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Observation of the Kapitza–Dirac effect


In their famous 1927 experiment, Davisson and Germer observed1 the diffraction of electrons by a periodic material structure, so showing that electrons can behave like waves. Shortly afterwards, Kapitza2 and Dirac3 predicted that electrons should also be diffracted by a standing light wave4. This Kapitza–Dirac effect is analogous to the diffraction of light by a grating, but with the roles of the wave and matter reversed. The electron and the light grating interact extremely weakly, via the ‘ponderomotive potential’5, so attempts to measure the Kapitza–Dirac effect had to wait for the development of the laser. The idea6 that the underlying interaction with light is resonantly enhanced for electrons in an atom led to the observation7 that atoms could be diffracted by a standing wave of light. Deflection of electrons by high-intensity laser light, which is also a consequence of the Kapitza–Dirac effect, has also been demonstrated8. But the coherent interference that characterizes wave diffraction has not hitherto been observed9,10. Here we report the diffraction of free electrons from a standing light wave—a realization of the Kapitza–Dirac effect as originally proposed.

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Figure 1: Schematic of our apparatus.
Figure 2: Experimental data.


  1. Davisson, C. & Germer, L. H. The scattering of electrons by a single crystal of nickel. Nature 119, 558–560 (1927).

    Article  CAS  ADS  Google Scholar 

  2. Mott, N. Man of courage. Nature 350, 31 (1991).

    Article  ADS  Google Scholar 

  3. Aitchison, I. Spin doctors. Nature 392, 771–773 (1998).

    Article  ADS  Google Scholar 

  4. Kapitza, P. L. & Dirac, P. A. M. The reflection of electrons from standing light waves. Proc. Camb. Phil. Soc. 29, 297–300 (1933).

    Article  ADS  Google Scholar 

  5. Boot, H. A. H. & Harvie, R. B. R.-S. Charged particles in a non-uniform radio-frequency field. Nature 180, 1187 (1957).

    Article  ADS  Google Scholar 

  6. Altshuler, S., Frantz, L. M. & Braunstein, R. Reflection of atoms from standing light waves. Phys. Rev. Lett. 17, 231–232 (1966).

    Article  CAS  ADS  Google Scholar 

  7. Gould, P. L., Ruff, G. A. & Pritchard, D. E. Diffraction of atoms by light: the near-resonant Kapitza–Dirac effect. Phys. Rev. Lett. 56, 827–830 (1986).

    Article  CAS  ADS  Google Scholar 

  8. Bucksbaum, P. H., Schumacher, D. W. & Bashkansky, M. High intensity Kapitza–Dirac effect. Phys. Rev. Lett. 61, 1182–1185 (1988).

    Article  CAS  ADS  Google Scholar 

  9. Adams, C. S., Sigel, M. & Mlynek, J. Atom optics. Phys. Rep. 240, 143–210 (1994).

    Article  CAS  ADS  Google Scholar 

  10. Fedorov, M. V. in Laser Science and Technology; An International Handbook No. 13, 1–77 (Harwood Academic, New York, 1991).

    Google Scholar 

  11. Batelaan, H. The Kapitza–Dirac effect. Contemp. Phys. 41, 369–381 (2000).

    Article  CAS  ADS  Google Scholar 

  12. Bartell, L. S., Roskos, R. R. & Thompson, H. B. Reflection of electrons by standing light waves: experimental study. Phys. Rev. 166, 1494–1504 (1968).

    Article  CAS  ADS  Google Scholar 

  13. Schwartz, H., Tourtelotte, H. A. & Gaertner, W. W. Direct observation of nonlinear scattering of electrons by laser beam. Phys. Lett. 19, 202–203 (1965).

    Article  ADS  Google Scholar 

  14. Takeda, Y. & Matsui, I. Electron reflection by standing wave of giant laser pulse. J. Phys. Soc. Jpn 25, 1202 (1968).

    Article  ADS  Google Scholar 

  15. Pfeiffer, H.-Chr. Experimentelle prüfung der streuwahrscheinlichkeit für elektronen beim Kapitza–Dirac-effekt. Phys. Lett. A 26, 362–363 (1968).

    Article  ADS  Google Scholar 

  16. Schwarz, H. The Kapitza–Dirac effect at high laser intensities. Phys. Lett. A 43, 457–478 (1973).

    Article  ADS  Google Scholar 

  17. Fedorov, M. V. Stimulated scattering of electrons by photons and adiabatic switching on hypothesis. Opt. Commun. 12, 205–209 (1974).

    Article  ADS  Google Scholar 

  18. Rasel, E., Oberthaler, M. K., Batelaan, H., Schmeidmayer, J. & Zeilinger, A. Atom wave interferometry with diffraction gratings of light. Phys. Rev. Lett. 75, 2633–2637 (1995).

    Article  CAS  ADS  Google Scholar 

  19. Forrey, R. C., Dalgarno, A. & Schmiedmayer, J. Determining the electron forward-scattering amplitude using electron interferometry. Phys. Rev. A 59, R942–R945 (1999).

    Article  CAS  ADS  Google Scholar 

  20. Meshulach, D. & Silverberg, Y. Coherent quantum control of two-photon transitions by a femtosecond laser pulse. Nature 396, 239–242 (1998).

    Article  CAS  ADS  Google Scholar 

  21. Larsen, J. J., Wendt-Larsen, I. & Stapelfeldt, H. Controlling the branching ratio of photodissociation using aligned molecules. Phys. Rev. Lett. 83, 1123–1126 (1999).

    Article  CAS  ADS  Google Scholar 

  22. Robinson, J. C. et al. Can a single-pulse standing wave induce chaos in atomic motion? Phys. Rev. Lett. 76, 3304–3307 (1996).

    Article  CAS  ADS  Google Scholar 

  23. Steck, D. A., Milner, V., Oskay, W. H. & Raizen, M. G. Quantitative study of amplitude noise effects on dynamical localization. Phys. Rev. E 62, 3461–3475 (2000).

    Article  CAS  ADS  Google Scholar 

  24. Bucksbaum, P. H. Atoms in Strong Fields (ed. Nicolaides, C. A.) 381–405 (Plenum, New York, 1990).

    Book  Google Scholar 

  25. Sleator, T., Pfau, T., Balykin, V., Carnal, O. & Mlynek, J. Experimental demonstration of the optical Stern–Gerlach effect. Phys. Rev. Lett. 68, 1996–1999 (1992).

    Article  CAS  ADS  Google Scholar 

  26. Batelaan, H., Gay, T. J. & Schwendiman, J. J. Stern–Gerlach effect for electron beams. Phys. Rev. Lett. 79, 4517–4521 (1997).

    Article  CAS  ADS  Google Scholar 

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We thank P. Burrow, G. Gallup and T. Gay for discussions. This work was supported by the Research Corporation, the NRI and the NSF Experimental Program to Stimulate Competitive Research.

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Correspondence to Herman Batelaan.

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Freimund, D., Aflatooni, K. & Batelaan, H. Observation of the Kapitza–Dirac effect. Nature 413, 142–143 (2001).

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