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Non-equilibrium quadratic measurement-feedback squeezing in a micromechanical resonator

Motoki Asano1, Takuma Aihara2, Tai Tsuchizawa2, and Hiroshi Yamaguchi1

  • 1NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan
  • 2NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan

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Phys. Rev. Research 3, 033121 – Published 6 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.033121

Abstract

Measurement and feedback control of thermomechanical motion in a micromechanical resonator has been actively studied to achieve extremely high sensing performance by controlling the stochastic thermal noise. Although linear measurement-feedback control in the phase space results in the feedback cooling, extending them to the nonlinear regime, i.e., utilizing quadratic of higher-order dynamic variables in both measurement and control, can further functionalize its operations. Here, we demonstrate fully quadratic measurement-feedback protocol in a micromechanical resonator by driving the second-order nonlinearity and directly measuring quadratic variables referred as Schwinger angular momentum. Our measurement-feedback protocol enables us to achieve a noise reduction at the level of −5.1±0.2 dB over the –3-dB limitation in the continuous parametric driving. We unveil that this strong noise reduction originates in the effective cooling effect by investigating entropy production rates. These results would be further extended to investigating general performance of nonlinear information thermodynamic machines, in which the higher-order moments (e.g., variance and correlations) can be controlled with avoiding the nonlinear instability, thanks to the existence of information flows.

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References (38)

  1. J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  2. S. Ciliberto, Experiments in Stochastic Thermodynamics: Short History and Perspectives, Phys. Rev. X 7, 021051 (2017).
  3. D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and A. Petrosyan, Entropy Production and Time Asymmetry in Nonequilibrium Fluctuations, Phys. Rev. Lett. 98, 150601 (2007).
  4. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality, Nat. Phys. 6, 988 (2010).
  5. J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state, Nat. Nanotechnol. 9, 358 (2014).
  6. F. Douarche, S. Ciliberto, A. Petrosyan, and I. Rabbiosi, An experimental test of the Jarzynski equality in a mechanical experiment, Europhys. Lett. 70, 593 (2005).
  7. M. Bonaldi, L. Conti, P. De Gregorio, L. Rondoni, G. Vedovato, A. Vinante, M. Bignotto, M. Cerdonio, P. Falferi, N. Liguori, S. Longo, R. Mezzena, A. Ortolan, G. A. Prodi, F. Salemi, L. Taffarello, S. Vitale, and J.-P. Zendri, Nonequilibrium Steady-State Fluctuations in Actively Cooled Resonators, Phys. Rev. Lett. 103, 010601 (2009).
  8. M. Serra-Garcia, A. Foehr, M. Molerón, J. Lydon, C. Chong, and C. Daraio, Mechanical Autonomous Stochastic Heat Engine, Phys. Rev. Lett. 117, 010602 (2016).
  9. M. Rossi, L. Mancino, G. T. Landi, M. Paternostro, A. Schliesser, and A. Belenchia, Experimental Assessment of Entropy Production in a Continuously Measured Mechanical Resonator, Phys. Rev. Lett. 125, 080601 (2020).
  10. P.-F. Cohadon, A. Heidmann, and M. Pinard, Cooling of a Mirror by Radiation Pressure, Phys. Rev. Lett. 83, 3174 (1999).
  11. D. Kleckner and D. Bouwmeester, Sub-Kelvin optical cooling of a micromechanical resonator, Nature (London) 444, 75 (2006).
  12. M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, Feedback Cooling of a Cantilever's Fundamental Mode Below 5 mK, Phys. Rev. Lett. 99, 017201 (2007).
  13. T. Munakata and M. L. Rosinberg, Entropy Production and Fluctuation Theorems for Langevin Processes Under Continuous Non-Markovian Feedback Control, Phys. Rev. Lett. 112, 180601 (2014).
  14. J. M. Horowitz and H. Sandberg, Second-law-like inequalities with information and their interpretations, New J. Phys. 16, 125007 (2014).
  15. M. Debiossac, D. Grass, J. J. Alonso, E. Lutz, and N. Kiesel, Thermodynamics of continuous non-Markovian feedback control, Nat. Commun. 11, 1360 (2020).
  16. A. Vinante and P. Falferi, Feedback-Enhanced Parametric Squeezing of Mechanical Motion, Phys. Rev. Lett. 111, 207203 (2013).
  17. M. Poot, K. Y. Fong, and H. X. Tang, Classical non-Gaussian state preparation through squeezing in an optoelectromechanical resonator, Phys. Rev. A 90, 063809 (2014).
  18. D. Rugar and P. Grütter, Mechanical Parametric Amplification and Thermomechanical Noise Squeezing, Phys. Rev. Lett. 67, 699 (1991).
  19. I. Mahboob, H. Okamoto, and H. Yamaguchi, An electromechanical Ising Hamiltonian, Sci. Adv. 2, e1600236 (2016).
  20. M. J. Seitner, M. Abdi, A. Ridolfo, M. J. Hartmann, and E. M. Weig, Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes, Phys. Rev. Lett. 118, 254301 (2017).
  21. G. Brawley, M. Vanner, P. E. Larsen, S. Schmid, A. Boisen, and W. Bowen, Nonlinear optomechanical measurement of mechanical motion, Nat. Commun. 7, 10988 (2016).
  22. R. Leijssen, G. R. La Gala, L. Freisem, J. T. Muhonen, and E. Verhagen, Nonlinear cavity optomechanics with nanomechanical thermal fluctuations, Nat. Commun. 8, 16024 (2017).
  23. M. Asano, R. Ohta, T. Aihara, T. Tsuchizawa, H. Okamoto, and H. Yamguchi, Optically probing Schwinger angular momenta in a micromechanical resonator, Phys. Rev. A 100, 053801 (2019).
  24. J. Schwinger, On Angular Momentum, in Quantum Theory of Angular Momentum, edited by L. C. Biedenharm and H. van Dam (Academic Press, New York, 1965).
  25. T. Munakata and M. Rosinberg, Entropy production and fluctuation theorems under feedback control: The molecular refrigerator model revisited, J. Stat. Mech.: Theory Exp. (2012) P05010.
  26. A. Imparato and L. Peliti, Fluctuation relations for a driven Brownian particle, Phys. Rev. E 74, 026106 (2006).
  27. T. Tomé and M. J. de Oliveira, Entropy production in irreversible systems described by a Fokker-Planck equation, Phys. Rev. E 82, 021120 (2010).
  28. R. E. Spinney and I. J. Ford, Entropy production in full phase space for continuous stochastic dynamics, Phys. Rev. E 85, 051113 (2012).
  29. H. Nha and J. Kim, Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebras: Detection of non-Gaussian entangled states, Phys. Rev. A 74, 012317 (2006).
  30. J. S. Bunch, A. M. Van Der Zande, S. S. Verbridge, I. W. Frank, D. M. Tanenbaum, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Electromechanical resonators from graphene sheets, Science 315, 490 (2007).
  31. M. Will, M. Hamer, M. Muller, A. Noury, P. Weber, A. Bachtold, R. Gorbachev, C. Stampfer, and J. Guttinger, High quality factor graphene-based two-dimensional heterostructure mechanical resonator, Nano Lett. 17, 5950 (2017).
  32. H. Okamoto, A. Gourgout, C.-Y. Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi, Coherent phonon manipulation in coupled mechanical resonators, Nat. Phys. 9, 480 (2013).
  33. T. Faust, J. Rieger, M. J. Seitner, J. P. Kotthaus, and E. M. Weig, Coherent control of a classical nanomechanical two-level system, Nat. Phys. 9, 485 (2013).
  34. I. Mahboob, H. Okamoto, K. Onomitsu, and H. Yamaguchi, Two-Mode Thermal-Noise Squeezing in an Electromechanical Resonator, Phys. Rev. Lett. 113, 167203 (2014).
  35. Y. S. Patil, S. Chakram, L. Chang, and M. Vengalattore, Thermomechanical Two-Mode Squeezing in an Ultrahigh-Q Membrane Resonator, Phys. Rev. Lett. 115, 017202 (2015).
  36. R. Lifshitz and M. Cross, Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators, edited by H. G. Schuster, Reviews of Nonlinear Dynamics and Complexity, Vol. 1 (Wiley-VCH, Weinheim, 2008), pp. 1–52.
  37. N. Shiraishi, K. Funo, and K. Saito, Speed Limit for Classical Stochastic Processes, Phys. Rev. Lett. 121, 070601 (2018).
  38. S. Ito and A. Dechant, Stochastic Time Evolution, Information Geometry, and the Cramér-Rao Bound, Phys. Rev. X 10, 021056 (2020).

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Phys. Rev. Research 3, 033121– Published 6 August, 2021
  • Received 6 April 2021
  • Revised 16 June 2021
  • Accepted 29 June 2021
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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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