Nano- and micromechanical oscillators with high quality (Q)-factors have gained much attention for their potential application as ultrasensitive detectors. In contrast to micro-fabricated devices, optically trapped nanoparticles in vacuum do not suffer from clamping losses, hence leading to much larger Q-factors. We find that for a levitated nanoparticle the thermal energy suffices to drive the motion of the nanoparticle into the nonlinear regime. First, we experimentally measure and fully characterize the frequency fluctuations originating from thermal motion and nonlinearities. Second, we demonstrate that feedback cooling can be used to mitigate these fluctuations. The high level of control allows us to fully exploit the force-sensing capabilities of the nanoresonator. Our approach offers a force sensitivity of 20 zN Hz−1/2, which is the highest value reported so far at room temperature, sufficient to sense ultraweak interactions, such as non-Newtonian gravity-like forces.
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Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nature Nanotech. 7, 301–304 (2012.).
Yang, Y. T., Callegari, C, Feng, X. L., Ekinci, K. L. & Roukes, M. L. Zeptogram-scale nanomechanical mass sensing. Nano Lett. 6, 583–586 (2006).
Cleland, A. N. & Roukes, M. L. A nanometre-scale mechanical electrometer. Nature 392, 160–162 (1998).
Rugar, D., Budakian, R., Mamin, H. J. & Chui, B. W. Single spin detection by magnetic resonance force microscopy. Nature 430, 329–332 (2004).
Stipe, B. C., Mamin, H. J., Stowe, T. D., Kenny, T. W. & Rugar, D. Noncontact friction and force fluctuations between closely spaced bodies. Phys. Rev. Lett. 87, 096801 (2001).
Moser, J. et al. Ultrasensitive force detection with a nanotube mechanical resonator. Nature Nanotech. 8, 493–496 (2013).
Postma, H. W. Ch., Kozinsky, I., Husain, A. & Roukes, M. L. Dynamic range of nanotube- and nanowire-based electromechanical systems. Appl. Phys. Lett. 86, 223105 (2005).
Cleland, A. N. & Roukes, M. L. Noise processes in nanomechanical resonators. J. Appl. Phys. 92, 2758–2769 (2002).
Ekinci, K. L., Yang, Y. T. & Roukes, M. L. Ultimate limits to inertial mass sensing based on nanoelectromechanical systems. J. Appl. Phys. 95, 2682–2689 (2004).
Ashkin, A. Optical levitation by radiation pressure. Appl. Phys. Lett. 19, 283–285 (1971).
Gieseler, J., Deutsch, B., Quidant, R. & Novotny, L. Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. Phys. Rev. Lett. 109, 103603 (2012).
Li, T., Kheifets, S. & Raizen, M. Millikelvin cooling of an optically trapped microsphere in vacuum. Nature Phys. 7, 527–530 (2011).
Romero-Isart, O., Juan, M. L., Quidant, R. & Cirac, J. I. Toward quantum superposition of living organisms. New J. Phys. 12, 033015 (2010).
Chang, D. E. et al. Cavity opto-mechanics using an optically levitated nanosphere. Proc. Natl Acad. Sci. USA 107, 1005–1010 (2010).
Epstein, P. S. On the resistance experienced by spheres in their motion through gases. Phys. Rev. 22, 710–733 (1923).
O’Hanlon, J. F. A User’s Guide to Vacuum Technology 3rd edn (Wiley, 2003).
Dykman, M. I. & Krivoglaz, M. A. Theory of nonlinear oscillator interacting with a medium. Phys. Rev. 5, 265–441 (1984).
Lifshitz, R. & Cross, M. C. Review of Nonlinear Dynamics and Complexity (Wiley-VCH, 2009).
Dykman, M. I., Mannella, R. R., McClintock, P. V. E., Soskin, S. M. & Stocks, N. G. Noise-induced narrowing of peaks in the power spectra of underdamped nonlinear oscillators. Phys. Rev. A 42, 7041–7049 (1990).
Neukirch, L. P., Gieseler, J., Quidant, R., Novotny, L. & Nick Vamivakas, A. Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond. Opt. Lett. 38, 2976–2979 (2013).
Geiselmann, M. et al. Three-dimensional optical manipulation of a single electron spin. Nature Nanotech. 8, 175–179 (2013).
Zurita-Sánchez, J., Greffet, J-J. & Novotny, L. Friction forces arising from fluctuating thermal fields. Phys. Rev. A 69, 022902 (2004).
Knünz, S. et al. Injection locking of a trapped-ion phonon laser. Phys. Rev. Lett. 105, 013004 (2010).
Arvanitaki, A. & Geraci, A. A. Detecting high-frequency gravitational waves with optically levitated sensors. Phys. Rev. Lett. 110, 071105 (2013).
Villanueva, L. G. et al. Surpassing fundamental limits of oscillators using nonlinear resonators. Phys. Rev. Lett. 110, 177208 (2013).
Mertz, J., Marti, O. & Mlynek, J. Regulation of a microcantilever response by force feedback. Appl. Phys. Lett. 62, 2344–2346 (1993).
Seifert, F., Kwee, P., Heurs, M., Willke, B. & Danzmann, K. Laser power stabilization for second-generation gravitational wave detectors. Opt. Lett. 31, 2000–2002 (2006).
Geraci, A. A., Papp, S. B. & Kitching, J. Short-range force detection using optically cooled levitated microspheres. Phys. Rev. Lett. 105, 101101 (2010).
This research was funded by ETH Zurich, Fundació Privada CELLEX, ERC-QMES (No. 338763) and ERC-Plasmolight (No. 259196). We thank A. Bachtold and M. Spasenović for valuable input and help and Iñaki Gonzalez for his assistance in preparing Fig. 1.
The authors declare no competing financial interests.
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Gieseler, J., Novotny, L. & Quidant, R. Thermal nonlinearities in a nanomechanical oscillator. Nature Phys 9, 806–810 (2013). https://doi.org/10.1038/nphys2798
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