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Three-Dimensional and Selective Displacement Sensing of a Levitated Nanoparticle via Spatial Mode Decomposition

Cyril Laplane, Thomas Dinter, Reece P. Roberts, Thomas Volz, Mikołaj K. Schmidt

Published Apr 1, 2026• 0 citations
Publisher

Abstract

We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.

DOI
10.1364/opticaopen.31898278

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We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scat tered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥tot , 𝜂𝑦tot , 𝜂𝑧tot ) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of 1.7×10^{-12} m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.
Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic and atomic scales. These systems scatter photons in almost every direction, and, with generally limited light collection efficiency, only partial information about the state of the system can be extracted. In this article, we present a setup to enhance information extraction of optomechanical measurements by constraining light scattering to a specific spatial direction. The setup consists of a hollow hemispherical mirror that controls the light scattered by a dipolar scatterer at high scattering angles outside the hole's region. Control of light scattering at high angles can be used to suppress the corresponding optomechanical backaction, which results in focusing of the measurement information at low angles. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.
We theoretically show that laser recoil heating in free-space levitated optomechanics can be arbitrarily suppressed by shining squeezed light onto an optically trapped nanoparticle. The presence of squeezing modifies the quantum electrodynamical light-matter interaction in a way that enables us to control the amount of information that the scattered light carries about a given mechanical degree of freedom. Moreover, we analyze the trade-off between measurement imprecision and back-action noise and show that optical detection beyond the standard quantum limit can be achieved. We predict that, with state-of-the-art squeezed light sources, laser recoil heating can be reduced by at least 60% by squeezing a single Gaussian mode with an appropriate incidence direction, and by 98% by squeezing a properly mode-matched mode. Our results, which are valid both for motional and librational degrees of freedom, will lead to improved feedback cooling schemes as well as boost the coherence time of optically levitated nanoparticles in the quantum regime.
We theoretically investigate the problem of position detection of an optically levitated Mie particle. The information radiation field (IRF) is proposed and defined to characterize the scattered light carrying complete information about the center-of-mass (c.m.) motion of the particle. Based on the IRF, we suggest an optimal detection scheme for the position of arbitrary particles. We calculate both the information losses of objective collection and mode-matching in levitated optomechanical experiments. Our results conclude that the backward detection scheme, using an incident Gaussian beam focused by a high numerical aperture lens, provides sufficient information to achieve the quantum ground state through cooling of the three-dimensional c.m. motion of the Mie particle.