In the last three decades, we have witnessed incredible advances in laser technology and in the understanding of nonlinear laser-matter interactions, crowned recently by the award of the Nobel prize to Gérard Mourou and Donna Strickland [1,2]. It is now routinely possible to produce few-cycle femtosecond (1 fs = 10 −15 s) laser pulses in the visible and mid-infrared regimes [3,4]. By focusing such ultrashort laser pulses on gas or solid targets, possibly in a presence of nano-structures [5], the targets are subjected to an ultra-intense electric field, with peak field strengths approaching the binding field inside the atoms themselves. Such fields permit the exploration of the interaction between strong electromagnetic coherent radiation and an atomic or molecular system with unprecedented spatial and temporal resolution [6]. On one hand, HHG nowadays can be used to generate attosecond pulses in the extreme ultraviolet [7,8], or even in the soft X-ray regime [9]. Such pulses themselves may be used for dynamical spectroscopy of matter; despite carrying modest pulse energies, they exhibit excellent coherence properties [10,11]. Combined with femtosecond pulses they can also be used to extract information about the laser pulse electric field itself [12]. HHG sources therefore offer an important alternative to other sources of XUV and X-ray radiation: synchrotrons, free electron lasers, X-ray lasers, and laser plasma sources. Moreover, HHG pulses can provide information about the structure of the target atom, molecule or solid [13][14][15]. Of course, to decode such information from a highly nonlinear HHG signal is a challenge, and that is why a possibly perfect, and possibly "as analytical as possible" theoretical understanding of these processes is in high demand. Here is the first instance where SFA offers its basic services.Since electronic motion is governed by the waveform of the laser electric field, an important quantity to describe the electric field shape is the so-called absolute phase or carrier-envelope phase (CEP). Control over the CEP is paramount for extracting information about electron dynamics, and to retrieve structural information from atoms and molecules [13,16,17]. For instance, in HHG an electron is liberated from an atom or molecule through ionization, which occurs close to the maximum of the electric field. Within the oscillating field, the electron can thus accelerate along oscillating trajectories, which may result in recollision with the parent ion, roughly when the laser field approaches a zero value. Control over the CEP is particularly important for HHG, when targets are driven by laser pulses comprising only one or two optical cycles. In that situation the CEP determines the relevant electron trajectories, i.e. the CEP determines whether emission results in a single or in multiple attosecond bursts of radiation [16,18].The influence of the CEP on electron emission is also extremely important. It was demonstrated for instance in an anti-correlation experiment, in which the number of AT...

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one-or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 10 13 W/cm 2 to 5 × 10 14 W/cm 2 . We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

The paper discusses analytical and numerical results for non-harmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, V (x) ∝ x 2n , under Gaussian white noise does not extend to other noise types. Nevertheless, in the longtime limit (t → ∞), the average energies grow as power-law with exponents dependent on the steepness of the potential n. Another special limit corresponds to n → ∞, i.e. to the infinite rectangular potential well, when the average total energy grows as a power-law with the same exponent for all considered noise types.

The harmonic oscillator is one of fundamental models in physics. In stochastic thermodynamics, such models are usually accompanied with both stochastic and damping forces, acting as energy counter-terms. Here, on the other hand, we study properties of the undamped harmonic oscillator driven by additive noises. Consequently, the popular cases of Gaussian white noise, Markovian dichotomous noise and Ornstein-Uhlenbeck noise are analyzed from the energy point of view employing both analytical and numerical methods. In accordance to one's expectations, we confirm that energy is pumped into the system. We demonstrate that, as a function of time, initially total energy displays abrupt oscillatory changes, but then transits to the linear dependence in the long-time limit. Kinetic and potential parts of the energy are found to display oscillatory dependence at all times.

Newtonian, undamped motion in single-well potentials belong to a class of well-studied conservative systems. Here, we investigate and compare long-time properties of fully deterministic motions in single-well potentials with analogous randomized systems. We consider a special type of energy-conserving randomization process: the deterministic motion is interrupted by hard velocity reversals v(t i ) → − v(t i ) at random time instants t i . In the 1D case, for fixed initial conditions, the differences in probability distributions disappear in the long-time limit making asymptotic densities insensitive to the selection of random time instants when velocity is reversed. Substantially different probability distributions can be obtained, for instance, through the additional randomization of initial conditions. Analogously, in 2D setups, the probability distributions asymptotically are insensitive to velocity reversals.

Strong field ionization provides a unique mean to address complex dynamics of an electron in competing Coulomb and laser fields. Recent streak camera experiment (Kübel, et al.,[1]) analyzed asymmetries in the low-energy region of ejected electron momenta distribution and associated them with multiple rescattering of the electron on the parent ion. In this work we directly confirm the multiple rescattering nature of the asymmetry in the low-energy region. Such electron-ion collisions cannot be described within one-dimensional simulations even taking into account focal-volume averaging. Using time-dependent Schrödinger equation simulation in two dimensions supplemented by the insight from strong field semi-classical approximation we identify the dominant interference features of the complex photoelectron momentum maps and find their traces in the experiment. In particular, the holographic structures remain visible in experimental results averaged over carrierenvelope phase (CEP). In the case of individual momentum maps when CEP or delay between the two pulses is varied, the structures arising due to rescattering events are influenced by interfering electrons ionized at main peaks of the electric field. With an increase of experimental resolution, such structures record the electron dynamics on a sublaser-cycle time scale. arXiv:1907.03291v1 [physics.atom-ph]

The interaction of strong pulsed femtosecond laser field with atoms having three equivalent electrons in the outer shell (p 3 configuration, e.g. nitrogen) is studied via numerical integration of a time-dependent Schrödinger equation on a spatial grid. Single ionisation, double ionisation (DI) and triple ionisation (TI) yields originating from a completely antisymmetric wave function are calculated and extracted using a restricted-geometry model with the soft-core potential and three active electrons. The observed suppression of the ionisation yields for the non-sequential processes, in both DI and TI cases, is attributed to the action of the Pauli principle. Compared against earlier results investigating the s 2 p 1 configuration, we propose that the differences found here might in fact be accessible through electron's momentum distribution.

We present a joint experimental and theoretical study of non-sequential double ionization (NSDI) in argon driven by a 3100-nm laser source. The correlated photoelectron momentum distribution (PMD) shows a strong dependence on the pulse duration, and the evolution of the PMD can be explained by an envelope-induced intensity effect. Determined by the time difference between tunneling and rescattering, the laser vector potential at the ionization time of the bound electron will be influenced by the pulse duration, leading to different drift momenta. Such a mechanism is extracted through a classical trajectory Monte Carlo-based model and it can be further confirmed by quantum mechanical simulations. This work sheds light on the importance of the pulse duration in NSDI and improves our understanding of the strong field tunnel-recollision dynamics under mid-IR laser fields.