Coherence lifetimes of excitations in an atomic condensate due to the thin spectrum

We study the quantum coherence properties of a finite sized atomic condensate using a toy model and the thin spectrum model formalism. The decoherence time for a condensate in the ground state, nominally taken as a variational symmetry breaking state, is investigated for both zero and finite temperatures. We also consider the lifetimes for Bogoliubov quasiparticle excitations, and contrast them to the observable window determined by the ground-state coherence time. The lifetimes are shown to exhibit a general characteristic dependence on the temperature, determined by the thin spectrum accompanying the spontaneous symmetry breaking ground state.