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What is the nature of tunnelling? This yet unanswered question is as pertinent today as it was at the dawn of quantum mechanics. This article presents a cross section of current perspectives on the interpretation, computational modelling, and numerical investigation of tunnelling processes in attosecond physics as debated in the Quantum Battles in Attoscience virtual workshop 2020.

We consider the process of high-order harmonics generation (HHG) in the xenon atom enhanced by the inter-shell correlation between the valence 5p and inner 4d shells. We derive the HHG spectrum from a numerical solution of the one-electron time-dependent Schr\"odinger equation multiplied by the enhancement factor taken as the photoionization cross-sections ratio calculated with and without the inter-shell correlation. Such a simplified approach is adequate to describe the experimental HHG spectrum reported by Shiner et al [Nat. Phys. 7, 464 (2011)] generated by a single color IR laser. Similarly, we find good agreement when applied to the two-color driven HHG spectra reported by Facciala et al [Phys. Rev. Lett. 117, 093902 (2016)].

Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schr\"odinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, we highlight a strong dependence of the width of the attoclock angular peak on the molecular orientation and attribute it to the two-center electron interference. This effect is further exemplified in the weakly bound neon dimer., Comment: 8 pages, 7 figures

We demonstrate a clear similarity between attoclock offset angles and Rutherford scattering angles taking the Keldysh tunnelling width as the impact parameter and the vector potential of the driving pulse as the asymptotic velocity. This simple model is tested against the solution of the time-dependent Schr\"odinger equation using hydrogenic and screened (Yukawa) potentials of equal binding energy. We observe a smooth transition from a hydrogenic to 'hard-zero' intensity dependence of the offset angle with variation of the Yukawa screening parameter. Additionally we make comparison with the attoclock offset angles for various noble gases obtained with the classical-trajectory Monte Carlo method. In all cases we find a close correspondence between the model predictions and numerical calculations. This suggests a largely Coulombic origin of the attoclock offset angle and casts further doubt on its interpretation in terms of a finite tunnelling time.

We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schr\"odinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy {\beta} parameter and Wigner time delay ${\tau}_W$ for the single XUV photon absorption which initiates the RABBITT process. Said {\beta} and ${\tau}_W$ parameters are compared with calculations in the random phase approximation with exchange (RPAE) which includes inter-shell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulation of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d-shell restricts the validity of the single active electron approximation to several tens of eV above the valence shell threshold.

Tunnelling, one of the key features of quantum mechanics, ignited an ongoing debate about the value, meaning and interpretation of 'tunnelling time'. Until recently the debate was purely theoretical, with the process considered to be instantaneous for all practical purposes. This changed with the development of ultrafast lasers and in particular, the 'attoclock' technique that is used to probe the attosecond dynamics of electrons. Although the initial attoclock measurements hinted at instantaneous tunnelling, later experiments contradicted those findings, claiming to have measured finite tunnelling times. In each case these measurements were performed with multi-electron atoms. Atomic hydrogen (H), the simplest atomic system with a single electron, can be 'exactly' (subject only to numerical limitations) modelled using numerical solutions of the 3D-TDSE with measured experimental parameters and acts as a convenient benchmark for both accurate experimental measurements and calculations. Here we report the first attoclock experiment performed on H and find that our experimentally determined offset angles are in excellent agreement with accurate 3D-TDSE simulations performed using our experimental pulse parameters. The same simulations with a short-range Yukawa potential result in zero offset angles for all intensities. We conclude that the offset angle measured in the attoclock experiments originates entirely from electron scattering by the long-range Coulomb potential with no contribution from tunnelling time delay. That conclusion is supported by empirical observation that the electron offset angles follow closely the simple formula for the deflection angle of electrons undergoing classical Rutherford scattering by the Coulomb potential. Thus we confirm that, in H, tunnelling is instantaneous (with an upperbound of 1.8 as) within our experimental and numerical uncertainty., Comment: 7 figures

We apply the convergent close-coupling (CCC) formalism to analyse the processes of laser assisted electron impact ionisation of He, and the attosecond time delay in the photodetachment of the H^{-} ion and the photoionisation of He. Such time dependent atomic collision processes are of considerable interest as experimental measurements on the relevant timescale (attoseconds 10^{-18} s) are now possible utilising ultrafast and intense laser pulses. These processes in particular are furthermore of interest as they are strongly influenced by many-electron correlations. In such cases their theoretical description requires a more comprehensive treatment than that offered by first order perturbation theory. We apply such a treatment through the use of the CCC formalism which involves the complete numeric solution of the integral Lippmann-Schwinger equations pertaining to a particular scattering event. For laser assisted electron impact ionisation of He such a treatment is of a considerably greater accuracy than the majority of previous theoretical descriptions applied to this problem which treat the field-free scattering event within the first Born approximation. For the photodetachment of H^{-} and photoionisation of He, the CCC approach allows for accurate calculation of the attosecond time delay and comparison with the companion processes of photoelectron scattering on H and He^{+}, respectively.