Signatures of electronic structure in bi-circular high-harmonic spectroscopy

High-harmonic spectroscopy driven by circularly-polarized laser pulses and their counter-rotating second harmonic is a new branch of attosecond science which currently lacks quantitative interpretations. We extend this technique to the mid-infrared regime and record detailed high-harmonic spectra of several rare-gas atoms. These results are compared with the solution of the Schrodinger equation in three dimensions and calculations based on the strong-field approximation that incorporate accurate scattering-wave recombination matrix elements. A quantum-orbit analysis of these results provides a transparent interpretation of the measured intensity ratios of symmetry-allowed neighboring harmonics in terms of (i) a set of propensity rules related to the angular momentum of the atomic orbitals, (ii) atom-specific matrix elements related to their electronic structure and (iii) the interference of the emissions associated with electrons in orbitals co- or counter-rotating with the laser fields. These results provide the foundation for a quantitative understanding of bi-circular high-harmonic spectroscopy.Comment: Accepted in Physical Review Letter

Theoretical Study of Molecular Electronic and Rotational Coherences by High-Harmonic Generation

The detection of electron motion and electronic wavepacket dynamics is one of the core goals of attosecond science. Recently, choosing the nitric oxide (NO) molecule as an example, we have introduced and demonstrated a new experimental approach to measure coupled valence electronic and rotational wavepackets using high-harmonic generation (HHG) spectroscopy [Kraus et al., Phys. Rev. Lett. 111, 243005 (2013)]. A short outline of the theory to describe the combination of the pump and HHG probe process was published together with an extensive discussion of experimental results [Baykusheva et al., Faraday Discuss 171, 113 (2014)]. The comparison of theory and experiment showed good agreement on a quantitative level. Here, we present the generalized theory in detail, which is based on a generalized density matrix approach that describes the pump process and the subsequent probing of the wavepackets by a semiclassical quantitative rescattering approach. An in-depth analysis of the different Raman scattering contributions to the creation of the coupled rotational and electronic spin-orbit wavepackets is made. We present results for parallel and perpendicular linear polarizations of the pump and probe laser pulses. Furthermore, an analysis of the combined rotational-electronic density matrix in terms of irreducible components is presented, that facilitates interpretation of the results.Comment: 14 figure

Witnessing Light-Driven Entanglement using Time-Resolved Resonant Inelastic X-Ray Scattering

Characterizing and controlling entanglement in quantum materials is crucial for next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in a material is theoretically and experimentally challenging. At equilibrium, the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopies and extending this approach to nonequilibrium states could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials through time-resolved resonant inelastic x-ray scattering, a recently developed solid-state pump-probe technique. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced quantum entanglement, due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via solid-state accessible ultrafast spectroscopic measurements.Comment: 11 pages, 6 figure

Attosecond Photoionization Dynamics: from Molecules over Clusters to the Liquid Phase

Photoionization is a process taking place on attosecond time scales. How its properties evolve from isolated particles to the condensed phase is an open question of both fundamental and practical relevance. Here, we review recent work that has advanced the study of photoionization dynamics from atoms to molecules, clusters and the liquid phase. The first measurements of molecular photoionization delays have revealed the attosecond dynamics of electron emission from a molecular shape resonance and their sensitivity to the molecular potential. Using electron-ion coincidence spectroscopy these measurements have been extended from isolated molecules to clusters. A continuous increase of the delays with the water-cluster size has been observed up to a size of 4-5 molecules, followed by a saturation towards larger clusters. Comparison with calculations has revealed a correlation of the time delay with the spatial extension of the created electron hole. Using cylindrical liquid-microjet techniques, these measurements have also been extended to liquid water, revealing a delay relative to isolated water molecules that was very similar to the largest water clusters studied. Detailed modeling based on Monte-Carlo simulations confirmed that these delays are dominated by the contributions of the first two solvation shells, which agrees with the results of the cluster measurements. These combined results open the perspective of experimentally characterizing the delocalization of electronic wave functions in complex systems and studying their evolution on attosecond time scales

Spin-orbit delays in photoemission

Attosecond delays between photoelectron wave packets emitted from different electronic shells are now well established. Is there any delay between electrons originating from the same electronic shell but leaving the cation in different fine-structure states? This question is relevant for all attosecond photoemission studies involving heavy elements, be it atoms, molecules or solids. We answer this fundamental question by measuring energy-dependent delays between photoelectron wave packets associated with the P3/22 and P1/22 components of the electronic ground states of Xe+ and Kr+. We observe delays reaching up to 33±6 as in the case of Xe. Our results are compared with two state-of-the-art theories. Whereas both theories quantitatively agree with the results obtained for Kr, neither of them fully reproduces the experimental results in Xe. Performing delay measurements very close to the ionization thresholds, we compare the agreement of several analytical formulas for the continuum-continuum delays with experimental data. Our results show an important influence of spin-orbit coupling on attosecond photoionization delays, highlight the requirement for additional theory development, and offer a precision benchmark for such workWe gratefully acknowledge funding from an ERC Starting Grant (Contract No. 307270-ATTOSCOPE) and the NCCR-MUST, a funding instrument of the Swiss National Science Foundation. S.P. is funded by the Alexander von Humboldt Foundation and by the NSF through a grant to ITAMP. A.S.K. acknowledges support from the Australian Research Council under Discovery Grant No. DP120101805. I.J. and M.H. contributed equally to this work

Femtosecond photoelectron circular dichroism of chemical reactions

Understanding the chirality of molecular reaction pathways is essential for a broad range of fundamental and applied sciences. However, the current ability to probe chirality on the time scale of chemical reactions remains very limited. Here, we demonstrate time-resolved photoelectron circular dichroism (TRPECD) with ultrashort circularly polarized vacuum-ultraviolet (VUV) pulses from a table-top source. We demonstrate the capabilities of VUV-TRPECD by resolving the chirality changes in time during the photodissociation of atomic iodine from two chiral molecules. We identify several general key features of TRPECD, which include the ability to probe dynamical chirality along the complete photochemical reaction path, the sensitivity to the local chirality of the evolving scattering potential, and the influence of electron scattering off dissociating photofragments. Our results are interpreted by comparison with novel high-level ab-initio calculations of transient PECDs from molecular photoionization calculations. Our experimental and theoretical techniques define a general approach to femtochirality.Comment: 17 pages, 6 figures, 57 references, Accepted in Science Advance

Attosecond synchronization of extreme ultraviolet high harmonics from crystals

The interaction of strong near-infrared (NIR) laser pulses with wide-bandgap dielectrics produces high harmonics in the extreme ultraviolet (XUV) wavelength range. These observations have opened up the possibility of attosecond metrology in solids, which would benefit from a precise measurement of the emission times of individual harmonics with respect to the NIR laser field. Here we show that, when high-harmonics are detected from the input surface of a magnesium oxide crystal, a bichromatic probing of the XUV emission shows a clear synchronization largely consistent with a semiclassical model of electron-hole recollisions in bulk solids. On the other hand, the bichromatic spectrogram of harmonics originating from the exit surface of the 200 $\mu$m-thick crystal is strongly modified, indicating the influence of laser field distortions during propagation. Our tracking of sub-cycle electron and hole re-collisions at XUV energies is relevant to the development of solid-state sources of attosecond pulses