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Generation of electron Airy beams

Nature volume 494, pages 331–335 (2013)Cite this article

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Abstract

Within the framework of quantum mechanics, a unique particle wave packet exists1 in the form of the Airy function2,3. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton’s laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized4 in the optical domain; later it was generalized to an orthogonal and complete family of beams5 that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories6. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram7,8,9, which imprinted on the electrons’ wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals10, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes5 or trajectories6.

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Figure 1: Exploring the propagation dynamics of the Airy lattice.
Figure 2: Comparison between electrons diffracting from an Airy grating and the electrons diffracting from a reference periodic Bragg grating.
Figure 3: Holographic generation of an electron Airy beam.
Figure 4: Self-healing properties of electron Airy wave packets.

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Acknowledgements

N.V.-B. is an Eshkol scholar. This work was partly supported by the Israel Science Foundation and by the Israeli Ministry of Science. The author wishes to thank K. Shemer and D. Bloch for conversations.

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Authors and Affiliations

  1. Department of Physical Electronics, School of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Noa Voloch-Bloch, Yossi Lereah, Yigal Lilach, Avraham Gover & Ady Arie

Authors
  1. Noa Voloch-Bloch
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  2. Yossi Lereah
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  3. Yigal Lilach
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  4. Avraham Gover
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  5. Ady Arie
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Contributions

N.V.-B. conceived the idea and designed the experiments. N.V.-B. and Y. Lereah carried out the experiment. Y. Lilach optimized the production process and fabricated the nanoscale holograms. A.G. and A.A. did the theoretical work and conceived ideas for applications. A.A. and N.V.-B. analysed the experimental results. A.G., A.A. and Y. Lereah provided experimental and theoretical guidance. A.A. and N.V.-B. developed and analysed the Airy lattice. All authors took part in writing the paper.

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Correspondence to Noa Voloch-Bloch.

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The authors declare no competing financial interests.

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Voloch-Bloch, N., Lereah, Y., Lilach, Y. et al. Generation of electron Airy beams. Nature 494, 331–335 (2013). https://doi.org/10.1038/nature11840

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