Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the timedependent Schrödinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise successful work horse of strong field laser physics: the "strong field approximation" (SFA). In the semi-classical limit, the SFA possesses an appealing interpretation in terms of interfering quantum trajectories. It is shown that a conceptually simple extension towards the inclusion of Coulomb effects yields very good agreement with exact TDSE results. Moreover, the Coulomb quantum orbits allow for a physically intuitive interpretation and detailed analysis of all low-energy features in the semi-classical regime, in particular the recently discovered "low-energy structure" [C.I. Blaga et al., Nature Physics 5, 335 (2009) The development of analytical and numerical methods capable of treating strongly-driven quantum systems is of great interest in many areas of physics. By "strongly-driven" we understand that conventional time-dependent perturbation theory is not applicable. A prime example for such a system is an atom in an intense laser field. The force on valence electrons due to the electric field of the electromagnetic wave delivered by present-day intense lasers can easily compete with the binding force. As a consequence, the photoelectron spectra may show strong nonperturbative features such as plateaus and cut-offs [1], instead of a simple exponential decrease with the number of absorbed photons, as expected from perturbation theory. Recently, an "ionization surprise" [2] at wavelength λ = 2 µm and intensity I = 80-150 TW/cm 2 , the socalled "low-energy structure" (LES) [3,4], has been reported. The LES is a strong but narrow enhancement of the differential ionization probability along the polarization direction of the laser at low energies. This result was so astonishing not only because it is unpredicted by the "strong field approximation" (SFA) [5] but also because it is observed in a regime where matters were actually expected to simplify. In fact, if the number of photons N of energyhω required to overcome the ionization potential I p is large, N = I p /hω ≫ 1, and the time the electron needs to tunnel through the Coulombbarrier is small compared to a laser period, i.e., the Keldysh parameter γ = I p /2U p with U p the ponderomotive potential, is small, a quasi-static tunneling theory appears to apply [6]. As the tunneling ionization rate in a static electric field is a smooth, featureless function of the final momenta p and p ⊥ parallel and perpendicular to the electric field, respectively, no LES has been expected. In the present Letter we reveal the origin of the LES using our trajectory-based Coulomb-SFA (TC-SFA). The fact that the TC-SFA allows recourse to trajectories provides an unprecedented insight into the origin of any spectral feature of interest, as constructive or destructive interference of trajectories or the Coulomb-focusing of them [7] can be analyz...

Midinfrared strong-field laser ionization offers the promise of measuring holograms of atoms and molecules, which contain both spatial and temporal information of the ion and the photoelectron with subfemtosecond temporal and angstrom spatial resolution. We report on the scaling of photoelectron holographic interference patterns with the laser pulse duration, wavelength, and intensity. High-resolution holograms for the ionization of metastable xenon atoms by 7-16  μm light from the FELICE free electron laser are presented and compared to semiclassical calculations that provide analytical insight.

The velocity map recorded in above-threshold ionization of xenon at 800 nm exhibits a distinct carpetlike pattern of maxima and minima for emission in the direction approximately perpendicular to the laser polarization. The pattern is well reproduced by a numerical solution of the time-dependent Schrödinger equation. In terms of the simple-man model and the strong-field approximation, it is explained by the constructive and destructive interference of the contribution of the long and the short orbit. Strictly perpendicular emission is caused by ionization at the two peaks of the laser field per cycle, which results in a 2ħω separation of the above-threshold ionization rings.