FIG. 3.

The lower bound on the quantum Fisher information per atom versus ρ with (a) increasing percentages of single-sided seeding into m = −1, and with (b) double-sided 0.1% seeding at various initial phases. The solid black line is $f_{\text{Bog,Q}}=(\mathcal{N}+2)$, which is the prediction for the unseeded case (open circles). The grey shading indicates the region of Fisher information per atom that does not reach standard quantum limit f_SQL = 1 (based on $\mathcal{N}$ atoms in the interferometer arms). The dashed line corresponds to F_Q = N (or f_Q = 1/ρ), which is the limit achievable using coherent states in a Mach-Zehnder interferometer having a total of N particles. The phases of the separatrix are θ_sep = ±2.86 rad.