Emergence of Time from Quantum Interaction with the Environment.

The nature of time as emergent for a system by separating it from its environment has been put forward by Page and Wootters [Phys. Rev. D 27, 2885 (1983)PRVDAQ0556-282110.1103/PhysRevD.27.2885] in a quantum mechanical setting neglecting interaction between system and environment. Here, we add strong support to the relational concept of time by deriving the time-dependent Schrödinger equation for a system from an energy eigenstate of the global Hamiltonian consisting of system, environment, and their interaction. Our results are consistent with concepts for the emergence of time where interaction has been taken into account at the expense of a semiclassical treatment of the environment. Including the coupling between system and environment without approximation adds a missing link to the relational time approach opening it to dynamical phenomena of interacting systems and entangled quantum states.

Widely tunable XUV harmonics using double IR pulses.

Tunable attosecond pulses are necessary for various attosecond resolved spectroscopic applications, which can potentially be obtained through the tuning of high harmonic generation. Here we show theoretically, using the time-dependent Schrödinger equation and strong field approximation, a continuously tunable spectral shift of high-order harmonics by exploiting the interaction of two delayed identical infrared (IR) pulses within the single-atom response. The tuning spans more than twice the driving frequency (∼2ω) range, for several near-cutoff harmonics, with respect to only one control parameter: the change in delay between the two IR pulses. We show that two distinct mechanisms contribute to the spectral shift of the harmonic spectra. The dominant part of the spectral shift of the harmonics is due to the modulation of the central frequency of the composite IR-IR pulse with respect to delay. The second contribution comes from the non-adiabatic phase-shift of the recolliding electron wavepacket due to the change in amplitude of the subcycle electric field within the double pulse envelope. For optical few-cycle pulses this scheme can produce tunable attosecond pulse trains (APT), and in the single-cycle regime the same can be used for tuning isolated attosecond pulses (IAP). We quantify the dependence of tuning range and tuning rate on the laser pulse duration. We envision that the proposed scheme can be easily implemented with compact in-line setups for generating frequency tunable APT/IAP.

In-line ultra-thin attosecond delay line with direct absolute-zero delay reference and high stability.

We introduce an ultra-thin attosecond optical delay line based on controlled wavefront division of a femtosecond infrared pulse after transmission through a pair of micrometer-thin glass plates with negligible dispersion effects. The time delay between the two pulses is controlled by rotating one of the glass plates from absolute zero to several optical cycles, with 2.5 as to tens of attosecond resolution with 2 as stability, as determined by interferometric self-calibration. The performance of the delay line is validated by observing attosecond-resolved oscillations in the yield of high harmonics induced by time delayed infrared pulses, in agreement with a numerical simulation for a simple model atom. This approach can be extended in the future for performing XUV-IR attosecond pump-probe experiments.

Proper Time Delays Measured by Optical Streaking.

In attosecond science it is assumed that Wigner-Smith time delays, known from scattering theory, are determined by measuring streaking shifts. Despite their wide use from atoms to solids this has never been proven. Analyzing the underlying process-energy absorption from the streaking light-we derive this relation. It reveals that only under specific conditions streaking shifts measure Wigner-Smith time delays. For the most relevant case, interactions containing long-range Coulomb tails, we show that finite streaking shifts, including relative shifts from two different orbitals, are misleading. We devise a new time-delay definition and describe a measurement technique that avoids the record of a complete streaking scan, as suggested by the relation between time delays and streaking shifts.

Dressed Ion-Pair States of an Ultralong-Range Rydberg Molecule.

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than R_{∞}/2.

Purifying Electron Spectra from Noisy Pulses with Machine Learning Using Synthetic Hamilton Matrices.

Photoelectron spectra obtained with intense pulses generated by free-electron lasers through self-amplified spontaneous emission are intrinsically noisy and vary from shot to shot. We extract the purified spectrum, corresponding to a Fourier-limited pulse, with the help of a deep neural network. It is trained on a huge number of spectra, which was made possible by an extremely efficient propagation of the Schrödinger equation with synthetic Hamilton matrices and random realizations of fluctuating pulses. We show that the trained network is sufficiently generic such that it can purify atomic or molecular spectra, dominated by resonant two- or three-photon ionization, nonlinear processes which are particularly sensitive to pulse fluctuations. This is possible without training on those systems.

Universal High-Energy Photoelectron Emission from Nanoclusters Beyond the Atomic Limit.

Rescattering by electrons on classical trajectories is central to understand photoelectron and high-harmonic emission from isolated atoms or molecules in intense laser pulses. By controlling the cluster size and the quiver amplitude of electrons, we demonstrate how rescattering influences the energy distribution of photoelectrons emitted from noble gas nanoclusters. Our experiments reveal a universal dependence of photoelectron energy distributions on the cluster size when scaled by the field driven electron excursion, establishing a unified rescattering picture for extended systems with the known atomic dynamics as the limit of zero extension. The result is supported by molecular dynamics calculations and rationalized with a one-dimensional classical model.

Adiabatic Passage to the Continuum: Controlling Ionization with Chirped Laser Pulses.

We demonstrate that, by changing the direction of the chirp in vacuum-ultraviolet pulses, one can switch between excitation and ionization with very high contrast, if the carrier frequency of the light is resonant with two bound states. This is a surprising consequence of rapid adiabatic passage if extended to include transitions to the continuum. The chirp phase locks the linear combination of the two resonantly coupled bound states whose ionization amplitudes interfere constructively or destructively depending on the chirp direction under suitable conditions. We derive the phenomenon in a minimal model and verify the effect with calculations for helium as a realistic example.

Electron Dynamics Driven by Light-Pulse Derivatives.

We demonstrate that ultrashort pulses carry the possibility for a new regime of light-matter interaction with nonadiabatic electron processes sensitive to the envelope derivative of the light pulse. A standard single pulse with its two peaks in the derivative separated by the width of the pulse acts in this regime like a traditional double pulse. The two ensuing nonadiabatic ionization bursts have slightly different ionization amplitudes. This difference is due to the redistribution of continuum electron energy during the bursts, negligible in standard photoionization. A time-dependent close-coupling approach based on cycle-averaged potentials in the Kramers-Henneberger reference frame permits a detailed understanding of light-pulse derivative-driven electron dynamics.

Essential Conditions for Dynamic Interference.

We develop general quantitative criteria for dynamic interference, a manifestation of a double-slit interference in time which should be realizable with brilliant state-of-the-art high-frequency laser sources. Our analysis reveals that the observation of dynamic interference hinges upon maximizing the difference between the dynamic polarization of the initial bound and the final continuum states of the electron during the light pulse while keeping depletion of the initial state small. These two properties, Stark shift and depletion, can be determined from electronic structure calculations avoiding expensive propagation in time. Confirmed by numerical results, we predict that this is impossible for the hydrogen ground state but feasible for excited states; this has been exemplified for the case of the hydrogen 2p state.

Enhancing scattering images for orientation recovery with diffusion map.

We explore the possibility for orientation recovery in single-molecule coherent diffractive imaging with diffusion map. This algorithm approximates the Laplace-Beltrami operator, which we diagonalize with a metric that corresponds to the mapping of Euler angles onto scattering images. While suitable for images of objects with specific properties we show why this approach fails for realistic molecules. We introduce a modification of the form factor in the scattering images which facilitates the orientation recovery and should be suitable for all recovery algorithms based on the distance of individual images.

Dynamical Characteristics of Rydberg Electrons Released by a Weak Electric Field.

The dynamics of ultraslow electrons in the combined potential of an ionic core and a static electric field is discussed. With state-of-the-art detection it is possible to create such electrons through strong intense-field photoabsorption and to detect them via high-resolution time-of-flight spectroscopy despite their very low kinetic energy. The characteristic feature of their momentum spectrum, which emerges at the same position for different laser orientations, is derived and could be revealed experimentally with an energy resolution of the order of 1 meV.

Prevailing features of x-ray-induced molecular electron spectra revealed with fullerenes.

X-ray photoabsorption from intense short pulses by a molecule triggers complicated electron and subsequently ion dynamics, leading to photoelectron spectra, which are difficult to interpret. Illuminating fullerenes offers a way to separate out the electron dynamics since the cage structure confines spatially the origin of photo- and Auger electrons. Together with the sequential nature of the photoprocesses at intensities available at x-ray free-electron lasers, this allows for a remarkably detailed interpretation of the photoelectron spectra, as we will demonstrate. The general features derived can serve as a paradigm for less well-defined situations in other large molecules or clusters.

Spatial correlations in finite samples revealed by Coulomb explosion.

We demonstrate that fast removal of many electrons uncovers initial correlations of atoms in a finite sample through a pronounced peak in the kinetic-energy spectrum of the exploding ions. This maximum is the result of an intricate interplay between the composition of the system from discrete particles and its boundary. The formation of the peak can be described analytically, accounting for correlations beyond a mean-field reference model. It can be experimentally detected with short and intense light pulses from 4th-generation light sources.

Electron-energy bunching in laser-driven soft recollisions.

We introduce soft recollisions in laser-matter interaction. They are characterized by the electron missing the ion upon recollision in contrast with the well-known head-on collisions responsible for high-harmonic generation or above-threshold ionization. We demonstrate analytically that soft recollisions can cause a bunching of photoelectron energies through which a series of low-energy peaks emerges in the electron yield along the laser polarization axis. This peak sequence is universal, it does not depend on the binding potential, and is found below an excess energy of one tenth of the ponderomotive energy.

Characterizing the dynamics of higher dimensional nonintegrable conservative systems.

The phase space dynamics of higher dimensional nonintegrable conservative systems is characterized via the effect of "sticky" motion on the finite time Lyapunov exponents (FTLEs) distribution. Since a chaotic trajectory suffers the sticky effect when chaotic motion is mixed to the regular one, it offers a way to separate the mixed from the totally chaotic regimes. To detect stickiness, four different measures are used, related to the distributions of the positive FTLEs, and provide conditions to characterize the dynamics. Conservative maps are systematically studied from the uncoupled two-dimensional case up to coupled maps of dimension 20. Sticky motion is detected in all unstable directions above a threshold K(d) of the nonlinearity parameter K for the high dimensional cases d = 10, 20. Moreover, as K increases we can clearly identify the transition from mixed to totally chaotic motion which occurs simultaneously in all unstable directions. Results show that all four statistical measures sensitively characterize the motion in high dimensional systems.