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Physical Review Letters

State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential

Eric Bonvin, Louisiane Devaud, Massimiliano Rossi, Andrei Militaru, Lorenzo Dania, Dmitry S. Bykov, Oriol Romero‐Isart, Tracy E. Northup, Lukáš Novotný, Martin Frimmer

Published Jun 21, 2024• 26 citations
Publisher

Abstract

We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.

DOI
10.1103/physrevlett.132.253602

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We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.
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.
While the wave packet of a massive particle grows linearly under free dynamics, it grows exponentially in an inverted harmonic potential, offering a pathway to rapidly increase quantum fluctuations to macroscopic dimensions. In this work, we experimentally demonstrate this principle by expanding the center-of-mass thermal state of a 125 n m silica nanoparticle to a position uncertainty of 43.4 n m within 260 µ s . This expansion, achieved using an inverted dark potential to minimize decoherence from photon recoil, represents a 952-fold increase, reaching a scale comparable to the nanoparticle's physical size. This work represents a key advancement toward preparing macroscopic quantum superpositions at unprecedented mass and length scales.
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 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.
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.
Abstract Optically levitated particles with that have their thermal motion suppressed / cooled down close to the quantum ground state promise to become a the key for upcoming quantum technology of macroscopic systems, such as ultra-precise nano-metrology. In order to employ such a quantum state in subsequent interactions with spatially varying light intensity profiles the particle state must be extended - amplified - to the dimensions comparable to the wavelength. Such an amplification may be achieved by the a precisely timed sequence of evolution in the trapping potential (rotation) and evolution in a stroboscopically changed potential. Here, we experimentally demonstrate the function of the nano-mechanical amplifier based on the nearly free expansion or the inverted unstable potential.