Many-body effects in quantum metrology

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 nonlinear Hamiltonians, studied in the field of nonlinear 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 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.