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arXiv:2509.17503 · Applied Physics Letters

Free expansion of a charged nanoparticle via electrostatic compensation

David Steiner, Yaakov Y. Fein, Gregor Meier, Stefan Lindner, Paul Juschitz, Mario Arnolfo Ciampini, Markus Aspelmeyer, Nikolai Kiesel

Published Nov 10, 2025• 6 citations
arXivHTMLPDF

Abstract

Coherent wavepacket expansion is a key component of recent proposals aiming to create non-classical states of a levitated dielectric nanoparticle. Free evolution, i.e., releasing the particle from its harmonic trapping potential and allowing its position variance to grow, is a simple but effective expansion scheme, but requires accurate force compensation to avoid significant mean displacements of the wavepacket during the free evolution. Here, using an optical trap–release–recapture sequence, we demonstrate an electrostatic compensation technique that enables free evolution without significant mean displacement in 3D, effectively compensating both gravity and stray electric fields. To achieve 100 μs free evolution times with charged particles, we developed methods to map and correct for force cross-talk, as well as to control the environmental charge state. Combined with a low decoherence environment, our approach enables the preparation of largely delocalized states without the need for long freefall trajectories or a low-gravity environment.

DOI
10.1063/5.0303460

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Coherent wavepacket expansion is a key component of recent proposals aiming to create non-classical states of a levitated dielectric nanoparticle. Free evolution, i.e., releasing the particle from its harmonic trapping potential and allowing its position variance to grow, is a simple but effective expansion scheme, but requires accurate force compensation to avoid significant mean displacements of the wavepacket during the free evolution. Here, using an optical trap–release–recapture sequence, we demonstrate an electrostatic compensation technique that enables free evolution without significant mean displacement in 3D, effectively compensating both gravity and stray electric fields. To achieve 100 μs free evolution times with charged particles, we developed methods to map and correct for force cross-talk, as well as to control the environmental charge state. Combined with a low decoherence environment, our approach enables the preparation of largely delocalized states without the need for long freefall trajectories or a low-gravity environment.
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We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality and, during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to 0.25 ms and observe a nearly two hundred-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in ultra-high vacuum, opening new opportunities for generating large delocalizations of levitated objects.
We perform free-fall experiments with a charge-neutral, optically levitated nanoparticle. This is achieved using an optical tweezer that can be rapidly toggled on and off and vertically displaced, enabling the particle to be released and recaptured after each free fall. The particle is insensitive to electric fields due to its charge neutrality and, during free evolution, is not subject to photon recoil heating. We achieve free-fall durations of up to 0.25 ms and observe a nearly two hundred-fold increase in the particle's position uncertainty at recapture. The current limit on the free-fall time arises from the performance of the initial cooling step. By implementing linear feedback techniques and reducing the background pressure, we expect to perform millisecond-scale free-fall experiments in ultra-high vacuum, opening new opportunities for generating large delocalizations of levitated objects.
Realizing quantum superpositions of massive objects provides a pathway to explore the quantum-to-classical transition. Levitated nanoparticles appear as a promising platform for this purpose due to their large mass and unbound motion. This thesis follows the proposal that particle evolution in a double-well potential expands the particle’s motional state within an inverted harmonic region, while the quartic potential generates the non-Gaussian states needed to certify quantum delocalization. As this protocol has been recently developed, we perform experiments in the classical regime as an important milestone to identify the technical challenges and the decoherence sources. While the nanoparticle’s motional state grows linearly under free evolution, inverted harmonic potentials offer exponentially accelerated state expansion. In this thesis, we experimentally demonstrate the expansion of the center-of-mass state of a 125 nm silica nanoparticle from an initial position uncertainty of 45.6 pm to 43.4 nm within 260 μs. This expansion represents a 952-fold increase, reaching a state size comparable to the particle’s radius, and is achieved by employing an electrostatic inverted potential to disable decoherence from photon recoil. The incoherent dynamics allow us to estimate the remaining decoherence sources in the dark. To accomplish dark dynamics, we developed two segmented linear Paul trap devices providing 2D confinement while generating DC potentials in the third axis of motion: a planar micro-fabricated chip and a PCB based wheel trap. Simulations of tunable double-well potentials of tens to hundreds of micrometers based on the device layouts are performed alongside a study of the resulting classical non-Gaussian states. This work marks a key advancement in the effort to generate macroscopic quantum superpositions at unprecedented mass and length scales.
Levitated nanoparticles in vacuum are prime candidates for generating macroscopic quantum superposition states of massive objects. Most protocols for preparing these states necessitate coherent expansion beyond the scale of the zero-point motion to produce sufficiently delocalized and pure phase-space distributions. Here, we spatially expand and subsequently recontract the thermal state of a levitated nanoparticle by modifying the stiffness of the trap holding the particle. We achieve state-expansion factors of 25 in standard deviation for a particle initially feedback-cooled to a center-of-mass thermal state of \SI{155}{\milli\kelvin}. Our method relies on a hybrid scheme combining an optical trap, for cooling and measuring the particle's motion, with a Paul trap for expanding its state. Consequently, state expansion occurs devoid of measurement backaction from photon recoil, making this approach suitable for coherent wavefunction expansion in future experiments.
We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 10 8 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10 −10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.