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

Abstract

Finding the energy levels of a quantum system is a significant task, for instance, to characterize the compatibility of materials or to analyze reaction rates in drug discovery and catalysis. In this paper we investigate quantum metrology, the research field focusing on the estimation of unknown parameters investigating 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 studied in various scenarios. Moreover, we introduce the Hilbert-Schmidt speed (HSS), a mathematical tool, as a powerful figure of merit for enhancing the estimation of the energy spectrum. This measure can be easily computed, since it does not require diagonalizing the density matrix of the system, verifying its efficiency to enhance quantum estimation in high-dimensional systems.