Attosecond X-ray Science

xuvSince the inception of the laser, more than 50 years ago, the generation of coherent x-ray light has been amongst the prime objectives of scientists since x-rays are perfectly matched to investigate the flow of energy and information of the nanoworld. Phase transitions of materials, ultrafast changes in magnetism or time-resolved structural investigations of biomolecular assemblies are just a few examples awaiting sources of coherent x-rays. High harmonic generation (HHG) provides such a route with the intrinsic possibility to generate attosecond duration bursts of x-rays. We have, for example, contributed to pioneering investigations into the frequency rate of high-harmonic light and pioneered schemes to increase the notoriously low yield in HHG. Currently we are aiming at coherent x-ray light in the biologically relevant water window around 0.5 keV and beyond. The development of such a tabletop source will have large impact in the before-mentioned fields and provide a route towards the zeptosecond (10-21s) temporal scale.


Isolated Attosecond Soft X-ray Pulse

lighthouseAttosecond pulses at photon energies that cover the principal absorption edges of the building blocks of materials are a prerequisite for time-resolved probing of the triggering events leading to electronic dynamics such as exciton formation and annihilation. We demonstrate experimentally the isolation of individual attosecond pulses at the carbon K-shell edge (284 eV) in the soft X-ray water window with pulse duration below 400 as and with a bandwidth supporting a 30-as pulse duration. Our approach is based on spatiotemporal isolation of long-wavelength-driven harmonics and validates a straightforward and scalable approach for robust and reproducible attosecond pulse isolation.

  1. F. Silva, S. Teichmann, S. L. Cousin, J. Biegert, “Spatio-temporal isolation of attosecond soft X-ray pulses in the water window”, Nature Commun. 6, 6611 (2015)
  2. S. M. Teichmann, F. Silva, S. L. Cousin, J. Biegert, “The importance of intensity to phase coupling for water window high harmonic generation with few-cycle pulses”, Phys. Rev. A. 91, 063817 (2015)

Quantum Path Interference

qpWe present theoretical and experimental studies on quantum path interferences in high-order harmonic generation. Simulations of the single-atom response allow us to calculate the different quantum paths contri- butions; their relative phases and the resulting interferences can be finely controlled through the laser intensity that provides an efficient means for controlling the electron trajectories with an accuracy on the ten attoseconds time scale. Simulations of the macroscopic response demonstrate the need of spatial and spectral filtering of the harmonic beam in order to observe the interferences between the two shortest quantum paths. Our numerical results are in very good agreement with experimental data. These investigations represent a step toward the full characterization and control of the atomic harmonic dipole.

  1. A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, A. Wyatt, A. Monmayrand, I. A. Walmsley, E. Cormier, T. Auguste, J. P. Caumes, P. Salieres, “Quantum path interferences in high-order harmonic generation”, Phys. Rev. Lett. 100, 143902 (2008)
  2. T. Auguste, P. Salieres, A.S. Wyatt, A. Monmayrant, I.A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation”, Phys. Rev. A. 80, 033817 (2009)

Coherent Control over Harmonics

enhancementWe show that attosecond pulse trains have a natural application in the control of strong field processes. In combination with an intense infrared laser field, the pulse train can be used to microscopically select a single quantum path contribution to a process that would otherwise consist of several interfering components. We present calculations that demonstrate this by manipulating the time-frequency properties of high order harmonics at the single atom level. This quantum path selection can also be used to define a high resolution attosecond clock.

  1. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, ”Strong field quantum control using attosecond pulse trains”, Phys. Rev. Lett. 92, 023003 (2004)
  2. M. B. Gaarde, and K. J. Schafer, a. Heinrich, J. Biegert, U. Keller, ”Large enhancement of macroscopic yield in attosecond pulse train-assisted harmonic generation”, Phys. Rev. A. 72, 013511 (2005)
  3. D. Faccio, C. Serrat, J. Cela, A. Farres, P. DiTrapani, J. Biegert, “Modulated phase matching and high order harmonic enhancement mediated by the carrier-envelope phase.”, Phys. Rev. A. 81, 011803R (2010)
  4. C. Serrat, J. Biegert, “All-regions tunable high harmonic enhancement by a periodic static electric field”, Phys. Rev. Lett. 104, 073901 (2010)

High Brightness Tabletop Soft X-rays

xafsWe report on the first table-top high-flux source of coherent soft x-ray radiation up to 400 eV, operating at 1 kHz. This source covers the carbon K-edge with a7 beam brilliance of (4.3 ± 1.2) × 10<sup>15</sup> photons∕s∕mm2 ∕strad∕10% bandwidth and a photon flux of (1.85 ± 0.12) × 10<sup>7</sup> photons∕s∕1% bandwidth. We use this source to demonstrate table-top x-ray near-edge fine-structure spectroscopy at the carbon K-edge of a polyimide foil and retrieve the specific absorption features corresponding to the binding orbitals of the carbon atoms in the foil.

  1. S.L. Cousin, F. Silva, S. Teichmann, M. Hemmer, B. Buades, J. Biegert, “High flux table-top soft X-ray source driven by sub-2-cycle, CEP stable, 1.85 μm 1 kHz pulses for carbon K-edge spectroscopy”, Opt. Lett. 39, 5383 (2014)
  2. S.L. Cousin, F. Silva, S. Teichmann, M. Hemmer, J. Biegert, “Molecular fine structure from water-window coherent soft-X-rays”, Optics and Photonics News, 12, 58 (2014), Optics in 2014 Highlight
  3. S. M. Teichmann, F. Silva, S. L. Cousin, J. Biegert, “The importance of intensity to phase coupling for water window high harmonic generation with few-cycle pulses”, Phys. Rev. A. 91, 063817 (2015)

Orbital Tomography

orbitaltomoWe study the polarization state of high-order harmonics produced by linearly polarized light interacting with two-center molecules. By generating high-harmonic “polarization maps” from Radon transformations of excited electronic wave functions, we show that the polarization of the harmonic radiation can be linked to the geometry of the molecular orbital. While in the Radon transformation the plane-wave approximation for the rescattered electron is implicitly assumed, numerical solutions of the two-dimensional time-dependent Schro ̈ dinger equation, in which this approximation is not made, confirm the validity of this topological connection. We also find that measuring two orthogonal amplitude components of the harmonics provides a method for quantum tomography that substantially improves the quality of reconstructed molecular states.

  1. G. Gibson, J. Biegert, “Influence of orbital symmetry on high-harmonic generation and quantum tomography”. Phys. Rev. A 78, 033423 (2008)
  2. E. Hijano, C. Serrat, G.N. Gibson, J. Biegert, “Orbital geometry determined by orthogonal high-order harmonic polarization components”, Phys. Rev. A 81, 041401R (2010)

Characterization of Harmonics

qpWe measure the chirp rate of harmonics 13 to 23 in argon by cross correlation with a 12 femtosecond probe pulse. Under low ionization conditions, we directly measure the negative chirp due to the atomic dipole phase, and show that an additional chirp on the pump pulse is transferred to the qth harmonic as q times the fundamental chirp. Our results are in accord with simulations using the experimentally measured 815 nm pump and probe pulses. The ability to measure and manipulate the harmonic chirp rate is essential for the charac- terization and optimization of attosecond pulse trains.

  1. J. Mauritson, R. Lopez-Martens, P. Johnsson, A. L’Huillier, W. Kornelis. J. Biegert, U. Keller, M. B. Gaarde, and K. J. Schafer, ”Measurement and control of the frequency chirp rate of high-order harmonic pulses”, Phys. Rev. A. 70, 021801R (2004)

Topography and Strong Fields

plasmonicsWe present theoretical studies of high-order-harmonic generation (HHG) produced by nonhomogeneous fields resulting from the illumination of plasmonic nanostructures with a short laser pulse. We show that both the inhomogeneity of the local fields and the confinement of the electron movement play an important role in the HHG process and lead to the generation of even harmonics and a significantly increased cutoff, more pronounced for the longer-wavelength cases studied. In order to understand and characterize the new HHG features, we employ two different approaches: the numerical solution of the time-dependent Schro ̈dinger equation and the semiclassical approach known as the strong-field approximation (SFA). Both approaches predict comparable results and show the new features, but by using the semiclassical arguments behind the SFA and time-frequency analysis tools, we are able to fully understand the reasons for the cutoff extension.

  1. M. F. Ciappina, Srdjan, S. Aćimović, T. Shaaran, J. Biegert, R. Quidant, M. Lewenstein, “Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures”, Opt. Exp. 20, 26261 (2012)
  2. M. Ciappina, J. Biegert, R. Quidant, M. Lewenstein, “High-order harmonic generation tailored using non-homogenous fields”, Phys. Rev. A. 85, 033828 (2012)
  3. M. F. Ciappina, J. A. Perez-Hernandez, T. Shaaran, J. Biegert, R. Quidant, M. Lewenstein , “Above threshold ionization by few-cycle spatially inhomogeneous fields”, Phys. Rev. A 86, 023413 (2012)