We 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)

We 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)

We 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)
× 10¹⁵ photons∕s∕mm2 ∕strad∕10% bandwidth and a photon flux of
(1.85 ± 0.12)
× 10⁷ 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)

We 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)

We 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)