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arXiv:2606.10042

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

Piotr T. Grochowski, Oriol Romero-Isart

quant-phSubmitted Jun 8, 2026• Announced Jun 10, 2026• 0 citations

Abstract

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.

Comments: 20 pages, 8 figures

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We present a theoretical proposal for preparing and manipulating a state of a single continuous-variable degree of freedom confined to a nonharmonic potential. By utilizing optimally controlled modulation of the potential's position and depth, we demonstrate the generation of non-Gaussian states, including Fock, Gottesman-Kitaev-Preskill, multi-legged-cat, and cubic-phase states, as well as the implementation of arbitrary unitaries within a selected two-level subspace. Additionally, we propose protocols for single-shot orthogonal state discrimination, algorithmic cooling, and correcting for nonlinear evolution. We analyze the robustness of this control scheme against noise. Since all the presented protocols rely solely on the precise modulation of the effective nonharmonic potential landscape, they are relevant to several experiments with continuous-variable systems, including the motion of a single particle in an optical tweezer or lattice, or current in circuit quantum electrodynamics.

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Levitated nanoparticles provide a controllable and isolated platform for probing fundamental quantum phenomena at the macroscopic scale. In this work we introduce an optimization method to determine optimal static potentials for the generation of largely delocalized and non-Gaussian quantum states of levitated nanoparticles. Our optimization strategy accounts for position-dependent noise sources originating from the fluctuations of the potential. We provide key figures of merit that allow for fast computation and capture relevant features of the dynamics, mitigating the computational demands associated with the multiscale simulation of this system. Specifically, we introduce coherence length and coherent cubicity as signatures of large delocalization and quantum non-Gaussian states, respectively. As a proof of principle, we apply the optimization approach to a family of quartic potentials and show that the optimal configuration depends on the strength and nature of the noise in the system. Additionally, we benchmark our results with a full quantum dynamics simulations of the system for the optimal potentials.

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Optomechanics with levitated nanoparticles is a promising way to combine very different types of quantum non-Gaussian aspects induced by continuous dynamics in a nonlinear or time-varying potential with the ones coming from discrete quantum elements in dynamics or measurement. First, it is necessary to prepare quantum non-Gaussian states using both methods. The nonlinear and time-varying potentials have been widely analyzed for this purpose. However, feasible preparation of provably quantum non-Gaussian states in a single mechanical mode using discrete photon detection has not been proposed yet for optical levitation. We explore pulsed optomechanical interactions combined with non-linear photon detection techniques to approach mechanical Fock states and confirm their quantum non-Gaussianity. We also predict the conditions under which the optomechanical interaction can induce multiple-phonon addition processes, which are relevant for

n

-phonon quantum non-Gaussianity. The practical applicability of quantum non-Gaussian states for sensing phase-randomized displacements is shown. Besides such applications, generating quantum non-Gaussian states of levitated nanoparticles can help to study fundamental questions of quantum thermodynamics, and macroscopic quantum effects.