Nonclassical State Generation and Quantum Metrology in the Double-Morse Potential

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.