Nonlinearity and quantum metrology in the double-Morse potential

We address the nonlinear properties of the double-Morse potential as a resource for single-mode quantum states due to its double-well structure and anharmonicity. We obtain analytical expressions for the ground-state wavefunction and the corresponding ground-state energy, using the asymmetry (width) parameter α as the primary control parameter. We then assess non-Gaussianity and nonclassicality as quantitative signatures of nonlinearity and quantumness, and we find that both increase monotonically with α . Furthermore, we analyze the metrological performance of the model for estimating the structural parameter α . By evaluating the corresponding Fisher information, we show that position measurements are optimal and can saturate the Cramér–Rao bound. In particular, the estimation of α is most precise in the shallow-well regime, where the quantum Fisher information is largest. For deep wells, enhanced sensitivity is instead obtained for the reparameterized control variable \(A=2e^{-\alpha x_{0}}\) , provided that \(x_{0}\) is independently calibrated. These results establish the double-Morse potential as a controllable source of non-Gaussianity and nonclassicality, with a metrological behavior that depends on the chosen estimation parameter. We highlight possible applications of this model in quantum sensing, continuous-variable quantum information, and quantum simulation.