb tf t Fig. 5 (a) Single pulse of width τ applied at time ta . (b) Sequence of two identical coherent pulses with the same widths applied at two different times ta and tb , and separated by an interval T.

The interaction Hamiltonian HI acts only on internal variables through the internal operator ε · p. According to the Wigner-Eckart theorem, the matrix elements of all vector operators between e and g are proportional. We can thus consider here the matrix elements of ε· D, where D is the electric dipole 8 See Chap. 12. 5in 18 Advances in atomic physics: an overview me = mg − 1 me = mg σ− me = mg + 1 π σ+ mg Fig. 2 Polarization selection rules for an electric dipole transition. The magnetic quantum number m changes by +1 for a σ+ -polarized excitation, by −1 for a σ− -polarized excitation and by 0 for a π-polarized excitation.

31) corresponding to11 θ = ϕ = π/2. These superpositions of states are important because they are at the origin of quantum interference effects that will be mentioned throughout this book. The simple example of a spin 1/2 studied here clearly shows that linear superpositions of states appear when the spin magnetic moment has transverse components with respect to the direction of the static field, which is the quantization axis for defining the energy levels of the spin. This connection between linear superpositions of states and the existence of a transverse magnetization remains valid for angular momenta other than 1/2.