By Andrei B. Klimov

Written by way of significant individuals to the sector who're popular in the neighborhood, this is often the 1st entire precis of the numerous effects generated via this method of quantum optics so far. As such, the e-book analyses chosen subject matters of quantum optics, targeting atom-field interactions from a group-theoretical standpoint, whereas discussing the important quantum optics types utilizing algebraic language. the general result's a transparent demonstration of the benefits of using algebraic easy methods to quantum optics difficulties, illustrated by means of a few end-of-chapter difficulties. a useful resource for atomic physicists, graduates and scholars in physics.

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Finally, we consider examples of the collective dynamics of an ensemble of two-level systems in general time-dependent ﬁelds. 1 Spin in a Constant Magnetic Field As we have already mentioned, a two-level atom can be described in terms of isotopic spin. Thus, the dynamics of a two-level atom in a classical external ﬁeld is equivalent to the dynamics of a spin 1/2 particle in a corresponding magnetic ﬁeld. We begin with the simplest example: the evolution in a constant magnetic ﬁeld. Let us denote the magnetic ﬁeld vector by H and the magnetic moment of the spin by µ = µσ, where σ = {σx , σy , σz }.

22) discussed in the previous section is not useful if the external ﬁeld is a pulse with vanishing amplitude at t → ±∞. 25 is impossible since the coefﬁcients of this equation diverge when t → ±∞. 22. 27) where f (t) must be real if H is to be Hermitian. 27 as t → ∞. 29) It can easily be seen that the functions ± cannot approach zero since f (t) is real. 22) for the operator U, different initial conditions for the functions α, β, and γ. 29. The substitutions . 33) = iω0 /2 we obtain η (−∞) and ξ (−∞) 1 η (−∞) = ξ (−∞) = √ e−iω0 t 2 Also, since the interaction disappears for t → ∞, we have − (∞) = iω0 /2 and thus 2 (t → ∞) = ω2 /4.

Hint: prove that S = −λ1 log λ1 − λ2 log λ2 , where λ1,2 = (1 ± 2P − 1)/2. e. |ψ0 is the eigenstate of the operator s(δ0 )). 56) 23 2 Atomic Dynamics In this chapter, we consider the simplest examples of the two-level system dynamics in an external classical ﬁeld. We start with the spin dynamics in a constant magnetic ﬁeld. Then we consider the resonance dynamics of a two-level atom in an oscillating electric ﬁeld for different cases of the ﬁeld polarization, and, in doing so, justify the rotating wave approximation (RWA).