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Direct measurement of Kramers turnover with a levitated nanoparticle

Nature Nanotechnology volume 12, pages 1130–1133 (2017)Cite this article

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Abstract

Understanding the thermally activated escape from a metastable state is at the heart of important phenomena such as the folding dynamics of proteins1,2, the kinetics of chemical reactions3 or the stability of mechanical systems4. In 1940, Kramers calculated escape rates both in the high damping and low damping regimes, and suggested that the rate must have a maximum for intermediate damping5. This phenomenon, today known as the Kramers turnover, has triggered important theoretical and numerical studies6. However, as yet, there is no direct and quantitative experimental verification of this turnover. Using a nanoparticle trapped in a bistable optical potential, we experimentally measure the nanoparticle's transition rates for variable damping and directly resolve the Kramers turnover. Our measurements are in agreement with an analytical model that is free of adjustable parameters. The levitated nanoparticle presented here is a versatile experimental platform for studying and simulating a wide range of stochastic processes and testing theoretical models and predictions.

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Figure 1: Double-trap set-up.
Figure 2: Transition kinetics.
Figure 3: Experimentally measured jumping rate R as a function of gas pressure Pgas (black dots) compared with the analytical model of equation (3).

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Acknowledgements

This research was supported by the Swiss National Science Foundation (no. 200021L_169319) in cooperation with the Austrian Science Fund (no. I 3163), ERC-QMES (no. 338763), CoG ERC-QnanoMECA (no. 64790), Fundació Privada CELLEX and the severo Ochoa programme. L.R. acknowledges support from an ETH – Marie Curie Cofund Fellowship. The authors thank M. Frimmer, V. Jain, E. Hebestreit, C. Moritz, P. Mestres, E. Pollak and P. Bharadwaj for discussions and experimental support.

Author information

Author notes

  1. Loïc Rondin

    Present address: Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405, Orsay Cedex, France

  2. Jan Gieseler

    Present address: Physics Department, Harvard University, Cambridge, Massachusetts, 02318, USA

Authors and Affiliations

  1. ETH Zürich, Photonics Laboratory, Zürich, 8093, Switzerland

    Loïc Rondin, Jan Gieseler & Lukas Novotny

  2. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain

    Francesco Ricci & Romain Quidant

  3. ICREA-Institució Catalana de Recerca i Estudis Avançats, Barcelona, 08010, Spain

    Romain Quidant

  4. Faculty of Physics, University of Vienna, Boltzmanngasse 5, Wien, 1090, Austria

    Christoph Dellago

  5. Erwin Schrödinger International Institute for Mathematics and Physics, University of Vienna, Boltzmanngasse 9, Wien, 1090, Austria

    Christoph Dellago

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  1. Loïc Rondin
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Contributions

L.R. and L.N. designed and conceived the experiment. L.R. performed the experiment and analysed the data, with input from J.G., C.D. and L.N. All authors discussed the results and contributed to writing the manuscript.

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Correspondence to Lukas Novotny.

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Rondin, L., Gieseler, J., Ricci, F. et al. Direct measurement of Kramers turnover with a levitated nanoparticle. Nature Nanotech 12, 1130–1133 (2017). https://doi.org/10.1038/nnano.2017.198

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