Many-body effects in quantum metrology

TL;DR

This paper investigates how many-body effects influence the fundamental limits of precision in quantum metrology, considering non-linear Hamiltonians and decoherence, with applications to atomic interferometry and BEC magnetometry.

Contribution

It provides a general framework for predicting precision scaling in many-body quantum systems and introduces an efficient method for deriving quantitative bounds.

Findings

Fundamental precision bounds depend on many-body interactions and decoherence.

Two-body losses significantly impact achievable measurement precision.

Atom number super-selection rules affect decoherence protection strategies.

Abstract

We study the impact of many-body effects on the fundamental precision limits in quantum metrology. On the one hand such effects may lead to non-linear Hamiltonians, studied in the field of non-linear quantum metrology, while on the other hand they may result in decoherence processes that cannot be described using single-body noise models. We provide a general reasoning that allows to predict the fundamental scaling of precision in such models as a function of the number of atoms present in the system. Moreover, we describe a computationally efficient approach that allows for a simple derivation of quantitative bounds. We illustrate these general considerations by a detailed analysis of fundamental precision bounds in a paradigmatic atomic interferometry experiment with standard linear Hamiltonian but with both single and two-body losses taken into account---a model which is motivated by the most recent Bose-Einstein Condensate (BEC) magnetometry experiments. Using this example we also highlight the impact of the atom number super-selection rule on the possibility of protecting interferometric protocols against decoherence.