Saturation of the Cram\'er-Rao Bound for the Atomic Resonance Frequency with Phased Array of Hyperbolic Secant Pulses

TL;DR

This paper analyzes the fundamental precision limits of atomic resonance frequency estimation using hyperbolic secant pulses, demonstrating that phase-alternating pulse sequences can achieve the quantum Cramér-Rao bound, thus optimizing measurement accuracy.

Contribution

It provides a theoretical analysis of the quantum Fisher information for resonance experiments with hyperbolic secant pulses and shows how to reach the ultimate precision limit.

Findings

Sequences of alternating-phase pulses saturate the quantum Cramér-Rao bound.

The fundamental limit of precision is set by the quantum Fisher information.

Resonance frequency estimation can be optimized using specific pulse sequences.

Abstract

Precise estimation of the atomic resonance frequency is fundamental for the characterization and control of quantum systems. The resonance experiment is a standard method for this measurement, wherein the drive field frequency is swept to invert the system population. We analyze the classical and quantum Fisher information for the resonance experiment driven by hyperbolic secant shaped $\pi$-pulses; setting a fundamental limit on the precision obtainable using the resonance method. We show that measurements using sequences of pulses with alternating phases globally saturates the quantum Cram\'er-Rao bound, achieving the theoretical limit of precision for atomic resonance frequency estimation.