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We demonstrate that the ambiguity of the particle content for quantum fieldsin a generally curved space-time can be experimentally investigated in anultracold gas of atoms forming a Bose-Einstein condensate. We explicitlyevaluate the response of a suitable condensed matter detector, an ``AtomicQuantum Dot,'' which can be tuned to measure time intervals associated todifferent effective acoustic space-times. It is found that the detectorresponse related to laboratory, ``adiabatic,'' and de Sitter time intervals isfinite in time and nonstationary, vanishing, and thermal, respectively.Comment: 9 pages, 2 figures; references updated, as published in Physical  Review

Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate