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Localization and loss of coherence in molecular double-slit experiments

Nature Physics volume 4, pages 649–655 (2008)Cite this article

Abstract

In molecular double-slit experiments, the interference between emitted core electrons of diatomic molecules gives rise to oscillations in the observed electron intensity. Here, we explore this behaviour for photoelectrons emitted from CO and N2 by soft X-ray ionization in the molecular frame, and we argue that in addition to the undisturbed emission process, intramolecular scattering can lead to electron interference between the scattered and unscattered wave in two ways: two-centre interference between two spatially coherent emitters and one-centre self-interference. The latter is the signature of a loss of spatial coherence. The spatial scale over which the transition from two-centre to one-centre coherence occurs is the de Broglie wavelength of the scattered photoelectron in units of the bond length. These results highlight the fact that the molecular double slit is based on two independent uncertainty principles, ΔpxΔx and ΔEΔt, the second of which causes ongoing tunnelling between the two centres, even after the collapse of the electron wavefunction in real space.

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Figure 1: Schematic diagram of the gas-phase photoelectron diffraction experiment on CO.
Figure 2: Photoelectron diffraction intensities versus electron momentum k and de Broglie wavelength λ (in units of the internuclear distance R) for CO molecules in the gas phase.
Figure 3: Schematic diagram of the experimental set-up for the high-resolution angle-resolved photoelectron–fragment ion coincidence experiment on N2.
Figure 4: Photoelectron diffraction intensity versus electron kinetic energy for electron emission along the direction of the molecular axis in the homonuclear molecule N2.
Figure 5: Scattering behaviour of the N+2(N(1s):g, u) photoelectrons.

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References

  1. Jönsson, C. Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten. Z. Phys. 161, 454–474 (1961).

    Article  ADS  Google Scholar 

  2. Zurek, H. W. Decoherence and the transition from quantum to classical. Phys. Today 36–44 (October 1991).

  3. Tegmark, M. Apparent wave function collapse caused by scattering. Found. Phys. Lett. 6, 571–590 (1993).

    Article  Google Scholar 

  4. Rauch, H. & Summhammer, J. Static versus time-dependent absorption in neutron interferometry. Phys. Lett. 104A, 44–46 (1984).

    Article  ADS  Google Scholar 

  5. Mittelstaedt, P., Prieur, A. & Schieder, R. Unsharp particle-wave duality in a photon split-beam experiment. Found. Phys. 17, 891–903 (1987).

    Article  ADS  Google Scholar 

  6. De Martini, F., De Dominicis, L., Cioccolanti, V. & Milani, G. Stochastic interferometer. Phys. Rev. A 45, 5144–5153 (1992).

    Article  ADS  Google Scholar 

  7. Dürr, S., Nonn, T. & Rempe, G. Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer. Nature 395, 33–37 (1998).

    Article  ADS  Google Scholar 

  8. Kokorowski, D.A., Cronin, A.D., Roberts, T. D. & Prichard, D.E. From single- to multiple-photon decoherence in an atom interferometer. Phys. Rev. Lett. 86, 2191–2195 (2001).

    Article  ADS  Google Scholar 

  9. Hackermüller, L., Hornberger, K., Brezger, B., Zeilinger, A. & Arndt, M. Decoherence of matter waves by thermal emission of radiation. Nature 427, 711–714 (2004).

    Article  ADS  Google Scholar 

  10. Cohen, H. D. & Fano, U. Interference in the photo-ionization of molecules. Phys. Rev. 150, 30–33 (1966).

    Article  ADS  Google Scholar 

  11. Englert, B.-G. Fringe visibility and which-way information: An inequality. Phys. Rev. Lett. 77, 2154–2157 (1996).

    Article  ADS  Google Scholar 

  12. Uiberacker, et al. Attosecond real-time observation of electron tunnelling in atoms. Nature 446, 627–632 (2007).

    Article  ADS  Google Scholar 

  13. Pavlychev, A. A. et al. Dynamic properties of N and O 1s−1σu* shape resonances in N2 and CO2 molecules. Phys. Rev. Lett. 81, 3623–3626 (1998).

    Article  ADS  Google Scholar 

  14. Dunningham, J. & Vedral, V. Nonlocality of a single particle. Phys. Rev. Lett. 99, 180404 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  15. Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein–Podolsky–Rosen–Bohm Gedanken experiment: A new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982).

    Article  ADS  Google Scholar 

  16. Rolles, D. et al. Isotope-induced partial localization of core electrons in the homonuclear molecule N2 . Nature 437, 711–715 (2005).

    Article  ADS  Google Scholar 

  17. Akoury, D. et al. The simplest double slit: Interference and entanglement in double photoionization of H2 . Science 318, 949–952 (2007).

    Article  ADS  Google Scholar 

  18. Wollenhaupt, M. et al. Interferences of ultrashort free electron wave packets. Phys. Rev. Lett. 89, 173001 (2002).

    Article  ADS  Google Scholar 

  19. Lindner, F. et al. Attosecond double-slit experiment. Phys. Rev. Lett. 95, 040401 (2005).

    Article  ADS  Google Scholar 

  20. Walborn, S. P., Terra Cunha, M. O., Pádua, S. & Monken, C. H. Double-slit quantum eraser. Phys. Rev. A 65, 33818 (2002).

    Article  ADS  Google Scholar 

  21. Walborn, S. P., Terra Cunha, M. O., Pádua, S. & Monken, C. H. Quantum erasure. Am. Sci. 91, 336–343 (2003).

    Article  Google Scholar 

  22. Liebsch, A. Theory of angular resolved photoemission from adsorbates. Phys. Rev. Lett. 32, 1203–1206 (1974).

    Article  ADS  Google Scholar 

  23. Kevan, S. D., Rosenblatt, D. H., Denley, D., Lu, B.-C. & Shirley, D. A. Normal photoelectron diffraction of the Se 3d level in Se overlayers on Ni (100). Phys. Rev. Lett. 41, 1565–1568 (1978).

    Article  ADS  Google Scholar 

  24. Shigemasa, E. et al. Angular distributions of 1s σ photoelectrons from fixed-in-space N2 molecules. Phys. Rev. Lett. 74, 359–362 (1995).

    Article  ADS  Google Scholar 

  25. Heiser, F. et al. Demonstration of strong forward–backward asymmetry in the C1s photoelectron angular distribution from oriented CO molecules. Phys. Rev. Lett. 79, 2435–2437 (1997).

    Article  ADS  Google Scholar 

  26. Landers, A. et al. Photoelectron diffraction mapping: Molecules illuminated from within. Phys. Rev. Lett. 87, 013002 (2001).

    Article  ADS  Google Scholar 

  27. Becker, U. Angle-resolved electron–electron and electron–ion coincidence spectroscopy: New tools for photoionization studies. J. Electron Spectrosc. Relat. Phenom. 112, 47–65 (2000).

    Article  Google Scholar 

  28. Lucchese, R. R., Raseev, G. & McKoy, V. Studies of differential and total photoionization cross sections of molecular nitrogen. Phys. Rev. A 25, 2572–2578 (1982).

    Article  ADS  Google Scholar 

  29. Zimmermann, B., Wang, K. & McKoy, V. Circular dichroism in K-shell ionization from fixed-in-space CO and N2 . Phys. Rev. A 67, 042711 (2003).

    Article  ADS  Google Scholar 

  30. Hergenhahn, U., Kugeler, O., Rüdel, A., Rennie, E. E. & Bradshaw, A. M. Symmetry-selective observation of the N 1s shape resonance in N2 . J. Phys. Chem. A 105, 5704–5708 (2001).

    Article  Google Scholar 

  31. Liu, X.-J. et al. Young’s double slit experiment using core-level photoemission from N2: Revisiting Cohen–Fano’s two centre interference phenomenon. J. Phys. B 39, 4801–4817 (2006).

    Article  ADS  Google Scholar 

  32. Walter, M. & Briggs, J. Photo-double ionization of molecular hydrogen. J. Phys. B 32, 2487–2501 (1999).

    Article  ADS  Google Scholar 

  33. Fojon, O. A., Fernandez, J., Palacios, A., Rivarola, R. D. & Martin, F. Interference effects in H2 photoionization at high energies. J. Phys. B 37, 3035–3042 (2004).

    Article  ADS  Google Scholar 

  34. Fernandez, J., Fojon, O., Palacios, A. & Martin, F. Interference from fast electron emission in molecular photoionization. Phys. Rev. Lett. 94, 043005 (2007).

    Article  ADS  Google Scholar 

  35. Juanes-Marcos, J. C., Althorpe, S. C. & Wrede, E. Theoretical study of geometric phase effects in the hydrogen-exchange reaction. Science 309, 1227–1230 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  36. Scully, M. O., Englert, W. & Walther, H. Quantum optical test of complementarity. Nature 351, 111–116 (1991).

    Article  ADS  Google Scholar 

  37. Stolterfoht, N. et al. Evidence for interference effects in electron emission from H2 colliding with 60 MeV/u Kr34+ ions. Phys. Rev. Lett. 87, 23201 (2001).

    Article  ADS  Google Scholar 

  38. Misra, D. et al. Interference effect in electron emission in heavy ion collisions with H2 detected by comparison with the measured electron spectrum from atomic hydrogen. Phys. Rev. Lett. 92, 153201 (2004).

    Article  ADS  Google Scholar 

  39. Schöffler, M. S. et al. Ultrafast probing of core hole localization in N2 . Science 320, 920–923 (2008).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support by the Bundesministerium für Bildung und Forschung (BMBF Contract No. 05KS4EB1/3). B.Z. and D.R. thank the Alexander von Humboldt Foundation for a Feodor Lynen fellowship. The authors are grateful to David Shirley for providing the initial beam time for this project at the Advanced Light Source. They also thank E. Moler for his help during this initial period, G. Prümper for his contribution to the development and implementation of the detector and D. Dowek and A. Roy for helpful comments and critical reading of the manuscript.

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Author notes

  1. Björn Zimmermann

    Present address: Present address: Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA (B.Z.),

  2. Daniel Rolles

    Present address: Present address: University of Western Michigan, Kalamazoo, Michigan 49008, USA (D.R.),

  3. Burkhard Langer

    Present address: Present address: Physikalische und Theoretische Chemie, Institut für Chemie, Freie Universität Berlin, 14195 Berlin, Germany (B.L.),

  4. Slobodan Cvejanovic

    Present address: Present address: Medical Faculty, Physics Department, University of Rijeka, 51000 Rijeka, Croatia (S.C.),

  5. Oliver Geßner

    Present address: Present address: Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (O.G.),

  6. Franz Heiser

    Present address: Present address: Ericsson AB, Torshamnsgatan 39 A, 16493 Kista, Sweden (F.H.),

  7. Toralf Lischke

    Present address: Present address: Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany (T.L.),

  8. Jens Viefhaus

    Present address: Present address: Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg, Germany (J.V.),

Authors and Affiliations

  1. California Institute of Technology, Pasadena, California 91125, USA

    Björn Zimmermann & Vincent McKoy

  2. Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany

    Daniel Rolles, Rainer Hentges, Markus Braune, Slobodan Cvejanovic, Oliver Geßner, Franz Heiser, Sanja Korica, Toralf Lischke, Axel Reinköster, Jens Viefhaus & Uwe Becker

  3. Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, 12489 Berlin, Germany

    Burkhard Langer

  4. Institut für Kernphysik, Universität Frankfurt, 60486 Frankfurt, Germany

    Reinhard Dörner

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Contributions

The calculations were carried out by B.Z. and V.M., whereas the measurements and the analysis of the experimental data were done by the other authors.

Corresponding author

Correspondence to Uwe Becker.

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Zimmermann, B., Rolles, D., Langer, B. et al. Localization and loss of coherence in molecular double-slit experiments. Nature Phys 4, 649–655 (2008). https://doi.org/10.1038/nphys993

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