XUV-beamline for photoelectron imaging spectroscopy with shaped pulses

We introduce an extreme ultraviolet (XUV)-beamline designed for the time-resolved investigation and coherent control of attosecond (as) electron dynamics in atoms and molecules by polarization-shaped as-laser pulses. Shaped as-pulses are generated through high-harmonic generation (HHG) of tailored white-light supercontinua (WLS) in noble gases. The interaction of shaped as-pulses with the sample is studied using velocity map imaging (VMI) techniques to achieve the differential detection of photoelectron wave packets. The instrument consists of the WLS-beamline, which includes a hollow-core fiber compressor and a home-built 4f polarization pulse shaper, and the high-vacuum XUV-beamline, which combines an HHG-stage and a versatile multi-experiment vacuum chamber equipped with a home-built VMI spectrometer. The VMI spectrometer allows the detection of photoelectron wave packets from both the multiphoton ionization (MPI) of atomic or molecular samples by the tailored WLS-pulses and the single-photon ionization (SPI) by the shaped XUV-pulses. To characterize the VMI spectrometer, we studied the MPI of xenon atoms by linearly polarized WLS pulses. To validate the interplay of these components, we conducted experiments on the SPI of xenon atoms with linearly polarized XUV-pulses. Our results include the reconstruction of the 3D photoelectron momentum distribution (PMD) and initial findings on the coherent control of the PMD by tuning the spectrum of the XUV-pulses with the spectral phase of the WLS. Our results demonstrate the performance of the entire instrument for HHG-based photoelectron imaging spectroscopy with prototypical shaped pulses. Perspectively, we will employ polarization-tailored WLS-pulses to generate polarization-shaped as-pulses.

Out-of-focus spatial map imaging of magnetically deflected sodium ammonia clusters

This paper introduces out-of-focus spatial map imaging (SMI) as a detection method for magnetic deflection of molecular/cluster beams, using Nam(NH3)n to illustrate its capabilities. This method enables imaging of the complete spatial distribution, simplifying measurements and allowing for cluster-size-resolved analysis by shifting away from traditional in-focus SMI conditions. Incorporating out-of-focus SMI with TOF-MS and velocity map imaging into a single setup allows for direct assessment of clusters' magnetic moments without needing to pre-select velocities. Key findings include a slower relaxation for Na(NH3)4 compared to Na(NH3)3 and Na(NH3)5, unexpectedly high deflection for larger clusters up to Na(NH3)9, hinting at changes in cluster dynamics as the first solvation shell closes. The study also covers the first measurements of Na2(NH3)1 and Na3(NH3)n, showing distinct deflection behaviors and underscoring the improved capabilities of the new detection method.

Generation of attosecond gigawatt soft x-ray pulses through coherent Thomson backscattering

Collision between relativistic electron sheets and counterpropagating laser pulses is recognized as a promising way to produce intense attosecond x rays through coherent Thomson backscattering (TBS). In a double-layer scheme, the electrons in an ultrathin solid foil are first pushed out by an intense laser driver and then interact with the laser reflected off a second foil to form a high-density relativistic electron sheet with vanishing transverse momentum. However, the repulsion between these concentrated electrons can increase the thickness of the layer, reducing both its density and subsequently the coherent TBS. Here, we present a systematic study on the evolution of the flying electron layer and find that its resulting thickness is determined by the interplay between the intrinsic space-charge expansion and the velocity compression induced by the drive laser. How the laser driver, the target areal density, the reflector, and the collision laser intensity affect the properties of the produced x rays is explored. Multidimensional particle-in-cell simulations indicate that employing this scheme in the nonlinear regime has the potential to stably produce soft x rays with several gigawatt peak power in hundreds of terawatt ultrafast laser facilities. The pulse duration can be tuned to tens of attoseconds. This compact and intense attosecond x-ray source may have broad applications in attosecond science.

Attosecond Probing of Nuclear Vibrations in the D2+ and HeH+ Molecular Ions

We study the ultrafast photodissociation of small diatomic molecules using attosecond laser pulses of moderate intensity in the (extreme) ultraviolet regime. The simultaneous application of subfemtosecond laser pulses with different photon energies─resonant in the region of the molecular motion─allows one to monitor the vibrational dynamics of simple diatomics, like the D2+ and HeH+ molecular ions. In our real-time wave packet simulations, the nuclear dynamics is initiated either by sudden ionization (D2+) or by explicit pump pulses (HeH+) via distortion of the potential energy of the molecule. The application of time-delayed attosecond pulses leads to the breakup of the molecules, and the information on the underlying bound-state dynamics is imprinted in the kinetic energy release (KER) spectra of the outgoing fragments. We show that the KER-delay spectrograms generated in our ultrafast pump-probe schemes are able to reconstruct the most important features of the molecular motion within a given electronic state, such as the time period or amplitude of oscillations, interference patterns, or the revival and splitting of the nuclear wave packet. The impact of probe pulse duration, which is key to the applicability of the presented mapping scheme, is investigated in detail.

Time-stretched multi-hit 3D velocity map imaging of photoelectrons

The 2D photoelectron velocity map imaging (VMI) technique is commonly employed in gas-phase molecular spectroscopy and dynamics investigations due to its ability to efficiently extract photoelectron spectra and angular distributions in a single experiment. However, the standard technique is limited to specific light-source polarization geometries. This has led to significant interest in the development of 3D VMI techniques, which are capable of measuring individual electron positions and arrival times, obtaining the full 3D distribution without the need for inversion, forward-convolution, or tomographic reconstruction approaches. Here, we present and demonstrate a novel time-stretched, 13-lens 3D VMI photoelectron spectrometer, which has sub-camera-pixel spatial resolution and 210 ps (σ) time-of-flight (TOF) resolution (currently limited by trigger jitter). We employ a kHz CMOS camera to image a standard 40 mm diameter microchannel plate (MCP)/phosphor anode detector (providing x and y positions), combined with a digitizer pick-off from the MCP anode to obtain the electron TOF. We present a detailed analysis of time-space correlation under data acquisition conditions which generate multiple electrons per laser shot, and demonstrate a major advantage of this time-stretched 3D VMI approach: that the greater spread in electron TOFs permits for an accurate time- and position-stamping of up to six electrons per laser shot at a 1 kHz repetition rate.

Manipulating twisted electrons in strong-field ionization

We investigate the discrete orbital angular momentum (OAM) of photoelectrons freed in strong-field ionization. We use these 'twisted' electrons to provide an alternative interpretation on existing experimental work of vortex interferences caused by strong field ionization mediated by two counter-rotating circularly polarized pulses separated by a delay. Using the strong field approximation, we derive an interference condition for the vortices. In computations for a neon target we find very good agreement of the vortex condition with photoelectron momentum distributions computed with the strong field approximation, as well as with the time-dependent methods Qprop and R-Matrix. For each of these approaches we examine the OAM of the photoelectrons, finding a small number of vortex states localized in separate energy regions. We demonstrate that the vortices arise from the interference of pairs of twisted electron states. The OAM of each twisted electron state can be directly related to the number of arms of the spiral in that region. We gain further understanding by recreating the vortices with pairs of twisted electrons and use this to determine a semiclassical relation for the OAM. A discussion is included on measuring the OAM in strong field ionization directly or by employing specific laser pulse schemes as well as utilizing the OAM in time-resolved imaging of photo-induced dynamics.

Asymmetries in ionization of atomic superposition states by ultrashort laser pulses

Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

STM Imaging of Electron Migration in Real Space and Time: A Simulation Study

Using a simulation protocol that mimics ultrafast scanning tunneling microscopy (STM) experiments, we demonstrate how pump-probe ultrafast STM may be used to image electron migration in molecules. Two pulses are applied to a model system, and the time-integrated current through the tip is calculated versus the delay time and tip position to generate STM images. With suitable pump and probe parameters, the images can track charge migration with atomistic spatial and femtosecond temporal resolutions.

A fast and adaptable method for high accuracy integration of the time-dependent Schrödinger equation

We present an adaptable, fast, and robust method for integrating the time-dependent Schrödinger equation. We apply the method to calculations of High Harmonic (HHG) and Above Threshold Ionisation (ATI) spectra for a single atomic electron in an intense laser field. Our approach implements the stabilized bi-conjugate gradient method (BiCG-STAB) for solving a sparse linear system to evolve the electronic wavefunction in time. The use of this established method makes the propagation scheme less restrictive compared to other schemes which may have particular requirements for the form of the equation, such as use of a three-point finite-difference approximation for spatial derivatives. Our method produces converged solutions significantly faster than existing methods, particularly if high accuracy is required. We demonstrate that this approach is suitable for a range of different parameters and show that in many circumstances significant gains can be made with the use of a fourth-order time propagator as opposed to the more common second-order Crank-Nicolson (CN) method.

Controlling the multi-electron dynamics in the high harmonic spectrum from N2O molecule using TDDFT

In this study, high harmonic generation from a multi-atomic nitrous oxide molecule was investigated. A comprehensive three-dimensional calculation of the molecular dynamics and electron trajectories through an accurate time-dependent density functional theory was conducted to efficiently explore a broad harmonic plateau. The effects of multi-electron and inner orbitals on the harmonic spectrum and generated coherent attosecond pulses were analyzed. The role of the valence electrons in controlling the process and extending the harmonic plateau was investigated. The main issue of producing a super-continuum harmonic spectrum via a frequency shift was considered. The time-frequency representation by means of a wavelet transform of the induced dipole acceleration provided a good insight into the distorted effects from the nonlinear processes in high harmonic emission. The effect of the chirped laser pulse on the production of broadband amplitude was justified in this model. By adjusting the optimal laser parameters to an input intensity of 2.5 × 10¹⁴ W cm^-2, an isolated 68 as pulse was generated.

Quantum control of coherent π-electron ring currents in polycyclic aromatic hydrocarbons

We present results for quantum optimal control (QOC) of the coherent π electron ring currents in polycyclic aromatic hydrocarbons (PAHs). Since PAHs consist of a number of condensed benzene rings, in principle, there exist various coherent ring patterns. These include the ring current localized to a designated benzene ring, the perimeter ring current that flows along the edge of the PAH, and the middle ring current of PAHs having an odd number of benzene rings such as anthracene. In the present QOC treatment, the best target wavefunction for generation of the ring current through a designated path is determined by a Lagrange multiplier method. The target function is integrated into the ordinary QOC theory. To demonstrate the applicability of the QOC procedure, we took naphthalene and anthracene as the simplest examples of linear PAHs. The mechanisms of ring current generation were clarified by analyzing the temporal evolutions of the electronic excited states after coherent excitation by UV pulses or (UV+IR) pulses as well as those of electric fields of the optimal laser pulses. Time-dependent simulations of the perimeter ring current and middle ring current of anthracene, which are induced by analytical electric fields of UV pulsed lasers, were performed to reproduce the QOC results.

Coincident velocity map image reconstruction illustrated by the single-photon valence photoionisation of CF3SF5

Photoion–photoelectron kinetic energy and angular anisotropy correlation maps reveal new details about the ionization mechanism.

Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics.

Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses

Exploring ultrafast charge migration is of great importance in biological and chemical reactions.

Laser-induced electron localization in H₂⁺: mixed quantum-classical dynamics based on the exact time-dependent potential energy surface

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett., 2010, 105, 123002] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes.