Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Fourier synthesis of radiofrequency nanomechanical pulses with different shapes

Nature Nanotechnology volume 10, pages 512–516 (2015)Cite this article

Subjects

Abstract

The concept of Fourier synthesis1 is heavily used in both consumer electronic products2 and fundamental research3. In the latter, pulse shaping is key to dynamically initializing, probing and manipulating the state of classical or quantum systems. In NMR, for instance, shaped pulses have a long-standing tradition4 and the underlying fundamental concepts have subsequently been successfully extended to optical frequencies3,5 and even to the implementation of quantum gate operations6. Transferring these paradigms to nanomechanical systems requires tailored nanomechanical waveforms. Here, we report on an additive Fourier synthesizer for nanomechanical waveforms based on monochromatic surface acoustic waves. As a proof of concept, we electrically synthesize four different elementary nanomechanical waveforms from a fundamental surface acoustic wave at f1 ≈ 150 MHz using a superposition of up to three discrete harmonics. We use these shaped pulses to interact with an individual sensor quantum dot and detect their deliberately and temporally modulated strain component via the optomechanical quantum dot response7,8,9. Importantly, and in contrast to direct mechanical actuation by bulk piezoactuators7, surface acoustic waves provide much higher frequencies (>20 GHz; ref. 10) to resonantly drive mechanical motion11. Thus, our technique uniquely allows coherent mechanical control12 of localized vibronic modes of optomechanical crystals13,14, even in the quantum limit when cooled to the vibrational ground state15.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Nanomechanical waveform synthesizer.
Figure 2: Calculated prototypical nanomechanical waveforms.
Figure 3: Single quantum dot sensing of nanomechanical waveforms.
Figure 4: Fourier analysis.

Similar content being viewed by others

References

  1. Fourier, J. Mémoire sur la propagation de la chaleur dans les corps solides. Nouveau Bulletin des Sciences par la Société Philomatique de Paris I, 112–116 (1808).

    Google Scholar 

  2. Hammond, L. Electrical musical instrument. US patent 1,956,350 (1934).

  3. Chan, H.-S. et al. Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics. Science 331, 1165–1168 (2011).

    Article  CAS  Google Scholar 

  4. Freeman, R. Shaped radiofrequency pulses in high resolution NMR. Prog. Nucl. Magn. Reson. Spectrosc. 32, 59–106 (1998).

    Article  CAS  Google Scholar 

  5. Vitanova, N. V., Fleischhauer, M., Shore, B. W. & Bergmann, K. Coherent manipulation of atoms and molecules by sequential laser pulses. Adv. At. Mol. Opt. Phys. 46, 55–190 (2001).

    Article  Google Scholar 

  6. Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037 (2005).

    Article  Google Scholar 

  7. Yeo, I. et al. Strain-mediated coupling in a quantum dot–mechanical oscillator hybrid system. Nature Nanotech. 9, 106–110 (2014).

    Article  CAS  Google Scholar 

  8. Metcalfe, M., Carr, S. M., Muller, A., Solomon, G. S. & Lawall, J. Resolved sideband emission of InAs/GaAs quantum dots strained by surface acoustic waves. Phys. Rev. Lett. 105, 037401 (2010).

    Article  CAS  Google Scholar 

  9. Gell, J. R. et al. Modulation of single quantum dot energy levels by a surface-acoustic-wave. Appl. Phys. Lett. 93, 081115 (2008).

    Article  Google Scholar 

  10. Kukushkin, I. V. et al. Ultrahigh-frequency surface acoustic waves for finite wave-vector spectroscopy of two-dimensional electrons. Appl. Phys. Lett. 85, 4526–4528 (2004).

    Article  CAS  Google Scholar 

  11. Beil, F. W. et al. Shock waves in nanomechanical resonators. Phys. Rev. Lett. 100, 026801 (2008).

    Article  Google Scholar 

  12. Beil, F. W. et al. Detection of coherent acoustic oscillations in a quantum electromechanical resonator. Appl. Phys. Lett. 90, 043101 (2007).

    Article  Google Scholar 

  13. Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).

    Article  CAS  Google Scholar 

  14. Pennec, Y. et al. Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs. Opt. Express 18, 14301–14310 (2010).

    Article  CAS  Google Scholar 

  15. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    Article  CAS  Google Scholar 

  16. White, R. M. & Voltmer, F. W. Direct piezoelectric coupling to surface elastic waves. Appl. Phys. Lett. 7, 314–316 (1965).

    Article  Google Scholar 

  17. Gustafsson, M. V., Santos, P. V., Johansson, G. & Delsing, P. Local probing of propagating acoustic waves in a gigahertz echo chamber. Nature Phys. 8, 338–343 (2012).

    Article  CAS  Google Scholar 

  18. Wixforth, A., Kotthaus, J. P. & Weimann, G. Quantum oscillations in the surface-acoustic-wave attenuation caused by a two-dimensional electron gas. Phys. Rev. Lett. 56, 2104–2106 (1986).

    Article  CAS  Google Scholar 

  19. Rocke, C. et al. Acoustically driven storage of light in a quantum well. Phys. Rev. Lett. 78, 4099–4102 (1997).

    Article  CAS  Google Scholar 

  20. Stotz, J. A. H., Hey, R., Santos, P. V. & Ploog, K. H. Coherent spin transport through dynamic quantum dots. Nature Mater. 4, 585–588 (2005).

    Article  CAS  Google Scholar 

  21. Violante, A. et al. Dynamics of indirect exciton transport by moving acoustic fields. New J. Phys. 16, 033035 (2014).

    Article  Google Scholar 

  22. Hermelin, S. et al. Electrons surfing on a sound wave as a platform for quantum optics with flying electrons. Nature 477, 435–438 (2011).

    Article  CAS  Google Scholar 

  23. McNeil, R. P. G. et al. On-demand single-electron transfer between distant quantum dots. Nature 477, 439–442 (2011).

    Article  CAS  Google Scholar 

  24. Couto, O. D. D. et al. Photon anti-bunching in acoustically pumped quantum dots. Nature Photon. 3, 645–648 (2009).

    Article  CAS  Google Scholar 

  25. Völk, S. et al. Enhanced sequential carrier capture into individual quantum dots and quantum posts controlled by surface acoustic waves. Nano Lett. 10, 3399–3407 (2010).

    Article  Google Scholar 

  26. Schülein, F. J. R. et al. Acoustically regulated carrier injection into a single optically active quantum dot. Phys. Rev. B 88, 085307 (2013).

    Article  Google Scholar 

  27. de Lima, M. M. & Santos, P. V. Modulation of photonic structures by surface acoustic waves. Rep. Prog. Phys. 68, 1639–1701 (2005).

    Article  CAS  Google Scholar 

  28. Fuhrmann, D. A. et al. Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons. Nature Photon. 5, 605–609 (2011).

    Article  CAS  Google Scholar 

  29. Atkinson, P., Zallo, E. & Schmidt, O. G. Independent wavelength and density control of uniform GaAs/AlGaAs quantum dots grown by infilling self-assembled nanoholes. J. Appl. Phys. 112, 054303 (2012).

    Article  Google Scholar 

  30. Qiang, H., Pollak, F. H. & Hickman, G. Piezo-photoreflectance of the direct gaps of GaAs and Ga0.78Al0.22As. Solid State Commun. 76, 1087–1091 (1990).

    Article  CAS  Google Scholar 

  31. Weiß, M. et al. Dynamic acoustic control of individual optically active quantum dot-like emission centers in heterostructure nanowires. Nano Lett. 14, 2256–2264 (2014).

    Article  Google Scholar 

  32. Montinaro, M. et al. Quantum dot opto-mechanics in a fully self-assembled nanowire. Nano Lett. 4, 4454–4460 (2014).

    Article  Google Scholar 

  33. Blattmann, R., Krenner, H. J., Kohler, S. & Hänggi, P. Entanglement creation in a quantum-dot–nanocavity system by Fourier-synthesized acoustic pulses. Phys. Rev. A 89, 012327 (2014).

    Article  Google Scholar 

  34. Gustafsson, M. V. et al. Propagating phonons coupled to a superconducting qubit. Science 346, 207–211 (2014).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) via the Emmy Noether Programme (KR 3790/2-1), the Nanosystems Initiative Munich (NIM), Sonderforschungsbereich SFB 631, by BMBF, via project QuaHL-Rep (contracts nos. 01BQ1032 and 01BQ1034) and by the European Union via the Seventh Framework Programme 209 (FP7/2007-2013) under grant agreement no. 601126 210 (HANAS). The authors also thank J. H. Davies, G. Bester and J. Ricardo Cardenas for enlightening discussions on strain tuning of quantum dots.

Author information

Authors and Affiliations

  1. Lehrstuhl für Experimentalphysik 1 and Augsburg Centre for Innovative Technologies (ACIT), Universität Augsburg, Universitätsstraße 1, Augsburg, 86159, Germany

    Florian J. R. Schülein, Achim Wixforth & Hubert J. Krenner

  2. Nanosystems Initiative Munich (NIM), Schellingstraße 4, München, 80339, Germany

    Florian J. R. Schülein, Achim Wixforth & Hubert J. Krenner

  3. Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstraße 20, Dresden, 01069, Germany

    Eugenio Zallo, Paola Atkinson, Oliver G. Schmidt & Armando Rastelli

  4. Institut des NanoSciences de Paris, Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR7588, 4 place Jussieu, Paris, F-75005, France

    Paola Atkinson

  5. Institute of Semiconductor and Solid State Physics, Johannes Kepler Universität Linz, Altenbergerstraße 69, Linz, 4040, Austria

    Rinaldo Trotta & Armando Rastelli

  6. Center for Nanoscience (CeNS), Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, München, 80539, Germany

    Achim Wixforth & Hubert J. Krenner

Authors
  1. Florian J. R. Schülein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eugenio Zallo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paola Atkinson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Oliver G. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Rinaldo Trotta
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Armando Rastelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Achim Wixforth
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hubert J. Krenner
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.J.R.S., A.W. and H.J.K. designed the research. F.J.R.S. designed the device, carried out experiments and performed numerical modelling. F.J.R.S. and H.J.K. performed data analysis and modelling (with input from A.W., A.R. and R.T.). E.Z., P.A., A.R. and O.G.S. performed crystal growth and sample characterization. All authors discussed the results. H.J.K., A.W. and F.J.R.S. wrote the manuscript with input from all other authors. H.J.K. supervised the project.

Corresponding author

Correspondence to Hubert J. Krenner.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1836 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schülein, F., Zallo, E., Atkinson, P. et al. Fourier synthesis of radiofrequency nanomechanical pulses with different shapes. Nature Nanotech 10, 512–516 (2015). https://doi.org/10.1038/nnano.2015.72

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2015.72

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing