Exact and approximate complex potentials for modelling time observables

¹ Departamento de Química-Física, Universidad del País Vasco Apdo. 644, 48080 Bilbao, Spain
² Institut für Theoretische Physik, Universität Göttingen Tammanstrasse 1, 37077 Göttingen, Germany

Received: 5 January 2004
Accepted: 3 May 2004

Abstract

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.