Zeptosecond Birth Time Delay in Molecular Photoionization

Photoionization is a fundamental quantum process that has become a powerful tool to study atoms, molecules, liquids, and solids. Facilitated by the advent of attosecond technology, nowadays it can even be addressed in the time domain. Timing in photoionization usually refers to the time it takes for an electron to escape to the continuum after absorption of the photon. In a recent work, we have uncovered another intriguing aspect of timing in photoionization: The electron is not launched at the same time across a molecular orbital. Rather, the birth time depends on the travel time of the photon across the molecule, which is up to 247 zeptoseconds for the average bond length of molecular hydrogen.
To measure the birth time delay, we utilized the close analogy between the double-slit experiment and electron emission from the two atoms of a homonuclear diatomic molecule (FIG. 1). We irradiated hydrogen molecules with 800 eV photons and measured the interference pattern of fast electrons in the molecular frame of reference (FIG. 2). Finally, we varied the orientation of the molecular frame of reference with respect to the photon propagation direction and observed changes in the electron interference pattern (FIG. 3). From the shifted position of the central interference maximum we calculated the birth time delay.

FIG. 1: Concept of birth time delay measurement. (A) Intensity distribution on a screen in the far field behind the double slit in panel B. (B) A plane wave impinges on a double slit. The phase shift [Δφ] in the right slit causes a tilt of the interference pattern. (C,D) Emission of a photoelectron wave from two indistinguishable atoms of a homonuclear diatomic molecule mimics the double-slit setup in panel B. Here, the angle α is enclosed by the electron momentum vector and the molecular axis. A time delay [Δt] between the emission from one of the two centers, e.g., originating from the travel time of the photon impinging from the left side in panel D, leads to a shift of the interference fringes in panel C. The ratio of slit distance [molecular bond length R, respectively] to wavelength is 1.65 in both cases (B,D). In panel B the right-hand part of the wave is delayed by Δφ = π/2, whereas in panel D a birth time delay of 247 zeptoseconds causes Δφ ≅ π/11 for R = 0.74 Å.

FIG. 2: Interference pattern of fast electrons [E = 735 eV] from one-photon double ionization of H₂ by 800 eV circularly polarized photons for the average internuclear distance of R = 0.74 Å [purple line] in panel A and as function of R in panel B. The blue line in panel A models a double-slit interference pattern for a slit distance of R = 0.74 Å and a wavelength of λ = 0.45 Å, which is the average de Broglie wavelength of the fast electron. The subset S of the data is used for panel A and for the subsequent analysis of the birth time delay.

FIG. 3: Birth time delay of fast electrons [E = 735 eV] from one-photon double ionization of H₂ by 800 eV circularly polarized photons for the average internuclear distance of R = 0.74 Å [selected subset S as shown in Fig. 2 B]. (A) Electron angular distribution with respect to the molecular axis which is aligned parallel to the light propagation direction [cos(β) > 0.87 corresponding to the top row of bins in panel B]. Red curve: Gaussian fit used to obtain the angular position of the zeroth-order maximum cos(α₀). (B) Electron angular distribution in the molecular frame of reference as function of cos(β). Dashed line: perpendicular to molecular axis, i.e., location of the zeroth-order maximum in the absence of birth time delays. (C) Location of the maxima of the zeroth-order interference fringe as function of cos(β). The maxima are obtained using Gaussian fits as indicated by the red line in panel A. The error bars include statistical and systematic errors and the purple-shaded error range indicates the systematical error. Left axis: cos(α₀), right axis: birth time delay. The blue line resembles a birth time delay given by the travel time of light across the molecule. Red line: prediction combining atomic nondipole effects and the travel time of the photon.

Publication:
Zeptosecond Birth Time Delay in Molecular Photoionization
Sven Grundmann, Daniel Trabert, Kilian Fehre, Nico Strenger, Andreas Pier, Leon Kaiser, Max Kircher, Miriam Weller, Sebastian Eckart, Lothar Ph. H. Schmidt, Florian Trinter, Till Jahnke, Markus S. Schöffler, Reinhard Dörner
Science 16 Oct 2020: Vol. 370, Issue 6514, pp. 339-341
DOI: 10.1126/science.abb9318
 
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