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

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.

Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert–Schmidt Speed-Based Witness

“…Recently, Hilbert-Schmidt speed (HSS) [60], a measure of quantum statistical speed which has the advantage of avoiding diagonalization of the evolved density matrix, has been proposed and employed as a faithful witness of non-Markovianity in Hermitian systems [61][62][63][64] and an efficient tool in quantum metrology [65,66]. These studies are so far especially limited to low-dimensional systems, while high-dimensional ones have not been investigated in detail.…”