- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Quantum-limited imaging of a nanomechanical resonator with a spatial mode sorter

M. E. Choi1, C. M. Pluchar1, W. He1, S. Guha2, and D. J. Wilson1

PDF

Phys. Rev. Research 7, L032031 – Published 8 August, 2025

DOI: https://doi.org/10.1103/6msj-wh2f

Abstract

We explore the use of a spatial mode sorter to image a nanomechanical resonator, with the goal of studying the quantum limits of active imaging and extending the toolbox for optomechanical force sensing. In our experiment, we reflect a Gaussian laser beam from a vibrating nanoribbon and pass the reflected beam through a commercial spatial mode demultiplexer (Cailabs Proteus). The intensity in each demultiplexed channel depends on the mechanical modeshapes and encodes information about their displacement amplitudes. As a concrete demonstration, we monitor the angular displacement of the ribbon’s fundamental torsion mode by illuminating in the fundamental Hermite-Gauss mode (HG00) and reading out in the HG10 mode. We show that this technique permits readout of the ribbon’s torsional vibration with a precision near the quantum limit. Our results highlight new opportunities at the interface of quantum imaging and quantum optomechanics.

View figure in article

Physics Subject Headings (PhySH)

Corrections

6 November, 2025

Correction: An incorrect version of Figure 2 was used for publication and has now been replaced with the correct version.

Article Text

Supplemental Material

References (43)

  1. B. R. Norris, J. Wei, C. H. Betters, A. Wong, and S. G. Leon-Saval, An all-photonic focal-plane wavefront sensor, Nat. Commun. 11, 5335 (2020).
  2. C. Rouvière, D. Barral, A. Grateau, I. Karuseichyk, G. Sorelli, M. Walschaers, and N. Treps, Ultra-sensitive separation estimation of optical sources, Optica 11, 166 (2024).
  3. N. K. Fontaine, R. Ryf, H. Chen, D. T. Neilson, K. Kim, and J. Carpenter, Laguerre-Gaussian mode sorter, Nat. Commun. 10, 1865 (2019).
  4. C. Rouvière, D. Barral, A. Grateau, G. Sorelli, I. Karuseichyk, M. Walschaers, and N. Treps, Experimental separation estimation of incoherent optical sources reaching the Cramér-Rao bound, in European Quantum Electronics Conference (Optica Publishing Group, Munich, Germany, 2023), p. 83.
  5. M. R. Grace and S. Guha, Identifying objects at the quantum limit for superresolution imaging, Phys. Rev. Lett. 129, 180502 (2022).
  6. H. Defienne, W. P. Bowen, M. Chekhova, G. B. Lemos, D. Oron, S. Ramelow, N. Treps, and D. Faccio, Advances in quantum imaging, Nat. Photon. 181024 (2024).
  7. V. Delaubert, N. Treps, C. C. Harb, P. K. Lam, and H.-A. Bachor, Quantum measurements of spatial conjugate variables: Displacement and tilt of a Gaussian beam, Opt. Lett. 31, 1537 (2006).
  8. M. Tsang, Subdiffraction incoherent optical imaging via spatial-mode demultiplexing, New J. Phys. 19, 023054 (2017).
  9. L. Santamaria, F. Sgobba, and C. Lupo, Single-photon sub-Rayleigh precision measurements of a pair of incoherent sources of unequal intensity, Opt. Quantum 2, 46 (2024).
  10. F. Grenapin, D. Paneru, A. D’Errico, V. Grillo, G. Leuchs, and E. Karimi, Superresolution enhancement in biphoton spatial-mode demultiplexing, Phys. Rev. Appl. 20, 024077 (2023).
  11. I. Padilla, A. Sajjad, B. N. Saif, and S. Guha, Quantum resolution limit of long-baseline imaging using distributed entanglement, arXiv:2406.16789.
  12. K. K. Lee, C. N. Gagatsos, S. Guha, and A. Ashok, Quantum-inspired multi-parameter adaptive bayesian estimation for sensing and imaging, IEEE J. Sel. Top. Signal Process. 17, 491 (2022).
  13. X.-J. Tan, L. Qi, L. Chen, A. J. Danner, P. Kanchanawong, and M. Tsang, Quantum-inspired superresolution for incoherent imaging, Optica 10, 1189 (2023).
  14. D. Rugar and P. Hansma, Atomic force microscopy, Phys. Today 43, 23 (1990).
  15. J. E. Sader, A. Gomez, A. P. Neumann, A. Nunn, and M. L. Roukes, Data-driven fingerprint nanoelectromechanical mass spectrometry, Nat. Commun. 15, 8800 (2024).
  16. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  17. T. Dinter, R. Roberts, T. Volz, M. K. Schmidt, and C. Laplane, Three-dimensional and selective displacement sensing of a levitated nanoparticle via spatial mode decomposition, arXiv:2409.08827.
  18. C. Gonzalez-Ballestero, M. Aspelmeyer, L. Novotny, R. Quidant, and O. Romero-Isart, Levitodynamics: Levitation and control of microscopic objects in vacuum, Science 374, eabg3027 (2021).
  19. N. J. Engelsen, A. Beccari, and T. J. Kippenberg, Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution, Nat. Nanotechnol. 19, 725 (2024).
  20. A. Militaru, M. Rossi, F. Tebbenjohanns, O. Romero-Isart, M. Frimmer, and L. Novotny, Ponderomotive squeezing of light by a levitated nanoparticle in free space, Phys. Rev. Lett. 129, 053602 (2022).
  21. S. Hao and T. P. Purdy, Back action evasion in optical lever detection, Optica 11, 10 (2024).
  22. C. M. Pluchar, W. He, J. Manley, N. Deshler, S. Guha, and D. J. Wilson, Imaging-based quantum optomechanics, Phys. Rev. Lett. 135, 023601 (2025).
  23. Specifically, 〈u1|u2〉=∫∫u1*(x,y)u2(x,y)dxdy, where x−y is the plane transverse to the optical axis.
  24. In the main text and in the Appendix, Sx[Ω] refers to the signal-sided power spectral density at Fourier frequency Ω, with units [x]2/Hz and normalization ∫0∞Sx[Ω]dΩ/(2π)=〈x2〉.
  25. Y. Enomoto, K. Nagano, and S. Kawamura, Standard quantum limit of angular motion of a suspended mirror and homodyne detection of a ponderomotively squeezed vacuum field, Phys. Rev. A 94, 012115 (2016).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6msj-wh2f for details on the theory, experiment, and data analysis described in the main text.
  27. C. Pluchar, A. Agrawal, and D. Wilson, Quantum-limited optical lever measurement of a torsion oscillator, Optica 12, 418 (2025).
  28. B. J. Puttnam, R. S. Luís, J. M. D. Mendinueta, J. Sakaguchi, W. Klaus, Y. Kamio, M. Nakamura, N. Wada, Y. Awaji, A. Kanno et al., Self-homodyne detection in optical communication systems, Photonics (MDPI, Basel, Switzerland, 2014), Vol. 1, pp. 110–130.
  29. W. Joyce and B. DeLoach, Alignment of Gaussian beams, Appl. Opt. 23, 4187 (1984).
  30. J. R. Pratt, A. R. Agrawal, C. A. Condos, C. M. Pluchar, S. Schlamminger, and D. J. Wilson, Nanoscale torsional dissipation dilution for quantum experiments and precision measurement, Phys. Rev. X 13, 011018 (2023).
  31. For details about the thermal noise calibration technique and uncertainties, see Supplemental Material of Refs. [27, 30]. For optical lever measurements made on similar devices, thermal noise and direct calibration typically differ by ∼10%.
  32. We have observed heating rates of ≲5 K/mW at λ=850 nm for ribbons with identical dimensions [27, 30] and ≲1 K/mW at 1550 nm for trampolines with tenfold narrower tethers [43]. This low heating stems from the low absorbance of Si3N4 [43] and large width of the ribbon (increasing thermal conductance).
  33. In practice, optimal sensitivity is achieved by increasing the beam diameter 2w0 to match the ribbon width wr (i.e., minimizing θD). In this case, a detailed analysis reveals that the ratio of the imprecision to the peak zero-point displacement spectral density scales as Sθimp/SθZP∝hr3/(wrQ0), where hr is the ribbon width and Q0 is the intrinsic material Q [27, 30].
  34. J. D. Teufel, T. Donner, M. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, Nanomechanical motion measured with an imprecision below that at the standard quantum limit, Nat. Nanotechnol. 4, 820 (2009).
  35. D. J. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. J. Kippenberg, Measurement-based control of a mechanical oscillator at its thermal decoherence rate, Nature (London) 524, 325 (2015).
  36. M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, Measurement-based quantum control of mechanical motion, Nature (London) 563, 53 (2018).
  37. R. Hamerly and H. Mabuchi, Advantages of coherent feedback for cooling quantum oscillators, Phys. Rev. Lett. 109, 173602 (2012).
  38. M. Ernzer, M. Bosch Aguilera, M. Brunelli, G.-L. Schmid, T. M. Karg, C. Bruder, P. P. Potts, and P. Treutlein, Optical coherent feedback control of a mechanical oscillator, Phys. Rev. X 13, 021023 (2023).
  39. Y. Xia, A. R. Agrawal, C. M. Pluchar, A. J. Brady, Z. Liu, Q. Zhuang, D. J. Wilson, and Z. Zhang, Entanglement-enhanced optomechanical sensing, Nat. Photon. 17, 470 (2023).
  40. N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, A quantum laser pointer, Science 301, 940 (2003).
  41. W. He, C. N. Gagatsos, D. J. Wilson, and S. Guha, Optimum classical beam-position sensing, Phys. Rev. Appl. 22, L041004 (2024).
  42. M. E. Choi and D. J. Wilson, Raw Data for Figs. 2 and 3, Zenodo (2024), https://zenodo.org/records/14549115.
  43. A. T. Land, M. Dey Chowdhury, A. R. Agrawal, and D. J. Wilson, Sub-ppm nanomechanical absorption spectroscopy of silicon nitride, Nano Lett. 24, 7578 (2024).

Outline

Information

Phys. Rev. Research 7, L032031– Published 8 August, 2025
  • Received 19 December 2024
  • Accepted 14 July 2025
  • Corrected 6 November 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation