Attosecond timing of photons and electrons one by one

We measured for the first time how the absorption and emission of a single photon alters the angular momentum dependent dynamics of an electron that is not bound to an atomic nucleus, but still feels its Coulomb potential.

[465] J. Fuchs, N. Douguet, S. Donsa, F. Martin. J. Burgdörfer, L. Argenti, L. Cattaneo, U. Keller 
Download "Time delays from one-​photon transitions in the continuum" (PDF, 2.5 MB)
Optica, vol. 7, No. 2, pp. 154-​161, 2020
doi: external page 10.1364/OPTICA.378639

ETH news: Photons and electrons one on one
English 
German

Phys.org: external page https://phys.org/

SpaceDaily.com: external page https://www.spacedaily.com/

Introduction

Free electrons can interact with light only via Compton scattering. In a Coulomb continuum, however, electrons can absorb or emit photons. Such continuum-continuum (cc) transitions [1] are commonly exploited in a variety of attosecond photoionization experiments in order to extract delays originating from the propagation of the liberated electron wave packet across the ionic potential [2]. In this work, we present a novel experimental protocol, which allows us to disentangle the contributions of multiple interfering quantum pathways in such experiments. This enables to retrieve a time delay arising purely due to the cc-transitions, which is a significant contribution to the total attosecond photoionization delay. 

Experimental Principle and Quantum Path Disentanglement

photoionization pathways and experimental anisotropy parameters
(a) Schematic of the photoionization pathways contributing to a sideband (SB) in the RABBITT experiment in Helium. (b)-(d) Experimental anisotropy parameters (β_0, β_2, β_4) of the angle resolved RABBITT spectra. Insets: angular distribution terms.

We perform angle resolved photoelectron spectroscopy in helium using a COLTRIMS detector [3] following the RABBITT scheme [4]. As illustrated in Figure 1a, four quantum pathways contribute to each sideband (SB), comprising the pathways with angular quantum numbers s->p->s and s->p->d for absorption and emission [5]. This allows us to reduce the angular dependence of the measured RABBITT spectra to a set of three anisotropy parameters (Figure 1b-d) for which analytic expression can be determined within second order perturbation theory. A simultaneous fit of the sideband oscillations of the anisotropy parameters then retrieves both, the amplitudes and the relative phases of the four contributing quantum pathways. Further, comparing the relative phase between pathways following the absorption of the same XUV photon, both XUV and Wigner phase cancel out and, hence, the contribution of the cc-transitions to the photoionization phase can be isolated.

Photoionization Time Delay and Discussion

We retrieve the energy-dependent phase difference between electron wave packets arising from cc-transitions to an s-wave with respect to a d-wave, both for absorption and emission, and across different energies, directly from the experiment. As shown in figure 2a, the experimentally retrieved values are in excellent agreement with the theoretical results from two independent simulation methods: a single-active-electron simulations [6] and an ab-initio calculation [7]. From the retrieved phase difference two interesting effects for the electron wave packet upon photoionization process can be inferred: (i) The d-wave packet is retarded with respect to the s-wave packet; (ii) there is a different offset phase of the partial wave packets center frequency with respect to their envelope, i.e. an analogue to the carrier envelope phase slip (CEP). Both quantities strongly depend on the center energy of the electron wave packet, as visualized in figure 2b. While (ii) is of pure quantum mechanical nature, (i) has a fundamental classical origin: the larger fraction of rotational energy of the d-wave implies a lower radial energy, and, hence, a slower outward propagation. This angular momentum contribution to the photoionization time delay is shown to be universal, i.e. independent of short-range potential contributions of different species [8], as e.g. simulations in atomic hydrogen suggest (figure 2a).

Retrieved phase difference
(a) Retrieved phase difference between continuum-continuum transitions to s- and d-wave for the absorption case. (b) Time delay and absolute phase offset between the s- and d-wave partial waves.

This work not only serves as a proof-of-principle demonstration how to disentangle the contributions of multiple interfering quantum pathways in photoionization experiments but also reveal new physical insights. Our novel technique enables to demonstrate and quantify the angular momentum contribution to the continuum part of the photoionization time delay. To the best of our knowledge, this is the first experimental evidence of time delays between one-photon transitions in the electronic continuum [8].

References

[1] J. M. Dahlström, D. Guénot, K. Klünder, M. Gisselbrecht, J. Mauritsson, A. L’Huillier, A. Maquet, and R. Taïeb, "Theory of attosecond delays in laser-assisted photoionization," Chemical Physics 414, 53-64 (2013).

[2] M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, "Delay in photoemission.," Science (New York, N.Y.) 328, 1658-1662 (2010).

[3] R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, and H. Schmidt-Böcking, "Cold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamics," Physics Reports 330, 95-192 (2000).

[4] L. Cattaneo, J. Vos, M. Lucchini, L. Gallmann, C. Cirelli, and U. Keller, "Comparison of attosecond streaking and RABBITT," Optics Express 24, 29060 (2016).

[5] S. Heuser, Á. Jiménez Galán, C. Cirelli, C. Marante, M. Sabbar, R. Boge, M. Lucchini, L. Gallmann, I. Ivanov, A. S. Kheifets, J. M. Dahlström, E. Lindroth, L. Argenti, F. Martín, and U. Keller, "Angular dependence of photoemission time delay in helium," Physical Review A 94, 063409 (2016).

[6] N. Douguet, A. N. Grum-Grzhimailo, E. V. Gryzlova, E. I. Staroselskaya, J. Venzke, and K. Bartschat, "Photoelectron angular distributions in bichromatic atomic ionization induced by circularly polarized VUV femtosecond pulses," Physical Review A 93, 033402 (2016).

[7] S. Donsa, I. Březinová, H. Ni, J. Feist, and J. Burgdörfer, "Polarization tagging of two-photon double ionization by elliptically polarized XUV pulses," Physical Review A 99, 023413 (2019).

[8] J. Fuchs, N. Douguet, S. Donsa, F. Martin, J. Burgdörfer, L. Argenti, L. Cattaneo, and U. Keller, "Time delays from one-photon transitions in the continuum," preprint ArXiv 1907.03607 (2019).