Optimal Ramsey interferometry with echo protocols based on one-axis twisting

TL;DR

This paper develops a unified variational framework for Ramsey protocols using one-axis twisting, optimizing measurement axes and interactions to maximize quantum Fisher information and approach fundamental sensitivity limits.

Contribution

It introduces a comprehensive variational class of Ramsey protocols with two OAT operations, unifying and optimizing existing echo protocols for enhanced quantum measurement sensitivity.

Findings

Quantum Fisher information can be saturated for most initial twist strengths.

The framework unifies various previously documented Ramsey echo protocols.

Optimized protocols approach fundamental sensitivity limits.

Abstract

We study a variational class of generalised Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimise the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given uniaxially twisted input state, can be saturated within our class of variational protocols for almost all initial twist strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.