Quantum Non-Gaussian State Preparation of Levitated Particles via Time-Dependent Control of Weakly Nonharmonic Hybrid Potentials

Levitated high-mass quantum systems provide access to unprecedented regimes in both fundamental science and technological applications. However, deterministic generation and manipulation of quantum non-Gaussian states, which are central to many continuous-variable quantum advantages, remain elusive in such platforms. In this work, we propose a theoretical protocol for preparing a continuous-variable degree of freedom of a levitated massive object in a variety of quantum states, including Fock and Schrödinger cat states, without coupling to auxiliary two-level systems. Our approach enhances otherwise weak nonharmonic effects by transient wave-function delocalization and combines this with optimal control of the potential. Specifically, time-dependent modulation of the linear component of the potential, in the presence of a static cubic nonharmonicity, provides a route to universal control of the mode. We analyze quantum state preparation under such control and estimate the required nonharmonicity, motional delocalization, and maximum tolerable decoherence for generating target non-Gaussian states. The proposed optimal-control scheme can also be readily extended beyond single-particle state preparation, for example, to unitary transformations and nonlinear measurements. As a concrete example, we demonstrate mechanical Bell-state preparation for two interacting particles using only local modulation of weakly nonharmonic potentials, while the interparticle interaction remains effectively linear. We emphasize that the protocols presented here apply to different mechanical degrees of freedom, such as center-of-mass motion and libration, and can also be implemented in other weakly nonharmonic systems with a leading cubic nonharmonicity.