We present an ellipticity resolved study of momentum distributions arising from strong-field ionization of Helium at constant intensity. 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 the presence of a 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.
Based on the strong-field approximation, we obtain analytical expressions for the initial momentum at the tunnel exit and instantaneous ionization rate of tunneling ionization in elliptically polarized laser fields with arbitrary ellipticity. The tunneling electron reveals a nonzero offset of the initial momentum at the tunnel exit in the elliptically polarized laser field. We find that the transverse and longitudinal components of this momentum offset with respect to the instantaneous field direction are directly related to the time derivatives of the instantaneous laser electric field along …
The longitudinal momentum of the electron at the tunneling exit is a useful quantity to make sense of the tunneling ionization process. It was usually assumed to be zero from a classical argument, but recent experiments show that it must be nonzero in order to explain the measured electron momentum distributions. In this article we show that the flow momentum of the probability fluid is a sensible quantum mechanical definition for tunneling-exit momentum, and it can be (and in general is) nonzero at the tunneling exit point where the kinetic energy is zero by definition. We show that this long…
Laser-induced electron tunneling underlies numerous emerging spectroscopic techniques to probe attosecond electron dynamics in atoms and molecules. The improvement of those techniques requires an accurate knowledge of the exit momentum for the tunneling wave packet. Here we demonstrate a photoelectron interferometric scheme to probe the electron momentum longitudinal to the tunnel direction at the tunnel exit by measuring the photoelectron holographic pattern in an orthogonally polarized two-color laser pulse. In this scheme, we use a perturbative 400-nm laser field to modulate the photoelectr…
We analyze tunnel ionization of a single atom based on the Wigner function over the classical phase space which inspires improved classical electron trajectories: these start with exit momenta based on the quantum momentum function and correspond very well to the subsequent quantum evolution. We derive an approximate analytic formula to reconstruct the tunnel exit time and exit momentum from electron momentum data that can be measured e.g. with a usual time-of-flight electron detector.
Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. M…
The problem of time delay in tunneling ionization is revisited. The origin of time delay at the tunnel exit is analysed, underlining the two faces of the concept of the tunnelling time delay: the time delay around the tunnel exit and the asymptotic time delay at a detector. We show that the former time delay, in the sense of a delay in the peak of the wavefunction, exists as a matter of principle and arises due to the sub-barrier interference of the reflected and transmitted components of the tunneling electronic wavepacket. We exemplify this by describing the tunnelling ionization of an elect…
We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and energy distribution in the instantaneous potential, we reveal the importance of quantum interference between tunneling and over-the-barrier pathways of escape. Tunneling is blurred both in space and time, and the contribution of tunneling at the mean energy is almost negligible. We suggest and justify improved initial conditions for a classical particle approximation of strong-field ionization, based…
After electrons tunnel out of a laser-Coulomb-formed barrier, %formed by the strong laser field and the atomic Coulomb potential, the movement of the tunneling electron can be affected by the Coulomb tail. We show that this Coulomb effect induces a large time difference (longer than a hundred attoseconds) between the exiting time at which the electron exits the barrier and the ionization time at which the electron is free. This large time difference has important influences on strong-field processes such as above-threshold ionization and high-harmonic generation, with remarkably changing time-…
The geometry-dependent ionization behavior of the ammonia molecule is investigated. Different theoretical approaches for obtaining the ionization yield are compared, all of them showing a strong dependence of the ionization yield on the inversion coordinate at long wavelengths ($\geq$ 800 nm). It is shown how this effect can be exploited to create and probe nuclear wave packets in neutral ammonia using Lochfraß. Furthermore, imaging of a wave packet tunneling through the barrier of a double-well potential in real time is discussed.
It is well-known from numerical and experimental results that the fraction of Rydberg states (excited neutral atoms) created by tunnel ionization declines dramatically with increasing ellipticity of laser light. We present a method to analyze this dependence on ellipticity, deriving a probability distribution of Rydberg states that agrees closely with recent experimental [1] and numerical results. In particular, contradicting the existing proposed mechanism [1] and general expectations, our results indicate that the dependence of Rydberg yield on laser ellipticity is not caused by a rescatteri…
Tunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during the ionization process. With this theoretical approach, it becomes possible to define unique moments when the electron enters and leaves with highest probability the classically forbidden region from first principles and a tunneling time can be specified unambiguously. It is shown that neither the moment when the electron enters the tunneling barrier nor when …
We introduce a method to investigate the longitudinal momentum spread resulting from strong-field tunnel ionization of Helium which, unlike other methods, is valid for all ellipticities of laser pulse. Semiclassical models consisting of tunnel ionization followed by classical propagation in the combined ion and laser field reproduce the experimental results if an initial longitudinal spread at the tunnel exit is included. The values for this spread are found to be of the order of twice the transverse momentum spread.
We assess the suitability of quantum and semiclassical initial value representations, exemplified by the coupled coherent states (CCS) method and the Herman Kluk (HK) propagator, respectively, for modeling the dynamics of an electronic wave packet in a strong laser field, if this wave packet is initially bound. Using Wigner quasiprobability distributions and ensembles of classical trajectories, we identify signatures of over-the-barrier and tunnel ionization in phase space for static and time-dependent fields and the relevant sets of phase-space trajectories in order to model such features. Ov…
We analyze the two-dimensional photoelectrons momentum distribution of Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below 2Up. By using a generalized quantum trajectory Monte Carlo (GQTMC) simulation and comparing with the numerical solution of time-dependent Schrodinger equation (TDSE), we show that in the deep tunneling regime, the rescattered electron trajectories plays unimportant role and the interplay between the intracycle and inter-cycle results in a ring-like interference pattern. The ring-like interference pattern will mask the holographic in…
The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of …
We study the nonlinear dynamics of wave packets in honeycomb lattices, and show that, in quasi-1D configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of left (or right) movers only does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propagation of a general wave packet can be described, within a good approximation, as a superposition of left and right moving self-similar (nonlinear) solutions. Finally, we find that Klein tunneling is not suppressed due …
The electron dynamics in the classically forbidden region during relativistic tunnel-ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge invariant total energy operator. Introducing position dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel-ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagat…
