Weakly invasive metrology: quantum advantage and physical implementations

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons N_abs are absorbed, for a total time T. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with N_abs and T, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of N_abs and T, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.