Eva Lindroth

Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure

A diagonalisation procedure of the Foldy-Wouthuysen type is considered for the single-electron Dirac Hamiltonian as a basis for many-body applications. A modified procedure is suggested. In the diagonalisation procedure the Dirac equation is completely decoupled into two equations of the Pauli type. The expressions for positive- and negative-energy projection operators in the transformed basis are then trivial and, by performing the inverse transformation, projection operators for Dirac functions are obtained. Applying a similar transformation to the two-electron Dirac-Coulomb Hamiltonian leads to a diagonalised single-electron part and a non-diagonal two-electron interaction. In principle, the effect of the exchange of virtual, transverse photons (Breit interactions) can also be included in the electron-electron interaction and transformed in a similar way. It is indicated how a diagonalisation procedure of this kind can be used as a basis for relativistic many-body calculations in the coupled cluster formulation in analogy with the corresponding non-relativistic procedure.

Resonance Effects in Photoemission Time Delays

We present measurements of single-photon ionization time delays between the outermost valence electrons of argon and neon using a coincidence detection technique that allows for the simultaneous measurement of both species under identical conditions. The analysis of the measured traces reveals energy-dependent time delays of a few tens of attoseconds with high energy resolution. In contrast to photoelectrons ejected through tunneling, single-photon ionization can be well described in the framework of Wigner time delays. Accordingly, the overall trend of our data is reproduced by recent Wigner time delay calculations. However, besides the general trend we observe resonance features occurring at specific photon energies. These features have been qualitatively reproduced and identified by a calculation using the multiconfigurational Hartree-Fock method, including the influence of doubly excited states and ionization thresholds.

Spectral phase measurement of a Fano resonance using tunable attosecond pulses.

Electron dynamics induced by resonant absorption of light is of fundamental importance in nature and has been the subject of countless studies in many scientific areas. Above the ionization threshold of atomic or molecular systems, the presence of discrete states leads to autoionization, which is an interference between two quantum paths: direct ionization and excitation of the discrete state coupled to the continuum. Traditionally studied with synchrotron radiation, the probability for autoionization exhibits a universal Fano intensity profile as a function of excitation energy. However, without additional phase information, the full temporal dynamics cannot be recovered. Here we use tunable attosecond pulses combined with weak infrared radiation in an interferometric setup to measure not only the intensity but also the phase variation of the photoionization amplitude across an autoionization resonance in argon. The phase variation can be used as a fingerprint of the interactions between the discrete state and the ionization continua, indicating a new route towards monitoring electron correlations in time.

Ionization branching ratio control with a resonance attosecond clock.

We investigate the possibility to monitor the dynamics of autoionizing states in real-time and control the yields of different ionization channels in helium by simulating extreme ultraviolet (XUV) pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates a coherent superposition of doubly excited states which is found to decay by ejecting electrons in bursts. Prominent interference fringes in the photoelectron angular distribution of the 2s and 2p ionization channels are observed, along with significant out-of-phase quantum beats in the yields of the corresponding parent ions.

Dielectronic Resonance Method for Measuring Isotope Shifts

Long standing problems in the comparison of very accurate hyperfine-shift measurements to theory were partly overcome by precise measurements on few-electron highly charged ions. Still the agreement between theory and experiment is unsatisfactory. In this Letter, we present a radically new way of precisely measuring hyperfine shifts, and demonstrate its effectiveness in the case of the hyperfine shift of 4s1/2 and 4p1/2 in 207Pb53+. It is based on the precise detection of dielectronic resonances that occur in electron-ion recombination at very low energy. This allows us to determine the hyperfine constant to around 0.6 meV accuracy which is on the order of 10%.

Measurements of relative photoemission time delays in noble gas atoms

We determine relative photoemission time delays between valence electrons in different noble gas atoms (Ar, Ne and He) in an energy range between 31 and 37 eV. The atoms are ionized by an attosecond pulse train synchronized with an infrared laser field and the delays are measured using an interferometric technique. We compare our results with calculations using the random phase approximation with exchange and multi-configurational Hartree-Fock. We also investigate the influence of the different ionization angular channels.

Photoionization in the time and frequency domain

Resetting the clock on photoemission The ability to produce attosecond pulses of light provides access to some of the fastest electronic processes occurring within atoms. Tracking the temporal dynamics of the photoemission process in which an atom absorbs a high-energy photon and the electron escapes has exposed a discrepancy between the initial experimental findings and subsequent theoretical modeling. Isinger et al. present an ultrafast process that can account for and distinguish the different contributions to the photoemission processes in neon atoms. The findings reveal an “electron shake-up” process that may explain the discrepancy, bringing closure to a 7-year discussion. Science, this issue p. 893 An ultrafast technique is developed that can disentangle the different processes in photoionization. Ultrafast processes in matter, such as the electron emission after light absorption, can now be studied using ultrashort light pulses of attosecond duration (10−18 seconds) in the extreme ultraviolet spectral range. The lack of spectral resolution due to the use of short light pulses has raised issues in the interpretation of the experimental results and the comparison with theoretical calculations. We determine photoionization time delays in neon atoms over a 40–electron volt energy range with an interferometric technique combining high temporal and spectral resolution. We spectrally disentangle direct ionization from ionization with shake-up, in which a second electron is left in an excited state, and obtain excellent agreement with theoretical calculations, thereby solving a puzzle raised by 7-year-old measurements.

Multiconfigurational Hartree-Fock close-coupling ansatz : Application to the argon photoionization cross section and delays

We present a robust, ab initio method for addressing atom-light interactions and apply it to photoionization of argon. We use a close-coupling ansatz constructed on a multiconfigurational Hartree-Fock description of localized states and B-spline expansions of the electron radial wave functions. In this implementation, the general many-electron problem can be tackled thanks to the use of the ATSP2K libraries [C. Froese Fischer et al., Comput. Phys. Commun. 176, 559 (2007)]. In the present contribution, we combine this method with exterior complex scaling, thereby allowing for the computation of the complex partial amplitudes that encode the whole dynamics of the photoionization process. The method is validated on the 3s3p(6)np series of resonances converging to the 3s extraction. Then, it is used for computing the energy dependent differential atomic delay between 3p and 3s photoemission, and agreement is found with the measurements of Guenot et al. [Phys. Rev. A 85, 053424 (2012)]. The effect of the presence of resonances in the one-photon spectrum on photoionization delay measurements is studied. DOI: 10.1103/PhysRevA.87.023420

Study of attosecond delays using perturbation diagrams and exterior complex scaling

We describe in detail how attosecond delays in laser-assisted photoionization can be computed using perturbation theory based on two-photon matrix elements. Special emphasis is laid on above-threshold ionization, where the electron interacts with an infrared field after photoionization by an extreme ultraviolet field. Correlation effects are introduced using diagrammatic many-body theory to the level of the random-phase approximation with exchange. Our aim is to provide an ab initio route to correlated multi-photon processes that are required for an accurate description of experiments on the attosecond time scale. Here, our results are focused on photoionization of the M-shell of argon atoms, where experiments have been carried out using the so-called reconstruction of attosecond beating by the two-photon interference transitions technique. An influence of autoionizing resonances in attosecond delay measurements is observed. Further, it is shown that the delay depends on both detection angle of the photoelectron and energy of the probe photon.

Diagrammatic approach to attosecond delays in photoionization

We study laser-assisted photoionization by attosecond pulses using a time-independent formalism based on diagrammatic many-body perturbation theory. Our aim is to provide an ab initio route to the delays for this above-threshold ionization process, which is essential for a quantitative understanding of attosecond metrology. We present correction curves for characterization schemes of attosecond pulses, such as streaking, that account for the delayed atomic response in ionization from neon and argon. We also verify that photoelectron delays from many-electron atoms can be measured using similar schemes if, instead, the so-called continuum-continuum delay is subtracted. Our method is general and it can be extended also to more complex systems and additional correlation effects can be introduced systematically. DOI: 10.1103/PhysRevA.86.061402