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Physical Review Letters

Quantum Delocalization of a Levitated Nanoparticle

Massimiliano Rossi, Andrei Militaru, N. Carlon Zambon, Andreu Riera-Campeny, Oriol Romero‐Isart, Martin Frimmer, Lukáš Novotný

Published Jun 24, 2025• 29 citations
Publisher

Abstract

Matter waves have been observed in double-slit experiments with microscopic objects, such as atoms or molecules. The wave function describing the motion of these objects must extend over a distance comparable to the slit separation, much larger than the characteristic size of the objects. Preparing such states for more massive objects, such as mechanical oscillators, remains an outstanding challenge. Here we delocalize the quantum ground state of an optically levitated nanosphere by modulating the stiffness of the confining potential. We show a more than threefold increase of the initial coherence length, which corresponds to mechanical momentum squeezing of more than 7 dB. Our work is a stepping stone toward the generation of coherence lengths comparable to the object size, a crucial regime for macroscopic quantum experiments.

DOI
10.1103/2yzc-fsm3

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Matter waves have been observed in double-slit experiments with microscopic objects, such as atoms or molecules. The wave function describing the motion of these objects must extend over a distance comparable to the slit separation, much larger than the characteristic size of the objects. Preparing such states for more massive objects, such as mechanical oscillators, remains an outstanding challenge. Here we delocalize the quantum ground state of an optically levitated nanosphere by modulating the stiffness of the confining potential. We show a more than threefold increase of the initial coherence length, which corresponds to mechanical momentum squeezing of more than 7 dB. Our work is a stepping stone toward the generation of coherence lengths comparable to the object size, a crucial regime for macroscopic quantum experiments.
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.
Abstract 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 [1, 2]. 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 [3]. 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 [4–7]. 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 [8], and towards quantum-enhanced force sensing with levitated particles [9].
We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments.
Quantum mechanics predicts that massive particles exhibit wave-like behavior. Matterwave interferometry has been able to validate such predictions through ground-breaking experiments involving microscopic systems like atoms and molecules. The wavefunction of such systems coherently extends over a distance much larger than their size, an achievement that is incredibly challenging for massive and more complex objects. Yet, reaching similar level of coherent diffusion will enable tests of fundamental physics at the genuinely macroscopic scale, as well as the development of quantum sensing apparata of great sensitivity. We report on experimentally achieving an unprecedented degree of position diffusion in a massive levitated optomechanical system through frequency modulation of the trapping potential. By starting with a pre-cooled state of motion and employing a train of sudden pulses yet of mild modulation depth, we surpass previously attained values of position diffusion in this class of systems to reach diffusion lengths that exceed the physical dimensions of the trapped nanoparticle.
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.
Levitated nanoparticles are a forerunner as an experimental platform to test the limits of quantum mechanics at a macroscopic scale. Some important initial steps have been made towards preparing a macroscopic quantum state of a relatively massive (femtogram) particle. Specifically, the community has achieved ground-state cooling of the center-of-mass motion of a nanoparticle levitated in an optical trap. One crucial further step is now to expand the wavefunction of the particle. This step should happen in the presence of a minimum of decoherence, which makes evolution in an optical trap (inevitably exerting measurement backaction) unsuitable.