We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator-normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding "tunneling time" obtained at the transmission side of the barrier becomes independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultra-opaque, classical-like regime dominated by wave packet components above the barrier.
Local and energy-independent complex potentials have been used in the past to phenomenologically simulate the measurements of arrival, traversal or dwell times of a quantum particle. We physically justify these complex potentials with a realistic model of atom detection by fluorescence. As approximate effective interactions in the short lifetime and zero detuning limit, purely imaginary local potentials emerge from exact non-local and energy-dependent complex potentials obtained by Feshbach's partitioning technique. Non-zero laser detunings lead instead to local complex potentials with a real part.
The well-known laser-induced Rabi oscillations of a two-level atom are shown
to be suppressed under certain conditions when the atom is entering a
laser-illuminated region. For temporal Rabi oscillations the effect has two
regimes: classical-like, at intermediate atomic velocities, and quantum at low
velocities, associated respectively with the formation of incoherent or
coherent internal states of the atom in the laser region. In the low velocity
regime the laser projects the atom onto a pure internal state that can be
controlled by detuning. Spatial Rabi oscillations are only suppressed in this
low velocity, quantum regime.Comment: 14 figure
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