# Optimal atomic interferometry robust to detection noise using spin-1 atomic condensates

## TL;DR

This paper identifies optimal configurations for spin-1 atomic Bose-Einstein condensate interferometry that maximize quantum Fisher information and are robust against detection noise, enabling Heisenberg scaling with current experimental methods.

## Contribution

It introduces a novel optimal interferometric configuration for spin-1 condensates, including an interaction-based readout protocol and dynamic inversion method, enhancing robustness and scalability.

## Key findings

- Three optimal configurations identified, one novel with highest quantum Fisher information.
- The proposed protocol achieves Heisenberg scaling with present-day techniques.
- Enhanced robustness against detection noise demonstrated through error-propagation analysis.

## Abstract

Implementation of the quantum interferometry concept to spin-1 atomic Bose-Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the quantum Fisher information in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the interaction-based readout protocol to reduce the destructive effect of detection noise. In order to obtain Heisenberg scaling accessible by present day experimental techniques, an efficient measurement and a method for the inversion of dynamics were developed, as necessary for the protocol's implementation.