Nonclassical Resources 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 inverse barrier-width parameter $\alpha$ 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 $\alpha$. Furthermore, we analyze the metrological performance of the model for estimating the inverse barrier-width parameter $\alpha$. By evaluating the corresponding Fisher information, we show that position measurements are optimal and can saturate the Cram\'er-Rao bound. In particular, the estimation of $\alpha$ 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.