  We theoretically investigate the possibility of performing high precision
estimation of an externally imposed acceleration using scalar bosons in a
single-well trap. We work at the level of a two-mode truncation, valid for weak
to intermediate two-body interaction couplings.The splitting process into two
modes is in our model entirely caused by the interaction between the
constituent bosons and is hence neither due to an externally imposed
double-well potential nor due to populating a spinor degree of freedom. The
precision enhancement gained by using various initial quantum states using a
two-mode bosonic system is well established. Here we therefore instead focus on
the effect of the intrinsic dynamics on the precision, where, in a single well,
the Hamiltonian assumes a form different from that of the typical double-well
case. We demonstrate how interactions can significantly increase the quantum
Fisher information maximized over initial states as well as the quantum Fisher
information for a fragmented or a coherent state, the two many-body states that
can commonly represent the ground state of our system.
