Electron-Energy Bunching in Laser-Driven Soft Recollisions

Abstract

We introduce soft recollisions in laser-matter interaction. They are characterized by the electron missing the ion upon recollision in contrast to the well-known head-on collisions responsible for high-harmonic generation or above-threshold ionization. We demonstrate analytically that soft recollisions can cause a bunching of photo-electron energies through which a series of low-energy peaks emerges in the electron yield along the laser polarization axis. This peak sequence is universal, it does not depend on the binding potential, and is found below an excess energy of one fifth of the ponderomotive energy.PACS numbers: 34.80. Qb,32.80.Rm, 32.80.Wr,32.80.Fb Recollision of an electron with its parent ion under a linearly polarized strong laser field has been shown to be the basis of a plethora of phenomena in atoms [1, 2], molecules [3], clusters [4] and solids [5]. In principle the recollision process is very simple and a single degree of freedom along the laser polarization axis is sufficient to describe it (often referred to as the three-step model [1]): Firstly, the bound electron is released from an atom due to the strong electric field of a laser. Secondly, it is accelerated and driven back to the ion. In the third step it either recombines in the atomic potential or is scattered from it. In the former case, high-order harmonics are generated (HHG) due to recombination of the electron [6]. In the latter case, the elastic head-on collision induces the high-energy phenomenon of above-threshold ionization (ATI) with fast electrons emitted [7,8]. The enormous impact of HHG up to recent proposals for imaging of molecular orbitals [3] and the generation of attosecond pulses [9] is not the least due to the simple yet accurate description with the three-step model. Recently, a surprising strong peak -the "low-energy structure" (LES) -was observed at few eV in the photoelectron spectrum of atoms in strong infra-red (a few µm wavelength) laser pulses [10,11] and confirmed numerically with classical calculations [12,13]. Although the LES peak contains about half of the photo electrons it was not seen in any of the numerous experiments done with 800 nm laser pulses.Here, we will give an analytical explanation of the LES by introducing a low-energy soft-recollision mechanism. It gives rise to a universal series of low-energy peaks in the momentum spectrum of the photo electron with well defined relative positions of 3/5, 5/7, 7/9 . . . on an absolute energy scale of about one fifth of the ponderomotive energy F 2 /(4ω 2 ), where F is the amplitude and ω the frequency of the laser field. These peaks do not require a special binding potential, e. g., long range, nor do they need more than one degree of freedom to appear, and they can be derived classically since they rely essentially on the well known strong-field trajectories as will become clear later.We will begin by working out the classical structures which are responsible for the LES [10], i.e., we consider a Hamiltonian H = H 0 + V with (throughout the paper we...

Low-energy peak structure in strong-field ionization by midinfrared laser pulses: Two-dimensional focusing by the atomic potential

“…Quantum simulations confirm this scenario. Resulting parameter dependences agree with experimental findings [1,2] and, in part, with other simulations [3][4][5]. …”

“…Meanwhile, several models have been proposed invoking different and, in part, contradictory notions. While the coupling between the longitudinal and transverse degrees of freedom by Coulomb scattering was emphasized in [3,4], the appearance of the LES was demonstrated in a strictly onedimensional model in the absence of a transverse degree of freedom [5]. Furthermore, an LES feature was also found for screened (short-ranged) model potentials [2] raising questions as to the role of long-range Coulomb scattering and focusing.…”

“…Traces of this 2D focusing are present also in the projection onto the energy axis. This explains the appearance of the LES feature and of focusing also in reduced-dimensional models [5]. The position of the resulting peak (E i , L i ) can be estimated from…”

“…Note that they are not related to the peak sequence due to multiple reversals in a monochromatic (constant amplitude) field identified in the 1D analysis [5]. A full quantum simulation for identical laser parameters (Fig.…”

Universal pulse dependence of the low-energy structure in strong-field ionization

“…However, the observation of new structures [10,11] in the electron spectrum at low energies posed a puzzle: reproduced by numerical solutions of the time-dependent Schrödinger equation as well as by classical simulations [11][12][13][14][15][16][17][18], these now called "low" [10] and "very-low" [13] energy structures (LES and VLES) evade the well established three-step model. Early numerical studies [11][12][13] clearly hinted the importance of the Coulomb potential from the parent ion during formation of the low energy structures.…”