We study a variational class of generalized Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimize 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 one-axis twisted input state, can be saturated within our class of variational protocols for almost all initial twisting 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.

• Received 19 July 2023
• Revised 6 October 2023
• Accepted 1 November 2023

DOI:https://doi.org/10.1103/PhysRevA.108.062611

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Published by the American Physical Society