The authors claim that sequences of 2N+1 hyperbolic secant pi-pulses with alternating phases saturate the quantum Cramér-Rao bound for atomic resonance frequency estimation at every detuning.
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Saturation of the Cram\'er-Rao Bound for the Atomic Resonance Frequency with Phased Array of Hyperbolic Secant Pulses
The authors claim that sequences of 2N+1 hyperbolic secant pi-pulses with alternating phases saturate the quantum Cramér-Rao bound for atomic resonance frequency estimation at every detuning.