  An ensemble density matrix model that includes one- and two-body losses is
derived for a trapped-atom clock. A trapped-atom clock is mainly affected by
one- and two-body losses, generally giving nonexponential decays of
populations; nevertheless, three-body recombination is also quantitatively
analyzed to demonstrate the boundaries of its practical relevance. The
importance of one-body losses is highlighted without which population trapping
behavior would be observed. The model is written with decay constants expressed
through experimental parameters. It can complement, e.g., the ISRE (identical
spin rotation effect) model to improve its predictions: ISRE dramatically
increases the ensemble coherence time, hence it enables one to observe the
influence of two-body losses on the interferometry contrast envelope. The
presented model is useful for Ramsey interferometry and is ready for immediate
experimental verification in existing systems.
