Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes

TL;DR

This paper applies quantum metrology techniques to estimate the energy levels of a three-level quantum system, introducing the Hilbert-Schmidt speed as an efficient figure of merit for spectral estimation.

Contribution

It presents a novel application of quantum metrology to energy level estimation in three-level systems and introduces the Hilbert-Schmidt speed as a practical, high-dimensional compatible measure.

Findings

Simultaneous estimation outperforms independent estimation in various scenarios.

Hilbert-Schmidt speed effectively enhances energy spectrum estimation.

HSS is computationally efficient without requiring state diagonalization.

Abstract

Determining the energy levels of a quantum system is a significant task, for instance, to analyze reaction rates in drug discovery and catalysis or characterize the compatibility of materials. In this paper we exploit quantum metrology, the research field focusing on the estimation of unknown parameters exploiting quantum resources, to address this problem for a three-level system interacting with laser fields. The performance of simultaneous estimation of the levels compared to independent one is also investigated in various scenarios. Moreover, we introduce, the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, as a powerful figure of merit for enhancing estimation of energy spectrum. This measure is easily computable, because it does not require diagonalization of the system state, verifying its efficiency in high-dimensional systems.