In this paper, we investigate the nonlinear properties of the double-Morse potential as a possible resource for single-mode quantum states because of its double-well structure and anharmonicity. We derive the ground state wave function and the associated energy spectrum analytically, using the asymmetry (width parameter) $\alpha$ as the primary control parameter. These results show a systematic and evident influence on $\alpha$. We assess the non-Gaussianity and non-classicality measures, quantifying their nonlinearity and quantum behavior. In particular, we discover that both metrics rise monotonically with $\alpha$. Furthermore, we examine the metrological performance for estimating $\alpha$. By calculating the pertinent Fisher information and building workable estimators, we show that optimal strategies can saturate the Cram\'er-Rao bound, with straightforward position measurements on shallow wells already producing high precision. These results collectively demonstrate that the double-Morse potential is a genuine, controllable source of non-Gaussianity, whose non-classicality and metrological applications increase with $\alpha$. We highlight the potential applications of this model in real-world quantum technologies and discuss the implications for continuous-variable quantum information processing and computation.
Categories: quant-ph