Abstract
We present a comprehensive numerical simulation of an echo-type atom interferometer. The simulation confirms a new theoretical description of this interferometer that includes effects due to spontaneous emission and magnetic sub-levels. Both the simulation and the theoretical model agree with the results of experiments. These developments provide an improved understanding of several observable effects. The evolution of state populations due to stimulated emission and absorption during the standing wave interaction imparts a time-dependent phase on each atomic momentum state. This manifests itself as an asymmetry in the signal shape that depends on the strength of the interaction as well as spontaneous emission due to a non-zero population in the excited states. The degree of asymmetry is a measure of a non-zero relative phase between interfering momentum states.
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