Exact and approximate complex potentials for modelling time observables

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.