Extended Data Fig. 2: Limits in multi-ensemble metrology.
From: Multi-ensemble metrology by programming local rotations with atom movements
a, Asymptotic scaling of the extended interrogation time factor as a function of the number of ensembles M employed. We numerically calculate the maximal interrogation time at a fixed phase slip probability for different dynamical decoupling block lengths τ, in terms of the local-oscillator coherence time TLO, assuming 1/f frequency noise and infinite atom number. The addition of more ensembles enables exponential scaling of the maximal interrogation time (solid line marks 2M−1) up to a saturation point set by the effective decoupling bandwidth. The latter can be extended by reducing the block length while maintaining a sufficiently high Rabi frequency with respect to the fast noise frequency. b, For the optimal decoupling sequence found in a, we plot the extended interrogation time as a function of the number of atoms per ensemble N. For a small number of atoms per ensemble, quantum projection noise results in an enhanced rate of false positive indication of a phase slip, negating any advantage. We find that N ≃ 20 atoms per ensemble suffice for efficient operation.
