In the research area of strong-laser-field interactions and attosecond science 1 , tunnelling of an electron through the barrier formed by the electric field of the laser and the atomic potential is typically assumed to be the initial key process that triggers subsequent dynamics [1][2][3] . Here we use the attoclock technique 4 to obtain experimental information about the electron tunnelling geometry (the natural coordinates of the tunnelling current flow) and exit point. We confirm vanishing tunnelling delay time, show the importance of the inclusion of Stark shifts 5,6 and report on multi-electron effects clearly identified by comparing results in argon and helium atoms. Our combined theory and experiment allows us to single out the geometry of the inherently one-dimensional tunnelling problem, through an asymptotic separation of the full three-dimensional problem. Our findings have implications for laser tunnel ionization in all atoms and in particular in larger molecular systems with correspondingly larger dipoles and polarizabilities.One of the most striking manifestations of the rules of quantum mechanics is the possibility for a particle to move from one side of a potential barrier to the other regardless of the energy height of that barrier. This includes the classically forbidden case, referred to as tunnelling, where the potential energy of the barrier is higher than the energy of the particle (Fig. 1a). In linearly polarized laser fields, electron tunnelling is expected to eventually lead to above-threshold ionization, enhanced double ionization and coherent emission up to the X-ray regime with high-order harmonic generation [7][8][9][10] . Therefore, a detailed understanding of the tunnelling step is of paramount importance for attosecond science, including generation of attosecond pulses 11,12 and attosecond measurement techniques 4,13,14 . The attoclock 4 is an attosecond streaking technique 13 . The rotating electric field vector of a close-to-circularly polarized laser field gives the time reference, in a manner similar to the hands of a clock, and the time is measured by counting fractions of cycles with the exact angular position of the rotating electric field. In this way it is possible to obtain attosecond time resolution by employing a femtosecond pulse. The attoclock was used to set an upper limit to the tunnelling delay time during the tunnel ionization process in helium 15 , and to measure the ionization times in double ionization of argon 16,17 . For the attoclock, a very short few-femtosecond pulse is used to both ionize an atom and to provide the time reference. The pulse duration is kept sufficiently short such that the ionization event is limited to within one optical cycle around the peak of the pulse. As a result of the close-to-circular polarization, re-scattering of the liberated electron with the parent ion is mostly suppressed. Assuming classical 1 Physics Department, ETH Zurich, 8093 Zurich, Switzerland, 2 Lundbeck Foundation Theoretical Center for Quantum System Research, De...

The combination of photoelectron spectroscopy and ultrafast light sources is on track to set new standards for detailed interrogation of dynamics and reactivity of molecules [1][2][3][4][5][6][7]. A crucial prerequisite for further progress is the ability to not only detect the electron kinetic energy, as done in traditional photoelectron spectroscopy, but also the photoelectron angular distributions (PADs) in the molecular frame [1,4,5,[7][8][9][10]. Until recently the only method relied on determining the orientation of the molecular frame after ionization [1,[11][12][13].This requires that ionization leads to fragmentation thereby limiting both the species and the specific processes that can be studied. An attractive alternative is to fix the molecular frame prior to ionization. The only demonstrations hitherto involved aligned small linear unpolar molecules [4,5,8]. A decisive milestone is extension to the general class of polar molecules. Here carbonylsulfide (OCS) and benzonitrile (C 7 H 5 N) molecules, fixed in space by combined laser and electrostatic fields, are ionized with intense, circularly polarized, 30 femtosecond laser pulses. For 1-dimensionally oriented OCS the molecular frame PADs exhibit pronounced anisotropies, perpendicular to the fixed permanent dipole moment, that are absent in PADs from randomly oriented molecules.For 3-dimensionally oriented C 7 H 5 N additional striking structures appear due to suppression of electron emission in nodal planes of the fixed electronic orbitals. Our theoretical analysis, relying on tunneling ionization theory [14,15], shows that the PADs reflect nodal planes, permanent dipole moments and polarizabilities of both the neutral molecule and its cation. The calculated results are exponentially sensitive to changes in these molecular properties thereby pointing to exciting opportunities for time-resolved probing of valence electrons dynamics by intense circularly polarized pulses. Molecular frame PADs from oriented molecules will prove important in other contexts notably in emerging free-electron-laser studies where localized inner shell electrons are knocked off by x-ray pulses.Experimentally a target of adiabatically aligned and oriented molecules is created by the combined action of a 10 nanosecond laser pulse and a weak static electric field [16,17].Here alignment refers to confinement of molecule-fixed axes along laboratory fixed axes, and orientation refers to the molecular dipole moment pointing in a particular direction 2 [18]. Before reaching the interaction point with the laser pulses and the static field the molecules are selected in the lowest-lying rotational quantum states by an electrostatic deflector [19]. Hereby alignment and orientation is optimized, which is crucial for observation of the molecular frame PAD effects discussed next. The degree of alignment and orientation is initially measured by Coulomb exploding the molecules using an intense femtosecond (fs) probe laser pulse ( Supplementary Information, SI).For the PAD experiments a circul...

Abstract. We present an ellipticity resolved study of momentum distribution arising from strong-field ionization of helium. The influence of the ion potential on the departing electron is considered within a semi-classical model consisting of an initial tunneling step and subsequent classical propagation. We find that the momentum distribution can be explained by including the longitudinal momentum spread of the electron at the exit from the tunnel. Our combined experimental and theoretical study provides an estimate of this momentum spread.In strong-field physics and attoscience, it is often assumed that tunnel ionization is the first step that initiates the subsequent dynamics [1]. Therefore, the understanding of the electron-parent ion interaction in the presence of a femtosecond laser pulse is of fundamental importance to draw conclusions on various types of experiments. Providing a physical insight into this interaction, semiclassical models are indispensable for guiding ultrafast experiments and inventing new ultrafast measurement techniques such as tomography of molecular orbitals [2] and the attoclock [3] for example.In the semiclassical model of strong-field ionization different steps explain the overall dynamics starting with the initial tunnel process followed by classical trajectories and potential rescattering or recombination. In a recent attoclock experiments [4] we obtained experimental information about the electron tunneling geometry (the natural coordinates of the tunneling current flow) and showed the importance of accurately accounting for the effective potential with the exact tunnel exit in semiclassical models. However, to date we did not address the momentum space distribution of the electron wavepacket at the tunnel exit. The momentum spread of the electronic wavepacket in the direction transverse to the field has been extensively studied both theoretically and experimentally [5]. Here we present experimental results, which can be explained with an initial longitudinal momentum spread of the electron at the tunnel exit.The momentum spread of the electronic wavepacket at the tunnel exit point in the longitudinal direction has recently raised substantial interest. Tunneling theories impose the longitudinal spread at the tunnel exit to be zero [6]. However, a zero initial longitudinal momentum spread has failed to explain our experimental results. We measured the ion momentum distributions arising from strongfield ionization of helium in the tunneling regime, recorded over the full range of ellipticity. By comparing the experimental momentum distributions with the classical trajectory Monte Carlo (CTMC) simulations based on the Tunnel Ionization in Parabolic coordinates with Induced dipole This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.