Attosecond timing of photons and electrons one by one

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. 

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).

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].