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

TL;DR

We address how a tunable double-Morse potential can generate non-Gaussian, nonclassical states suitable for quantum metrology. By solving the ground state analytically and quantifying nonlinearity via the Bures distance and non-Gaussianity, e.g., $\eta_{NG}$, as well as Wigner negativity and entanglement potential, and applying local quantum estimation theory to derive the quantum Fisher information $\mathcal{F}(\alpha)$, we show position measurements saturate the quantum Cramér–Rao bound. The main findings are that the ground state becomes more non-Gaussian and nonclassical with width $\alpha$, while $\mathcal{F}(\alpha)$ decreases with $\alpha$ and the entanglement potential increases, implying high-precision sensing in shallow wells. This work provides a tunable platform for continuous-variable quantum information processing and molecular-scale sensing, enabling non-Gaussian resource generation and efficient parameter estimation.

Abstract

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) $α$ as the primary control parameter. These results show a systematic and evident influence on $α$. 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 $α$. Furthermore, we examine the metrological performance for estimating $α$. By calculating the pertinent Fisher information and building workable estimators, we show that optimal strategies can saturate the Cramér-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 $α$. 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.

Figures (8)

• Figure 1: Double Morse potential profiles for various values of $\alpha$.
• Figure 2: Ground-state probability density $|\psi_0(x)|^2$ of the double-Morse oscillator for several values of $\alpha$. Increasing $\alpha$ narrows the distribution in $x$ and enhances localization at the well minima.
• Figure 3: Non-Gaussianity measure as a function of $\alpha$ for values of $x_0 = 1,2$ and $3$. The dashed black line is $\eta_{\text{NG}[V]} \approx 0.0615$.
• Figure 4: (Color online) Ground-state Wigner distribution $W_0(x,p)$ for $\alpha=5$ and $x_0=1$. Surface height equals $W_0(x,p)$; red (blue) shading indicates positive (negative) values. Axes are dimensionless and $W_0$ is normalized so that $\iint W_0\,\mathrm{d}x\,\mathrm{d}p=1$. The appearance of negative-valued regions provides a direct signature of nonclassicality for a pure state. For animations of the Wigner function, see https://github.com/firozchogle/Wigner_animation/blob/main/Wigner_dist_animation.gif.
• Figure 5: Nonclassicality measure $\eta_{\mathrm{NC}}$ as a function of $\alpha$ for the ground state with $x_0=1,2,3$. The dashed line marks $\eta_{\mathrm{NC}}\approx 0.009$.