Adiabatic quantum metrology with strongly correlated quantum optical systems

We show that the quasiadiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, which leads to the collapse of the wave function into one of two possible ground states. The scaling of the final-state properties with the number of atoms and with the intensity of the symmetry-breaking field can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.