• Українська
  • English
  • Русский
ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)


Maizelis, ZА

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: mjkp@ukr.net

Language: Russian

For detecting and establishing the nature of frequency noises in the oscillating system, it is very important to separate different types of noises. For determination of characteristics of the frequency noise it is necessary to study statistical properties not of actual coordinate and its derivative, but of complex coordinate of oscillator. Its moments do not depend on the amplitude noises that often can prevail in the system. The growing interest in noises of frequency is related to the fact that they determine the loss of coherence of vibrations in many systems, from the devices based on Josephson contacts, to the nanomechanical resonators. The knowledge of statistical characteristics of frequency noises inevitably present in the devices of information read-out in quantum computers will allow correct processing of the information in them. Here the influence of the telegraph unbalanced noise of frequency on properties of electromechanical resonator is studied. It is shown that the dependencies of the higher cumulants contain features, which allow to separate the effects related to the presence of noise of frequency. The results may be useful in the theory of nanomechanical resonators, in processing the data, obtained in the radio-technical devices and devices, based on Josephson contacts, in quantum computers, in the estimation of precision of atomic clock.

Keywords: electromechanical resonator, noise cumulant, noise of frequency

Manuscript submitted  16.12.2015
PACS     65.25.Jk; 05.40.Ca
Radiofiz. elektron. 2016, 21(1): 71-76
Full text (PDF)

  1. Gitterman, M., 2005. The Noisy Oscillator. Singapore: World Scientific. DOI: https://doi.org/10.1142/5949
  2. Clarke, J. and Wilhelm, F. K., 2008. Superconducting quantum bits. Nature, 453(7198), pp. 1031–1042. DOI: https://doi.org/10.1038/nature07128
  3. Okamoto, H., Gourgout, A., Chang, Ch.-Yu., Onomitsu, K., Mahboob, I., Chang, Ed. Y. and Yamaguchi H., 2013. Coherent phonon manipulation in coupled mechanical resonators. Nat. Phys., 9, pp. 480–484.
  4. Cleland, A. N. and Roukes, M. L., 2002. Noise processes in nanomechanical resonators. J. Appl. Phys., 92(5), pp. 2758–2769. DOI: https://doi.org/10.1063/1.1499745
  5. Faust, T., Rieger, J., Seitner, M. J., Kotthaus, J. P. and Weig, E. M., 2013. Coherent control of a classical nanomechanical two-level system. Nat. Phys., 9, pp. 485–488.
  6. Kippenberg, T. J. and Vahala, K. J., 2008. Cavity optomechanics: back-action at themesoscale. Science, 321(5893), pp. 1172–1176. DOI: https://doi.org/10.1126/science.1156032
  7. Rubiola, E. and Giordano, V., 2007. On the 1/f frequency noise in ultra-stable quartz oscillators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 54(1), pp. 15–22. DOI: https://doi.org/10.1109/TUFFC.2007.207
  8. Rugar, D., Budakian, R., Mamin, H. J. and Chui, B. W., 2004. Single spin detection by magnetic resonance force microscopy. Nature, 430(6997), pp. 329–332. DOI: https://doi.org/10.1038/nature02658
  9. Giessibl, F. J., 2003. Advances in atomic force microscopy. Rev. Mod. Phys., 75(3), pp. 949–983. DOI: https://doi.org/10.1103/RevModPhys.75.949
  10. Sullivan, D. B., Allan, D. W., Howe, D. A. and Walls, E. L., eds., 1990. Characterization of Clocks and Oscillators. National Institute of Standards and Technology (NIST) Tech. Note 1337. Washington: U. S. Government printing office.
  11. Clerk, A. A., Marquardt, F. and Harris, J. G. E., 2010. Quantum Measurement of Phonon Shot Noise. Phys. Rev. Lett., 104(21), pp. 213603 (4 p.).
  12. Yang, Y. T., Callegari, C., Feng, X. L. and Roukes, M. L., 2011. Surface adsorbate fluctuations and noise in nanoelectromechanical systems. Nano Lett., 11(4), pp. 1753–1759. DOI: https://doi.org/10.1021/nl2003158
  13. Jensen, K., Kim, K., Zettl, A. and Jensen, K., 2008. An atomic-resolution nanomechanical mass sensor. Nat. Nanotech. 3(9), pp. 533–537. DOI: https://doi.org/10.1038/nnano.2008.200
  14. Atalaya, J., Isacsson, A. and Dykman, M. I., 2011. Diffusion-induced dephasing in nanomechanical resonators. Phys. Rev. B, 83, pp. 045419 (9 p.).
  15. Fong, K. Y., Pernice, W. H. P. and Tang, H. X., 2012. Frequency and phase noise of ultrahigh Q silicon nitride nanomechanical resonators. Phys. Rev. B, 85(16), pp. 161410 (5 p.).
  16. Eichler, A., 2011. Nonlinear damping in mechanical resonators made from carbon nanotubes and grapheme. Nat. Nanotech., 6, pp. 339–342. DOI: https://doi.org/10.1038/nnano.2011.71
  17. Maizelis, Z. A., Roukes, M. L. and Dykman, M. I., 2011. Detecting and characterizing frequency fluctuations of vibrational modes. Phys. Rev. B, 84, pp. 14430 (7 p.).