Precision bounds for frequency estimation under collective dephasing and dynamical decoupling

Parallel, dephasing, noise is an ubiquitous source of decoherence in current atomic sensors. In this work, we derive rigorous, state-independent bounds to precision in the context of frequency estimation subject to collective dephasing. We find that no scaling gains over the noiseless classical limit are allowed for temporally uncorrelated noise, as well as for colored noise with a rapidly decaying spectrum. Furthermore, we prove that when the fluctuations are stemming from a classical noise source, application of instantaneous pulsed dynamical decoupling is unable to improve asymptotic scaling of precision. However, superclassical asymptotic performance may be reached when the relevant phase fluctuations have a smoothly decaying high-frequency tail. We show how to saturate these bounds with squeezed input states and non-linear readouts, which are available in state-of-the-art atomic interferometers. Interestingly, the optimal noiseless protocol, which requires a pre-measurement anti squeezing echo, remains best possible regardless of the noise correlations.