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

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