Self-Consistent Many-Body Metrology

We investigate the classical and quantum metrology of performing parameter estimation with interacting trapped bosons, which we theoretically treat by a self -consistent many -body approach of the multiconfigurational Hartree type. Focusing on a tilted double -well geometry, we compare a self -consistently determined and monitored two -mode truncation, with dynamically changing orbitals, to the conventional two -mode approach of fixed orbitals, where only Fock space coefficients evolve in time. We demonstrate that, as a consequence, various metrological quantities associated to a concrete measurement such as the classical Fisher information and the maximum likelihood estimator are deeply affected by the orbitals ' change during the quantum evolution. Self -consistency of the quantum many -body dynamics of interacting trapped ultracold gases thus fundamentally affects the attainable parameter estimation accuracy of a given metrological protocol.