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Three-dimensional and selective displacement sensing of a levitated nanoparticle via spatial mode decomposition

Thomas J. Dinter1, Reece Roberts1,2, Thomas Volz1,2, Mikolaj K. Schmidt1,2, and Cyril Laplane1,2,3,*,†

  • *Present address: School of Physics, The University of Sydney, Sydney, NSW 2006, Australia.
  • †Contact author: cyril.laplane@sydney.edu.au
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Phys. Rev. Research 8, 023220 – Published 28 May, 2026

DOI: https://doi.org/10.1103/9mnc-ddvw

Abstract

We propose and experimentally demonstrate a detection method that significantly improves the precision of real-time measurement of the three-dimensional (3D) 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 backscattered 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)×10−14m/Hz below the zero-point motion (xzpm,yzpm,zzpm)=(2.2,2.4,1.6)×10−12m 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 (ηtotx,ηtoty,ηtotz)=(0.13,0.18,0.33)>19, which would enable the 3D motional quantum ground state of a levitated optomechanical system.

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Phys. Rev. Research 8, 023220– Published 28 May, 2026
  • Received 4 November 2024
  • Accepted 11 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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