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  • Letter
  • Open Access

Strong thermomechanical noise squeezing stabilized by feedback

Aida Mashaal1,2,*, Lucio Stefan1,2,*, Andrea Ranfagni1,2, Letizia Catalini3,4, Ilia Chernobrovkin1,2, Thibault Capelle1,2, Eric C. Langman1,2, and Albert Schliesser1,2,†

  • *These authors contributed equally to this work.
  • †Contact author: albert.schliesser@nbi.ku.dk

Phys. Rev. Research 7, L012071 – Published 17 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012071

Abstract

Squeezing the quadrature noise of a harmonic oscillator enhances its sensitivity. Stabilization of the antisqueezed quadrature can overcome the 3 dB squeezing limit by parametric modulation. Here, we apply this method to soft-clamped membrane resonators, which hold promise for both classical and quantum sensing applications. We compare piezoelectric and capacitive parametric modulation and observe thermomechanical squeezing by up to 17 and 21 dB, respectively. Finally, we provide a full quantum theory of combining this approach with quantum-limited motion measurement. We conclude that quantum squeezing is feasible at moderate cryogenic temperatures and realistic device parameters.

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References (33)

  1. A. Eichler, Ultra-high-Q nanomechanical resonators for force sensing, Mater. Quantum Technol. 2, 043001 (2022).
  2. O. Gerberding, F. G. Cervantes, J. Melcher, J. R. Pratt, and J. M. Taylor, Optomechanical reference accelerometer, Metrologia 52, 654 (2015).
  3. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, A nanomechanical mass sensor with yoctogram resolution, Nat. Nanotechnol. 7, 301 (2012).
  4. T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sorensen, K. Usami, A. Schliesser, and E. S. Polzik, Optical detection of radio waves through a nanomechanical transducer, Nature (London) 507, 81 (2014).
  5. A. Simonsen, S. A. Saarinen, J. D. Sanchez, J. H. Ardenkjær-Larsen, A. Schliesser, and E. S. Polzik, Sensitive optomechanical transduction of electric and magnetic signals to the optical domain, Opt. Express 27, 18561 (2019).
  6. V. B. Braginsky and F. Y. Khalili, in Quantum Measurement, edited by K. S. Thorne (Cambridge University Press, Cambridge, U.K., 1992).
  7. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  8. D. Mason, J. Chen, M. Rossi, Y. Tsaturyan, and A. Schliesser, Continuous force and displacement measurement below the standard quantum limit, Nat. Phys. 15, 745 (2019).
  9. H. Yu, L. McCuller, M. Tse, N. Kijbunchoo, L. Barsotti, and N. Mavalvala, Quantum correlations between light and the kilogram-mass mirrors of LIGO, Nature (London) 583, 43 (2020).
  10. D. Rugar and P. Grütter, Mechanical parametric amplification and thermomechanical noise squeezing, Phys. Rev. Lett. 67, 699 (1991).
  11. J. S. Huber, G. Rastelli, M. J. Seitner, J. Kölbl, W. Belzig, M. I. Dykman, and E. M. Weig, Spectral evidence of squeezing of a weakly damped driven nanomechanical mode, Phys. Rev. X 10, 021066 (2020).
  12. S. Sonar, V. Fedoseev, M. J. Weaver, F. Luna, E. Vlieg, H. van der Meer, D. Bouwmeester, and W. Löffler, Strong thermomechanical squeezing in a far-detuned membrane-in-the-middle system, Phys. Rev. A 98, 013804 (2018).
  13. R. Singh, R. J. T. Nicholl, K. I. Bolotin, and S. Ghosh, Motion transduction with thermo-mechanically squeezed graphene resonator modes, Nano Lett. 18, 6719 (2018).
  14. A. Szorkovszky, G. A. Brawley, A. C. Doherty, and W. P. Bowen, Strong thermomechanical squeezing via weak measurement, Phys. Rev. Lett. 110, 184301 (2013).
  15. S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock, Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019).
  16. E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, Quantum squeezing of motion in a mechanical resonator, Science 349, 952 (2015).
  17. J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, Squeezing of quantum noise of motion in a micromechanical resonator, Phys. Rev. Lett. 115, 243601 (2015).
  18. F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Quantum nondemolition measurement of a nonclassical state of a massive object, Phys. Rev. X 5, 041037 (2015).
  19. Y. Seis, T. Capelle, E. Langman, S. Saarinen, E. Planz, and A. Schliesser, Ground state cooling of an ultracoherent electromechanical system, Nat. Commun. 13, 1507 (2022).
  20. Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution., Nat. Nanotechnol. 12, 776 (2017).
  21. D. Hälg, T. Gisler, Y. Tsaturyan, L. Catalini, U. Grob, M.-D. Krass, M. Héritier, H. Mattiat, A.-K. Thamm, R. Schirhagl, E. C. Langman, A. Schliesser, C. L. Degen, and A. Eichler, Membrane-based scanning force microscopy, Phys. Rev. Appl. 15, L021001 (2021).
  22. M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, Measurement-based quantum control of mechanical motion, Nature (London) 563, 53 (2018).
  23. G. Huang, A. Beccari, N. J. Engelsen, and T. J. Kippenberg, Room-temperature quantum optomechanics using an ultralow noise cavity, Nature (London) 626, 512 (2024).
  24. S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, Coherent sensing of a mechanical resonator with a single-s qubit, Science 335, 1603 (2012).
  25. J. Košata, O. Zilberberg, C. L. Degen, R. Chitra, and A. Eichler, Spin detection via parametric frequency conversion in a membrane resonator, Phys. Rev. Appl. 14, 014042 (2020).
  26. A. Vinante and P. Falferi, Feedback-enhanced parametric squeezing of mechanical motion, Phys. Rev. Lett. 111, 207203 (2013).
  27. A. Pontin, M. Bonaldi, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, E. Serra, and F. Marin, Squeezing a thermal mechanical oscillator by stabilized parametric effect on the optical spring, Phys. Rev. Lett. 112, 023601 (2014).
  28. M. Poot, K. Y. Fong, and H. X. Tang, Deep feedback-stabilized parametric squeezing in an opto-electromechanical system, New J. Phys. 17, 043056 (2015).
  29. T. Briant, P. Cohadon, M. Pinard, and A. Heidmann, Optical phase-space reconstruction of mirror motion at the attometer level, Eut. Phys. J. D 22, 131 (2003).
  30. L. Catalini, Y. Tsaturyan, and A. Schliesser, Soft-clamped phononic dimers for mechanical sensing and transduction, Phys. Rev. Appl. 14, 014041 (2020).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012071 for additional details on the experimental setup, electrode design, and theoretical derivations.
  32. E. Planz, X. Xi, T. Capelle, E. C. Langman, and A. Schliesser, Membrane-in-the-middle optomechanics with a soft-clamped membrane at millikelvin temperatures, Opt. Express 31, 41773 (2023).
  33. D. Bothner, S. Yanai, A. Iniguez-Rabago, M. Yuan, Y. M. Blanter, and G. A. Steele, Cavity electromechanics with parametric mechanical driving, Nat. Commun. 11, 1589 (2020).

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