Self-consistent many-body metrology

TL;DR

This paper explores how a self-consistent many-body approach to interacting bosons in a double-well setup impacts quantum metrology, revealing that dynamic orbitals significantly influence measurement precision and estimation accuracy.

Contribution

It introduces a self-consistent multiconfigurational Hartree method for analyzing quantum metrology with interacting bosons, highlighting the importance of orbital dynamics.

Findings

Dynamic orbitals affect Fisher information and estimators.

Self-consistent dynamics alter achievable measurement precision.

Traditional fixed-orbital models may underestimate metrological capabilities.

Abstract

We investigate performing classical and quantum metrology and parameter estimation by using 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.