Ramsey interferometry with generalized one-axis twisting echoes

TL;DR

This paper analyzes and optimizes Ramsey interferometry protocols enhanced by squeezing and un-squeezing operations, revealing a new protocol with Heisenberg scaling under dephasing.

Contribution

It provides an analytical optimization framework for squeezing echo protocols and introduces a novel over-un-twisting protocol with superior sensitivity.

Findings

Optimal squeezing and un-squeezing parameters derived for various particle numbers.

Recovery of known quantum metrological protocols as optimal cases.

Discovery of a new over-un-twisting protocol with Heisenberg scaling under dephasing.

Abstract

We consider a large class of Ramsey interferometry protocols which are enhanced by squeezing and un-squeezing operations before and after a phase signal is imprinted on the collective spin of $N$ particles. We report an analytical optimization for any given particle number and strengths of (un-)squeezing. These results can be applied even when experimentally relevant decoherence processes during the squeezing and un-squeezing interactions are included. Noise between the two interactions is however not considered in this work. This provides a generalized characterization of squeezing echo protocols, recovering a number of known quantum metrological protocols as local sensitivity maxima, thereby proving their optimality. We discover a single new protocol. Its sensitivity enhancement relies on a double inversion of squeezing. In the general class of echo protocols, the newly found over-un-twisting protocol is singled out due to its Heisenberg scaling even at strong collective dephasing.