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.

  • Article
  • Published:

Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy

Nature Photonics volume 11, pages 793–797 (2017)Cite this article

Subjects

Abstract

Ultrafast electron and X-ray imaging and spectroscopy are the basis for an ongoing revolution in the understanding of dynamical atomic-scale processes in matter. The underlying technology relies heavily on laser science for the generation and characterization of ever shorter pulses. Recent findings suggest that ultrafast electron microscopy with attosecond-structured wavefunctions may be feasible. However, such future technologies call for means to both prepare and fully analyse the corresponding free-electron quantum states. Here, we introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond electron pulse trains. Phase-locked optical fields coherently control the electron wavefunction along the beam direction. We establish a new variant of quantum state tomography—‘SQUIRRELS’—for free-electron ensembles. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron–matter entanglement and new forms of ultrafast electron microscopy down to the attosecond regime.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Experimental scheme.
Fig. 2: SQUIRRELS reconstruction of the free-electron quantum state.
Fig. 3: Application of SQUIRRELS to spatially separated optical near-fields.
Fig. 4: Experimental demonstration of attosecond electron pulse trains.

Similar content being viewed by others

References

  1. Gustafsson, M. G. L. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J. Microsc. 198, 82–87 (2000).

    Article  Google Scholar 

  2. Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 1929–1960 (2000).

    Article  ADS  Google Scholar 

  3. Mukamel, S. Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations. Annu. Rev. Phys. Chem. 51, 691–729 (2000).

    Article  ADS  Google Scholar 

  4. Kira, M., Koch, S. W., Smith, R. P., Hunter, A. E. & Cundiff, S. T. Quantum spectroscopy with Schrödinger-cat states. Nat. Phys. 7, 799–804 (2011).

    Article  Google Scholar 

  5. Guzzinati, G. et al. Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nat. Commun. 8, 14999 (2017).

    Article  ADS  Google Scholar 

  6. McMorran, B. J. et al. Electron vortex beams with high quanta of orbital angular momentum. Science 331, 192–195 (2011).

    Article  ADS  Google Scholar 

  7. Verbeeck, J., Tian, H. & Schattschneider, P. Production and application of electron vortex beams. Nature 467, 301–304 (2010).

    Article  ADS  Google Scholar 

  8. Echternkamp, K. E., Feist, A., Schäfer, S. & Ropers, C. Ramsey-type phase control of free-electron beams. Nat. Phys. 12, 1000–1004 (2016).

    Article  Google Scholar 

  9. Kruit, P. et al. Designs for a quantum electron microscope. Ultramicroscopy 164, 31–45 (2016).

    Article  Google Scholar 

  10. Bressler, C. & Chergui, M. Ultrafast X-ray absorption spectroscopy. Chem. Rev. 104, 1781–1812 (2004).

    Article  Google Scholar 

  11. Wernet, P. et al. Orbital-specific mapping of the ligand exchange dynamics of Fe(CO)5 in solution. Nature 520, 78–81 (2015).

    Article  ADS  Google Scholar 

  12. Beaud, P. et al. A time-dependent order parameter for ultrafast photoinduced phase transitions. Nat. Mater. 13, 923–927 (2014).

    Article  ADS  Google Scholar 

  13. Miller, R. J. D. Femtosecond crystallography with ultrabright electrons and X-rays: capturing chemistry in action. Science 343, 1108–1116 (2014).

    Article  ADS  Google Scholar 

  14. Kealhofer, C. et al. All-optical control and metrology of electron pulses. Science 352, 429–433 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).

    Article  ADS  Google Scholar 

  16. Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).

    Article  ADS  Google Scholar 

  17. Grguraš, I. et al. Ultrafast X-ray pulse characterization at free-electron lasers. Nat. Photon. 6, 852–857 (2012).

    Article  ADS  Google Scholar 

  18. Chapman, H. N. et al. Femtosecond X-ray protein nanocrystallography. Nature 470, 73–77 (2011).

    Article  ADS  Google Scholar 

  19. Popmintchev, T. et al. Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers. Science 336, 1287–1291 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  20. Silva, F., Teichmann, S. M., Cousin, S. L., Hemmer, M. & Biegert, J. Spatiotemporal isolation of attosecond soft X-ray pulses in the water window. Nat. Commun. 6, 6611 (2015).

    Article  ADS  Google Scholar 

  21. Maxson, J. et al. Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance. Phys. Rev. Lett. 118, 154802 (2017).

    Article  ADS  Google Scholar 

  22. Chatelain, R. P., Morrison, V. R., Godbout, C. & Siwick, B. J. Ultrafast electron diffraction with radio-frequency compressed electron pulses. Appl. Phys. Lett. 101, 081901 (2012).

    Article  ADS  Google Scholar 

  23. Gliserin, A., Walbran, M., Krausz, F. & Baum, P. Sub-phonon-period compression of electron pulses for atomic diffraction. Nat. Commun. 6, 8723 (2015).

    Article  ADS  Google Scholar 

  24. van Oudheusden, T. et al. Compression of subrelativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction. Phys. Rev. Lett. 105, 264801 (2010).

    Article  ADS  Google Scholar 

  25. Wimmer, L. et al. Terahertz control of nanotip photoemission. Nat. Phys. 10, 432–436 (2014).

    Article  Google Scholar 

  26. Feist, A. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200–203 (2015).

    Article  ADS  Google Scholar 

  27. Kozak, M. et al. Optical gating and streaking of free electrons with sub-optical cycle precision. Nat. Commun. 8, 14342 (2017).

    Article  ADS  Google Scholar 

  28. Zewail, A. H. Four-dimensional electron microscopy. Science 328, 187–193 (2010).

    Article  ADS  Google Scholar 

  29. Flannigan, D. J. & Zewail, A. H. 4D electron microscopy: principles and applications. Acc. Chem. Res. 45, 1828–1839 (2012).

    Article  Google Scholar 

  30. Weathersby, S. P. et al. Mega-electron-volt ultrafast electron diffraction at SLAC National Accelerator Laboratory. Rev. Sci. Instrum. 86, 073702 (2015).

    Article  ADS  Google Scholar 

  31. Feist, A. et al. Ultrafast transmission electron microscopy using a laser-driven field emitter: femtosecond resolution with a high coherence electron beam. Ultramicroscopy 176, 63–73 (2017).

    Article  Google Scholar 

  32. Baum, P. & Zewail, A. H. Attosecond electron pulses for 4D diffraction and microscopy. Proc. Natl Acad. Sci. USA 104, 18409–18414 (2007).

    Article  ADS  Google Scholar 

  33. Hilbert, S. A., Uiterwaal, C. J., Barwick, B., Batelaan, H. & Zewail, A. H. Temporal lenses for attosecond and femtosecond electron pulses. Proc. Natl Acad. Sci. USA 106, 10558–10563 (2009).

    Article  ADS  Google Scholar 

  34. Hassan, M. T., Baskin, J. S., Liao, B. & Zewail, A. H. High-temporal-resolution electron microscopy for imaging ultrafast electron dynamics. Nat. Photon. 11, 425–430 (2017).

    Article  ADS  Google Scholar 

  35. Barwick, B., Flannigan, D. J. & Zewail, A. H. Photon-induced near-field electron microscopy. Nature 462, 902–906 (2009).

    Article  ADS  Google Scholar 

  36. Park, S. T., Lin, M. & Zewail, A. H. Photon-induced near-field electron microscopy (PINEM): theoretical and experimental. New J. Phys. 12, 123028 (2010).

    Article  ADS  Google Scholar 

  37. García de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Multiphoton absorption and emission by interaction of swift electrons with evanescent light fields. Nano Lett. 10, 1859–1863 (2010).

    Article  ADS  Google Scholar 

  38. Piazza, L. et al. Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field. Nat. Commun. 6, 6407 (2015).

    Article  Google Scholar 

  39. García de Abajo, F. J. Optical excitations in electron microscopy. Rev. Mod. Phys. 82, 209–275 (2010).

    Article  ADS  Google Scholar 

  40. Wollenhaupt, M., Bayer, T. & Baumert, T. in Ultrafast Dynamics Driven by Intense Light Pulses (eds Kitzler, M. & Gräfe, S.) 63–122 (Springer, Switzerland, 2016).

  41. Paris, M. & Řeháček, J. (eds) Quantum State Estimation (Springer, Berlin, 2004).

    MATH  Google Scholar 

  42. Schleich, W. P. Quantum Optics in Phase Space (Wiley-VCH, Hoboken, NJ, 2015).

    MATH  Google Scholar 

  43. Trebino, R. Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, Berlin, 2000).

    Book  Google Scholar 

  44. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).

    Article  ADS  Google Scholar 

  45. Wigner, E. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932).

    Article  ADS  MATH  Google Scholar 

  46. Nogues, G. et al. Measurement of a negative value for the Wigner function of radiation. Phys. Rev. A 62, 54101 (2000).

    Article  ADS  Google Scholar 

  47. Hemsing, E. et al. Echo-enabled harmonics up to the 75th order from precisely tailored electron beams. Nat. Photon. 10, 512–515 (2016).

    Article  ADS  Google Scholar 

  48. Sears, C. M. S. et al. Production and characterization of attosecond electron bunch trains. Phys. Rev. ST Accel. Beams 11, 061301 (2008).

    Article  ADS  Google Scholar 

  49. Diosi, L. A Short Course in Quantum Information Theory: An Approach From Theoretical Physics (Springer, Berlin, 2011).

    Book  MATH  Google Scholar 

  50. Engl, H. W., Hanke, M. & Neubauer, A. Regularization of Inverse Problems (Kluwer Academic, Dorcrecht, 2000).

    MATH  Google Scholar 

  51. Kaipio, J. P. & Somersalo, E. Statistical and Computational Inverse Problems (Springer-Verlag, New York, 2005).

    MATH  Google Scholar 

  52. Vandenberghe, L. & Boyd, S. Semidefinite Programming. SIAM Rev. 38, 49–95 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  53. Rockafellar, R. T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877–898 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  54. Toh, K. C., Tütüncü, R. H. & Todd, M. J. Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Pac. J. Optim. 3, 135–164 (2007).

    MathSciNet  MATH  Google Scholar 

  55. Toh, K. C., Todd, M. J. & Tütüncü, R. H. SDPT3—a Matlab software package for semidefinite programming, Version 1.3. Optim. Method. Softw. 11, 545–581 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  56. Bourassin-Bouchet, C. & Couprie, M.-E. Partially coherent ultrafast spectrography. Nat. Commun. 6, 6465 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) (Schwerpunktprogramm (SPP) 1840 ‘Quantum Dynamics in Tailored Intense Fields’, Sonderforschungsbereich (SFB) 1073 ‘Atomic Scale Control of Energy Conversion’, project A05, and SFB 755 ‘Nanoscale Photonic Imaging’, projects C08 and C09), support by the Lower Saxony Ministry of Science and Culture, and funding of the instrumentation by the DFG and VolkswagenStiftung. The authors thank O. Kfir for discussions. T.H. thanks A. Fischer (Göttingen) and K.-C. Toh (Singapore) for discussions on semidefinite programming.

Author information

Authors and Affiliations

  1. 4th Physical Institute – Solids and Nanostructures, University of Göttingen, Göttingen, Germany

    Katharina E. Priebe, Christopher Rathje, Sergey V. Yalunin, Armin Feist, Sascha Schäfer & Claus Ropers

  2. Institut für Numerische und Angewandte Mathematik, University of Göttingen, Göttingen, Germany

    Thorsten Hohage

  3. International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany

    Claus Ropers

Authors
  1. Katharina E. Priebe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher Rathje
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergey V. Yalunin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thorsten Hohage
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Armin Feist
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sascha Schäfer
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Claus Ropers
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

K.E.P. built the two-colour interferometer set-up, conducted the two-colour experiments with contributions from A.F., analysed the data, and tested the reconstruction algorithm. Ch.R. conducted measurements of the attosecond pulse trains and analysed the data, both with contributions from K.E.P. S.V.Y. and Cl.R. devised the quantum state reconstruction scheme, which was implemented by S.V.Y. The reconstruction algorithm using regularization and semidefinite programming (SDP) was developed by T.H. with contributions from S.V.Y. The manuscript was written by K.E.P. and Cl.R., with contributions from all authors. Cl.R. and S.S. conceived and directed the study. All authors discussed the results and the interpretation.

Corresponding author

Correspondence to Claus Ropers.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Supplementary Information

Supplementary Figures 1–7.

Experiment code

Code for the SQUIRRELS algorithm used to reconstruct the free-electron density matrix.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Priebe, K.E., Rathje, C., Yalunin, S.V. et al. Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy. Nature Photon 11, 793–797 (2017). https://doi.org/10.1038/s41566-017-0045-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-017-0045-8

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