The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.

We investigate plasmon-assisted photoelectron emission using a one-dimensional time-dependent densityfunctional theory model. The plasmons are excited nonlinearly by three laser photons. Photoelectron spectra are computed with the time-dependent surface-flux method. In addition to the expected above-threshold ionization comb, we observe peaks that arise from long-lived plasmon oscillations and the associated electron emission occurring after the laser pulse. We further analyze the positions of these peaks and their scaling behavior with the laser intensity.

High-harmonic generation (HHG) in inversion-symmetric systems is typically restricted to odd harmonics by symmetry. Here, we show that this selection rule can be broken without modifying the underlying Hamiltonian. We investigate a boundary-driven Su-Schrieffer-Heeger (SSH) chain coupled to source and sink reservoirs and demonstrate that dissipative dynamics generates a nonequilibrium steady state carrying a finite DC current. While the SSH Hamiltonian retains inversion symmetry, the current-carrying steady-state density matrix does not, leading to the emergence of even harmonics in the emitted spectrum. Using a correlation-matrix approach based on the Lindblad master equation, we obtain the steady state and calculate the resulting HHG response. We find that the intensity of the even harmonics is directly controlled by the transport current, establishing a link between nonequilibrium charge transport and HHG selection rules. Our results uncover a mechanism for even-harmonic generation that relies solely on nonequilibrium steady-state symmetry breaking and provide a route to probing transport currents through ultrafast nonlinear spectroscopy in centrosymmetric quantum systems.

We utilize few-level model systems to analyze the polarization and phase properties of below-threshold harmonics generated from aligned molecules. In a two-level system, we find that the phase of emitted harmonics undergoes a distinct change. For harmonics with photon energies below the transition energy between the dominant field-dressed states, the phase alternates by π between successive odd harmonic orders. In contrast, the phase remains constant for harmonics above the transition energy. Exploiting this behavior, we construct a four-level model composed of two uncoupled two-level systems aligned along orthogonal directions. We demonstrate that with selected transition frequencies lower-order harmonics follow the polarization of the linearly polarized driving field while higher-order harmonics exhibit a mirrored polarization. The model predicts that aligned systems with orthogonal transition dipoles may show analogous phase and polarization features in the below-threshold regime.

We investigate High-Harmonic Generation (HHG) in the Su-Schrieffer-Heeger (SSH) chain with electron-phonon coupling modeled via the Holstein interaction. The system dynamics are simulated using the tight-binding approximation, with local phonons approximated as quantum harmonic oscillators. Phononic degrees of freedom significantly expand the Hilbert space dimension. This interaction modifies the eigenenergy spectrum by introducing new states within previously existing gaps, enhancing the harmonic yield through additional allowed transitions.

It has been found previously that the presence or absence of topological edge states in the Su-Schrieffer-Heeger (SSH) model has a huge impact on harmonic generation spectra. More specifically, the yield of harmonics for harmonic orders that correspond to photon energies below the band gap is many orders of magnitude different in the trivial and topological phases. It is shown in this work that this effect is still present if electron-electron interaction is taken into account, i.e., if a Hubbard term is added to the SSH Hamiltonian. To that end, finite SSH-Hubbard chains at half filling are considered that are short enough to be accessible to exact diagonalization but already show edge states in the topological phase. We show that the huge difference in the harmonic yield between the trivial and topological phases can be reproduced with few-level models employing only the manybody ground state and a few excited many-body states.

The existence of boundary states and their protection against symmetry-preserving perturbations are a hallmark feature of topological systems. While this concept originally emerged in the context of sin-gle-particle phenomena in condensed-matter physics, particle interactions have recently been identi-fied as alternative means to establish topological phases. As a consequence, nonlinear topological insu-lators gained much interest as a model system for many interacting particles. However, as their mean-field model inevitably breaks down for small numbers of particles, to date, topological states composed of only few interacting particles remain experimentally largely unexplored. In our work, we explore the physics of extended interaction-induced two-particle topological states, so-called Dou-blons. We experimentally implement non-local-interactions via non-adiabatic periodic driving and dimensional mapping in an artificial photonic solid. The resonant formation of extended Doublon qua-si-particles at specific local interaction strengths is observed, allowing us to probe the topologically protected motion of these entities through the bulk of the system. Our approach is compatible to a number of established experimental platforms and paves the way for studying topological few-particle phenomena with finite interaction strength.

High-order harmonic generation (HHG) is a powerful tool for probing electronic structure and ultrafast dynamics in matter. Traditionally studied in atomic and molecular gases, HHG has recently been extended to condensed matter, enabling all-optical investigations of electronic and crystal structures. Here, we experimentally demonstrate HHG in a new class of materials: thin organic molecular crystals with perfectly aligned molecules, using pentacene as a model system. Organic molecular crystals, characterized by weak intermolecular coupling, flat electronic bands, and large unit cells, differ fundamentally from conventional covalent or ionic crystals and have attracted significant interest as promising candidates for organic electronics. We show that pentacene crystals endure laser intensities sufficient for efficient HHG up to the 17th order. The harmonic yield as a function of laser polarization reveals a strong dependence on intermolecular interactions, with higher harmonic orders particularly sensitive to both nearest- and next-nearest-neighbor couplings. Model calculations indicate that weaker intermolecular interactions necessitate probing with higher harmonic orders to resolve the crystal structure. These findings suggest that HHG may serve as a powerful tool for probing the electronic structure of organic molecular crystals, enhancing all-optical techniques for studying electronic properties and ultrafast dynamics in complex organic materials.

We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse along their respective chains, independent from one another. Interaction between them, whether attractive or repellent, leads to an energetic separation of configurations where the particles are close to each other and those where they are farther separated. The energy difference causes close -by particles to remain bound together, forming a doublon. Their relative position in the starting configuration determines whether the doublon moves to the left or right or remains stationary due to the periodic driving.

Periodic driving may cause topologically protected, chiral transport along edges of a 2D lattice that, without driving, would be topologically trivial. We study what happens if one adds a different on-site potential along the diagonal of such a 2D grid. In addition to the usual bulk and edge states, the system then also exhibits doublon states, analogous to two interacting particles in one dimension. A particle initially located at an edge propagates along the system’s boundary. Its wavefunction splits when it hits the diagonal and continues propagating simultaneously along the edge and the diagonal. The strength of the diagonal potential determines the ratio between both parts. We show that for specific values of the diagonal potential, hopping onto the diagonal is prohibited so that the system effectively separates into two triangular lattices. For other values of the diagonal potential, we find a temporal delay between the two contributions traveling around and through the system. This behavior could enable the steering of topologically protected transport of light along the edges and through the bulk of laser-inscribed photonic waveguide arrays.

We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schrödinger equation (TDSE) an ideal candidate to benefit from it. Our N-shaped partition method optimizes the implementation of the numerical calculation on parallel architectures, without memory size constraints. Specifically, we discuss the realization of our method on graphics processing units (GPUs) and the Message Passing Interface (MPI). In GPU implementations, our scheme is particularly advantageous for systems whose size exceeds the global memory of a single processor. Moreover, because of its lack of memory constraints and the generality of the algorithm, it is well-suited for mixed architectures, typically available in large high performance computing (HPC) centers. We also provide an analytical estimation of the optimal parameters to implement our algorithm, and test numerically the suitability of our formula in a GPU implementation. Our method will be helpful to tackle problems which require large spatial grids for which ab-initio studies might be otherwise prohibitive both because of large shared-memory requirements and computation times.

In frequently studied two-band models for solid-state high-harmonic generation, interband harmonics in principle can range from the minimum to the maximum bandgap. However, it is known that a laser-intensity dependent cutoff exists that may be well below the maximum bandgap unless the laser intensity is so high that the electrons explore the entire Brillouin zone. We show that this laser-intensity dependent cutoff is formed by destructive interference of the emission of electrons starting at different initial states in the Brillouin zone. The calculations in this work are for Su-Schrieffer-Heeger chains but our findings apply to other two-band systems as well. Only when the sampling of the Brillouin zone is fine enough or, equivalently, a finite chain is long enough in position space, the destructive interference is complete and forms the cutoff. For coarser sampling and shorter chains all harmonics between minimum and maximum bandgap are emitted. A time-frequency analysis shows how certain trajectories are responsible for the formation of the cutoff.

Strong-field imaging techniques such as laser-induced electron diffraction (LIED) provide unprecedented combined picometer spatial and attosecond temporal resolution by “self-imaging” a molecular target with its own rescattering electrons. Accessing the rich information contained in these experiments requires the ability to accurately manipulate the dynamics of these electrons—namely, their ionization amplitudes, and times of ionization and rescattering—with attosecond to femtosecond precision. The primary challenge is imposed by the multitude of quantum pathways of the photoelectron, reducing the effective measurement to a small range of energies and providing very limited spatial resolution. Here, we show how this ambiguity can be virtually eliminated by manipulating the rescattering pathways with a tailored laser field. Through combined experimental and theoretical approaches, a phase-controlled two-color laser waveform is shown to facilitate the selection of a specific quantum pathway, allowing a direct mapping between the electron’s final momentum and the rescattering time. Integrating attosecond control with Ångstrom-scale resolution could advance ultrafast imaging of field-induced quantum phenomena.

While topological single-particle systems have been extensively studied [1], topologically protected entangled two-boson states [2] and many-boson states [3] have recently come into the focus of research. However, interacting particle pairs in these systems have yet to be studied experimentally. This work focuses on the topological center-of-mass motion of bound two-particle states - so-called doublons [4], arising in a 1D lattice for discrete potentials with repulsive interaction. The tight-binding dynamics of a repulsive interacting two-particle state on such a 1D chain can be mapped onto a single particle evolving in a 2D lattice (Fig. 1a), where the main diagonal sites experience an on-site potential $U$ [5]. For the 2D case, we choose a square lattice driven by a conventional anomalous Floquet protocol with a full wave packet transfer in each hopping and uniformly distributed couplings $c$ [6]. The driving scheme preserves the mapping and adds a long-range interaction between the two particles in the 1D lattice.

The presence of topologically protected edge states is usually determined by angular-resolved photoelectron spectroscopy, requiring clean surfaces and ultrahigh vacuum. Now, an all-optical technique, based on high-harmonic radiation, has been shown to detect topological phase transitions under ambient conditions.

Magnesium atoms fully embedded in helium nanodroplets are exposed to two-color laser pulses, which trigger multiphoton above-threshold ionization (ATI). This allows exemplary study of the contribution of a dense, neutral, and finite medium on single electron propagation. The angular-resolved photoelectron spectra show striking differences with respect to results obtained on free atoms. Scattering of the individual Mg photoelectrons, when traversing the neutral helium environment, causes the angular distribution to become almost isotropic. Furthermore, the appearance of higher-energy electrons is observed, indicating the impact of the droplet on the concerted emission process. Phase-of-the-phase spectroscopy, however, reveals a marked loss in the 2ω-ω phase dependence of the electron signal. Taking into account sideband formation on a quantitative level, a Monte Carlo simulation which includes laser-assisted electron scattering can reproduce the experimental spectra and give insights into the strong-field-induced electron emission from disordered systems.

Two particles move alternatingly on two coupled chains. Interaction between them suppresses diffusion. At correct timing, it also leads to directional transport. The particles’ starting positions determine the direction of their leapfrogging movement.

High-harmonics spectroscopy reveals the closure of the bandgap between adjacent conduction bands in solids driven by high-intensity laser fields, providing insight into light-driven modifications of band structures