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2]). In contrast, the recent progress in laser technology and the ability to manipulate atomic motion and the internal states of quantum systems nowadays allows the experimental investigation of specific issues concerning time in quantum mechanics. Early contributions to an operational understanding of arrival times are due to Allcock [6] who considered the absorption rate of particles in an absorbing potential that has the meaning of a “detector”. Further progress in this direction has been made by Muga et al.

From the Hamiltonian equations of motion one sees that the x-dependence in the electric field leads to a change of the center-of-mass momentum of the dipole. 2 Laser-based approach to quantum arrival-time distributions 39 Delay: The second effect that causes a difference between Π(t) and ideal distributions is the delay in the photon emission due to the excitation time and the lifetime of the upper level. 77) γ 2 − 4Ω2 . For the mean waiting time follows ∞ tW = dt W (t)t = 0 γ 2 + 2Ω2 . 78) By means of this expression, there are seen useful limits to overcome the delay problem.

86), integrating over x and inserting the result together with Eq. 87) into Eq. 91) ∞ dt eiνt Πid (ν) −∞ ∞ → ν . k−k ∞ dk ψ(k)ψ(k )ei dk 2πm 0 = J(t, x = 0), (k 2 −k 2 )/2m k 0 for γ → ∞. 92) This remarkable result of Ref. [24] relates the operational arrival-time distribution to the quantum mechanical flux for the free wave function ψ(x, t) at x = 0. Thus, the first-photon detection provides an approach to measuring the flux, if a deconvolution is performed afterwards on the experimental data.

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