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arXiv:2509.13398 · Nature Physics

Quantum ground-state cooling of two librational modes of a nanorotor

Stephan Troyer, Florian Fechtel, Lorenz Hummer, Henning Rudolph, Benjamin A. Stickler, Uroš Delić, Markus Arndt

Published Apr 1, 2026• 5 citations
arXivHTMLPDF

Abstract

Abstract Controlling the motion of nanoscale objects at the quantum limit promises opportunities to test fundamental quantum physics and advances in quantum sensing. Rotational motion is of particular interest, as its nonlinear dynamics in a compact, closed configuration space provides access to phenomena such as rotational interferometry, tunnelling between angular configurations and quantum-enhanced torque sensing. A key requirement for such experiments is the capability to trap nanorotors and cool their orientation close to the two-dimensional librational quantum ground state. When rotational motion is confined in a harmonic potential, it becomes librational. Here we demonstrate that coherent scattering into a high-finesse cavity enables the ground-state cooling of two orthogonal librational modes of an optically levitated SiO 2 nanoparticle. Using a laser-induced desorption loading technique, we trap and cool several dimers and trimers of silica nanospheres to their respective ground states, all within a single day. The simultaneous cooling of both librational degrees of freedom allows us to align an individual nanorotor with respect to a space-fixed axis with an angular precision better than 20 µrad—close to the quantum-mechanical zero-point fluctuations.

DOI
10.1038/s41567-026-03219-1

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Ground-state cooling is a prerequisite for exploring macroscopic quantum effects in mechanical motion of massive objects. Here we construct a polarization-angle-controllable coupled cavity-levitated-nanoparticle system in which two nanoparticles trapped by individual tweezers are coupled to a single-mode field in a cavity. We also study the simultaneous ground-state cooling of six mechanical displacement modes of the two levitated nanoparticles through the coherent scattering mechanism. By deriving the Hamiltonian of the system and performing the linearization, we obtain a linearized seven-mode Hamiltonian, which can exhibit the coupling structure and cooling mechanism. We confirm the physical condition for the appearance of dark modes, which will suppress the simultaneous ground-state cooling of these mechanical modes. We also find that, by properly tuning the polarization angle θθθ between the cavity field and the optical tweezer fields, the coupling channels can be controlled on demand and simultaneous ground-state cooling of these six motional modes of the two nanoparticles can be realized. Our work paves the way for generation and manipulation of collective macroscopic quantum effects in multiple levitated nanoparticles.
Abstract Optically levitated nanoparticles emerged as an interesting platform for probing fundamental physics. Quantum control of their motion (including potential shaping) predisposes them for emulating various physical systems and studying quantum phenomena with massive objects. Extending these capabilities to quantum many-body systems requires feasible strategies to couple and entangle nanoparticles directly or via an optical bus. We propose a variable, deterministic scheme to generate Gaussian entanglement in the motional steady state of levitated nanoparticles using coherent scattering. Coupling multiple nanoparticles to a common cavity mode allows cooling of a collective Bogoliubov mode; cooling multiple Bogoliubov modes (by trapping each nanoparticle in multiple tweezers, each scattering into a separate cavity mode) removes most thermal noise, leading to strong entanglement. Numerical simulations for three nanoparticles show great tuneability of entanglement with realistic experimental parameters. Our proposal paves the way towards complex motional quantum states for advanced quantum sensing protocols and many-body quantum simulations.
A nanoparticle trapped and cooled Cooling massive particles to the quantum ground state allows fundamental tests of quantum mechanics to be made; it would provide an experimental probe of the boundary between the classical and quantum worlds. Delić et al. laser-cooled an optically trapped solid-state object (a ∼150-nanometer-diameter silic a nanoparticle) into its quantum ground state of motion starting from room temperature. Because the object is levitated using optical forces, the experimental configuration can be switched to free fall, thereby providing a test bed for several macroscopic quantum experiments. Science , this issue p. 892
Every massive particle behaves like a wave, according to quantum physics. Yet, this characteristic wave nature has only been observed in double-slit experiments with microscopic systems, such as atoms and molecules. The key aspect is that the wavefunction describing the motion of these systems extends coherently over a distance comparable to the slit separation, much larger than the size of the system itself. Preparing these states of more massive and complex objects remains an outstanding challenge. While the motion of solid-state oscillators can now be controlled at the level of single quanta, their coherence length remains comparable to the zero-point motion, limited to subatomic distances. Here, we prepare a delocalized state of a levitating solid-state nanosphere with coherence length exceeding the zero-point motion. We first cool its motion to the ground state. Then, by modulating the stiffness of the confinement potential, we achieve more than a threefold increment of the initial coherence length with minimal added noise. Optical levitation gives us the necessary control over the confinement that other mechanical platforms lack. Our work is a stepping stone towards the generation of delocalization scales comparable to the object size, a crucial regime for macroscopic quantum experiments, and towards quantum-enhanced force sensing with levitated particles.