Jarosław H. Bauer

Ionization of hydrogen atoms by intense vacuum ultraviolet radiation

We study the ionization of hydrogen atoms by an intense pulsed beam of photons with energies of 17 or 50 eV. The work is motivated by the demonstration of the free-electron laser (FEL) action at the DESY Laboratory. The parameters chosen for the incident field are in the regime accessible by the FEL. Ionization yields are obtained within three different approaches, namely the strong-field approximation, the Floquet method and a numerical solution of the timedependent Schr¨ odinger equation. A marked stabilization effect for 50 eV photons is shown.

Comparison of two forms of the S-matrix element of strong-field photoionization

We numerically compare ionization rates and photoelectron energy spectra resulting from the so-called length gauge (LG) and velocity gauge (VG) forms of the Keldysh–Faisal–Reiss (KFR) theory for a circularly polarized laser field. To this end, we use the well-known analytical formulae for the ground state of a hydrogen atom and we derive analogous formulae for its first excited (degenerate) state. It appears that both forms of the KFR theories show qualitatively different behaviour of ionization rate as a function of frequency and intensity of the laser field. In the LG KFR theory, one obtains much smaller stabilization of the hydrogen atom than in the VG KFR theory. Unlike the latter one, the LG KFR theory shows that for sufficiently strong laser field (in the non-relativistic and dipole approximations) ionization rate from a given initial state is only a function of intensity, but not of frequency of the laser field. We also find substantial differences in the shape of photoelectron energy spectra for both theories. In contrast to the VG KFR theory, the LG one shows a minimum in photoelectron energy spectra for some initial states of the hydrogen atom. We discuss our results by comparing them, where possible, to other theoretical calculations.

Quasistatic limit of the strong-field approximation describing atoms in intense laser fields: Circular polarization

In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency {omega} (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to {omega}{sup 4} for H(1s) and H(2s) atoms, to {omega}{sup 6} for H(2p{sub x}) and H(2p{sub y}) atoms, and to {omega}{sup 8} for H(2p{sub z}) atoms. The analytical expressions for asymptotic ionization rates (which become nearly accurate in the limit {omega}{yields}0) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared) these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.

Ionization and excitation of the excited hydrogen atom in strong circularly polarized laser fields

In the recent work of Herath et al. [T. Herath, L. Yan, S. K. Lee, and W. Li, Phys. Rev. Lett. 109, 043004 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.043004] the first experimental observation of a dependence of strong-field ionization rate on the sign of the magnetic quantum number m [of the initial bound state (n,l,m)] was reported. The experiment with nearly circularly polarized light could not distinguish which sign of m favors faster ionization. We perform ab initio calculations for the hydrogen atom initially in one of the four bound substates with the principal quantum number n=2, and irradiated by a short circularly polarized laser pulse of 800nm. In the intensity range of 1012-1013W/cm2 excited bound states play a very important role, but also up to some 1015W/cm2 they cannot be neglected in a full description of the laser-atom interaction. We explore the region that with increasing intensity switches from multiphoton to over-the-barrier ionization and we find, unlike in tunneling-type theories, that the ratio of ionization rates for electrons initially counter-rotating and corotating (with respect to the laser field) may be higher or lower than 1.

Qualitatively different theoretical predictions for strong-field photoionization rates

We give examples showing that two well-known versions of the S-matrix theory, which describes a nonresonant multiphoton ionization of atoms and ions in intense laser fields, lead to qualitatively different results. The latter refer not only to total ionization rates, but also to energy distributions of photoelectrons, for instance, in a polarization plane of the laser field. It should be possible to make experiments testing predictions of both theories in the near future.

A generalization of the Keldysh–Faisal–Reiss model

We calculate the ionization rate for a hydrogen atom interacting with a circularly polarized electromagnetic plane wave. Coulomb effects in the final state of the outgoing electron are taken into account. Our approximate theory is valid when the classical radius of motion of a free electron in a plane-wave field is much larger than the radius of the atom in its initial state.

Comparison of two forms of the S-matrix element of strong-field photoionization: II. (n, l, m) = (2, 1, ±1) states

In our previously published work (Bauer 2008 J. Phys. B: At. Mol. Opt. Phys. 41 185003) we numerically compared ionization rates and photoelectron energy (or momentum) spectra resulting from the so-called length gauge (LG) and velocity gauge (VG) forms of the Keldysh–Faisal–Reiss theory for a strong circularly polarized laser field. Our investigations concerned initial (bound) states of a hydrogen atom with the principal quantum number equal to 1 or 2. However, some of these states were not taken into account in this work, but only their linear combinations (quantum-mechanical superpositions). The main purpose of the present work is to fill this gap. It is appropriate to add that excited bound states (of the hydrogen atom) considered here are easier to achieve from an experimental point of view. As in our previous work, we find substantial differences in the shape of photoelectron energy spectra for both (LG and VG) theories. Differently from the VG theory, the LG one shows a multipeak envelope in photoelectron energy spectra for most initial states of the hydrogen atom. We give examples showing that the multipeak effect may be observed also in the polarization plane of the laser field. The field parameters (frequency and intensity) applied by us in the calculations indicate that one should be able to observe experimentally the above-mentioned effect in the near future.

Lorentz force on an electron in a strong plane-wave laser field and the low-frequency limit for ionization

A motion of a classical free charge in an electromagnetic plane wave can be found exactly in a fully relativistic case. I have found an approximate non-parametric form of the suitable equations of motion. In a linearly polarized wave, in the simplest frame of reference, the charge moves along the well-known figure-eight path. I have numerically calculated the Lorentz force acting on the charge as a function of time. By virtue of this, for the low-frequency ionization (or detachment) rate, I discuss a manifestation of nondipole and relativistic effects. When intensity of the plane wave increases, these effects can first appear in angular distributions, then in spectra of outgoing electrons, but have quite little effect on total ionization rates. I try to give an explanation of the latter fact.

Low-frequency-high-intensity limit of the Keldysh-Faisal-Reiss theory

When a frequency of the circularly polarized laser field approaches zero the above threshold ionization rate should approach the well-known static-field limit of tunneling ionization. In the high-intensity limit of the laser field the Keldysh-Faisal-Reiss (KFR) theory is expected to be valid. For the ground state of a hydrogen atom we study various forms of the KFR theory when both conditions: {omega}<<1 a.u. and {gamma}<<1 ({omega} is the frequency and {gamma} the Keldysh parameter) are satisfied. For the circularly polarized laser field ionization rate in the Keldysh theory [which utilizes the length gauge (d(vector sign){center_dot}E(vector sign)) form of the matrix element] is calculated analytically. We show numerically that if the WKB Coulomb correction in the final state of the ionized electron is included, the Keldysh theory gives the correct result in the tunneling domain. In the barrier-suppression regime the Keldysh theory without this correction gives ionization rates close to the exact static-field results. The Reiss theory [which utilizes the velocity gauge (p(vector sign){center_dot}A(vector sign)) form of the matrix element] leads to too small ionization rates in the limit {omega}{yields}0, {gamma}{yields}0.

Coulomb-corrected Volkov-type solution for an electron in an intense circularly polarized laser field

A simple analytical approximation exists for the wavefunction of an unbound electron interacting both with a strong circularly polarized laser field and an atomic Coulomb potential (Reiss and Krainov 1994 Phys. Rev. A 50 R910). This wavefunction is the Volkov state with a first-order Coulomb correction coming from some perturbative expansion of the potential in the Kramers-Henneberger reference frame. The expansion is valid, if the distance from the centre of the Coulomb force is smaller than the classical radius of motion of a free electron in a plane-wave field. We improve the approximate Coulomb-Volkov wavefunction by including the next term in the perturbative expansion of the atomic potential.