|Probing Core-Hole Localization in Molecular Nitrogen|
The behavior of the core hole created in molecular x-ray photoemission experiments has provided molecular scientists with a valuable window through which to probe the electronic structure and dynamics of molecules. But the answer to one fundamental quantum question—whether the core hole is localized or delocalized—has remained elusive for diatomic molecules in which both atoms are the same element. An international team of scientists from the University of Frankfurt in Germany, Berkeley Lab, Kansas State University, and Auburn University has now resolved the issue with an appropriate twist of quantum fuzziness. By means of coincident detection of the photoelectron ejected from molecular nitrogen and the Auger electron emitted femtoseconds later, the team found that how the measurements are done determines which description—localized or delocalized—is valid.
In order to investigate the transition between an atomic (localized) and a molecular (delocalized) description of bound electrons in N2, the researchers made use of circularly polarized photons with an energy 9 eV above the nitrogen 1s-threshold provided by ALS Beamline 11.0.2 to remove one of the innermost electrons from the nitrogen molecule. The photoelectron leaves behind a vacancy in the inner core shell N2+(1s-1), which within 7 fs is filled by an outer shell electron, resulting in the emission of a second electron (an Auger electron) carrying the excess energy. When the photoelectron and Auger electron are detected in coincidence, the Auger electron acts as a probe that in principle can determine exactly where the original hole was created.
The researchers used the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technology to measure the three-dimensional momentum vectors of all four particles simultaneously (angular distribution patterns). Whether an electron is localized or delocalized is encoded in the emission pattern for the ejected electrons; however, to obtain a valid answer, the complete system must be taken into account (photoelectron, Auger electron and N2++ ionic state). Experimentally, one measures the coincident distribution of the photoelectron for a fixed direction of the Auger electron relative to the molecular axis and of the Auger electron for a fixed direction of the photoelectron, as well as the overall (non-coincident) distribution pattern for both electrons.
In this way, the team was able for the first time to identify the existence of a Bell (entangled) state formed by the photoelectron and the Auger electron. In an entangled state, the two electrons are linked in such a way that one cannot be described without reference to the other. In the simplest cases, this means that as soon as a property of one is measured (e.g., the spin of one photon in a two-photon system with net zero spin), the corresponding property of the second is fixed as well. This feature of quantum theory, which stems from the Bell Inequality named for the late European physicist John S. Bell and provides the basis for quantum computation, allowed the team to directly address the question of localization.
Combining the entanglement feature with the symmetry of the components of the electron wave functions, it is possible for certain fixed emission directions to conclude that the innermost electron is localized, so that the second electron can then be assigned to either one of the two nuclei, which causes a right or left asymmetric emission pattern, as the case may be. For certain other fixed emission directions, it proves impossible to determine whether the first electron originated from the left or the right atom of the first electron. In this case the second electron is also delocalized, resulting in a symmetric angular distribution with respect to the molecular axis. In sum, whether you observe localized or delocalized behavior depends on how you look!
Research conducted by M.S. Schöffler, J. Titze, N. Petridis, T. Jahnke, K. Cole, L. Ph.H. Schmidt, A. Czasch, O. Jagutzki, H. Schmidt-Böcking, and R. Dörner (Johann Wolfgang Goethe-Universität Frankfurt am Main, Germany); D. Akoury (Johann Wolfgang Goethe-Universität Frankfurt am Main, Germany, and Berkeley Lab); J.B. Williams and A.L. Landers (Auburn University); N.A. Cherepkov and S.K. Semenov (State University of Aerospace Instrumentation, Russia); C.W. McCurdy, T.N. Rescigno, T. Osipov, S. Lee, M.H. Prior, A. Belkacem and Th. Weber (Berkeley Lab); and C.L. Cocke (Kansas State University)
Research funding: INTAS; the Deutsche Forschungsgemeinschaft; and the U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.
Publication about this research: M.S. Schöffler, J. Titze, N. Petridis, T. Jahnke, K. Cole, L. Ph.H. Schmidt, A. Czasch, D. Akoury, O. Jagutzki, J.B. Williams, N.A. Cherepkov, S.K. Semenov, C.W. McCurdy, T.N. Rescigno, C.L. Cocke, T. Osipov, S. Lee, M.H. Prior, A. Belkacem, A.L. Landers, H. Schmidt-Böcking, Th. Weber, and R. Dörner; "Ultrafast Probing of Core Hole Localization in N2", Science 320, 920 (2008).
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