Precision Measurement in Nonlinear Quantum Oscillators: A Quantum Metrology Approach

Abstract

The present research addresses the nonlinear characteristics of the double Morse potential, focusing on its role in quantum systems. It is hypothesized that the asymmetry parameter, α, which governs the skewness of the double-well structure, is a key indicator of the system’s nonlinearity and quantum behavior. Analytical solutions for the bound states and their corresponding energy spectra are obtained, revealing a clear dependence on α. Measures of non-Gaussianity and non-classicality are employed to quantify the system’s nonlinearity, both of which increase with α, supporting the initial hypothesis. A monotonic relationship between these two measures is also established. Furthermore, optimal measurement strategies are presented that enable precise estimation of α by minimizing the associated variance. Potential applications of this model in quantum information processing and computation are discussed, highlighting its promise for future quantum technologies.

Date of Award	2025
Original language	American English
Supervisor	Berihu Teklu Gebrehiwot (Supervisor)