Optimal quantum phase estimation in an atomic gyroscope based on Bose-Hubbard model

TL;DR

This paper identifies the optimal quantum state for an atomic gyroscope modeled by the Bose-Hubbard framework, demonstrating that entangled even squeezed states improve phase estimation precision under certain loss conditions.

Contribution

It introduces a Hermitian operator and an equivalent unitary transformation to compute quantum Fisher information for any initial state, enabling the identification of the optimal probe state.

Findings

Entangled even squeezed state enhances phase estimation accuracy.

The method applies to both lossless and lossy conditions.

Optimal states depend on loss rates and system parameters.

Abstract

We investigate the optimal quantum state for an atomic gyroscope based on a three-site Bose-Hubbard model. In previous studies, various states such as the uncorrelated state, the BAT state and the NOON state are employed as the probe states to estimate the phase uncertainty. In this article, we present a Hermitian operator $\mathcal{H}$ and an equivalent unitary parametrization transformation to calculate the quantum Fisher information for any initial states. Exploiting this equivalent unitary parametrization transformation, we can seek the optimal state which gives the maximal quantum Fisher information on both lossless and lossy conditions. As a result, we find that the entangled even squeezed state (EESS) can significantly enhance the precision for moderate loss rates.