  In view of the coherent properties of a large number of atoms, Bose-Einstein
Condensates (BECs) have a high potential for sensing applications. Several
proposals have been put forward to use collective excitations such as phonons
in BECs for quantum enhanced sensing in quantum metrology. However, the
associated highly non-classical states tend to be very vulnerable to
decoherence. In this article, we investigate the effect of decoherence due to
the omnipresent process of three-body loss in BECs. We find strong restrictions
for a wide range of parameters and we discuss possibilities to limit these
restrictions.
