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By Seidel D.

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In the following section it is shown that the time evolution of a quantum particle, moving in one dimension under the influence of a complex-valued potential, can be considered as a limiting case of the time evolution of a moving two-level atom, 50 Chapter 3. Operational approaches to quantum arrival times interacting with a laser field. The advantage of this point of view is that the physical background of the laser model provides an easy understanding of the one-channel problem and in particular of the absorption mechanism.

0. 3 and in the atomic units defined in Appendix D. Remark: Experimentally, it might be difficult to observe the very first photon emitted from the two-level atom due to a limited detector efficiency and the subsequent emission of many photons. With respect to the conditional time evolution, this problem can be solved by considering a three-level atom with an irreversible decay to a sink state |3 as shown in Fig. 1b. 55) remains the same, since it describes the time evolution before the first photon emission.

57) Φk (x) = √ 2π    1 1  C+ eik+ x + C− eik− x , x ≥ 0, 2λ+ /Ω 2λ− /Ω where k 2 + imγ/ , Im q > 0, i λ± = − (γ ∓ γ 2 − 4Ω2 ), 4 k± = k 2 − 2mλ± / , Im k± > 0. 60) The amplitudes R1 , R2 , C+ and C− are given by the matching conditions at x = 0. Solving Eqs. 64) 36 Chapter 3. Operational approaches to quantum arrival times with the common denominator D = (k + k − )(q + k + )λ+ − (k + k + )(q + k − )λ− . 66) 0 where ψ(k) denotes the momentum amplitude that the initial wave packet would have at t = 0 in absence of the laser.

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