Attosecond control of orbital parity mix interferences and the relative phase of even and odd harmonics in an attosecond pulse train

Separation of photoionization and measurement-induced delays

Photoionization of matter is one of the fastest electronic processes in nature. Experimental measurements of photoionization dynamics have become possible through attosecond metrology. However, all experiments reported to date contain a so-far unavoidable measurement-induced contribution, known as continuum-continuum (CC) or Coulomb-laser-coupling delay. In traditional attosecond metrology, this contribution is nonadditive for most systems and nontrivial to calculate. Here, we introduce the concept of mirror symmetry-broken attosecond interferometry, which enables the direct and separate measurement of both the native one-photon ionization delays and the CC delays. Our technique solves the longstanding challenge of experimentally isolating these two contributions. This advance opens the door to the next generation of accurate measurements and precision tests that will set standards for benchmarking the accuracy of electronic structure and electron-dynamics methods.

Ultrafast Molecular Frame Quantum Tomography

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

Attosecond Intramolecular Scattering and Vibronic Delays

We study the temporal and vibrational signature of the universal nuclear recoil associated with the electron emission and intramolecular scattering that accompanies the photoelectric effect. We illustrate these phenomena in the photoionization of the CO molecule from the C-1s orbital using an analytical model that reproduces the entangled character of the nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Photoionization by a broadband x-ray pulse results in a coherent vibrational ionic state delayed compared to the classical sudden-photoemission limit.

Quantitative uncertainty determination of phase retrieval in RABBITT

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is one of the most widely used approaches to measure the time delays in photoionization. The time delay, which corresponds to a phase difference of two oscillating signals, is usually retrieved by cosine fitting or fast Fourier transform (FFT). We propose two estimators for the phase uncertainty of cosine fitting from the signal per se of an individual experiment: (i) σ(φ _fit)≈B A2N, where B/A is the mean-value-to-amplitude ratio, and N is the total count number, and (ii) σ(φ _fit)≈1-R ² R ² n _bins, where n_bins is the total number of bins in the time domain, and R² is the coefficient of determination. The former estimator is applicable for the statistical fluctuation, while the latter includes the effects from various uncertainty sources, which is mathematically proven and numerically validated. This leads to an efficient and reliable approach to determining quantitative uncertainties in RABBITT experiments and evaluating the observed discrepancy among individual measurements, as demonstrated on the basis of experimental data.

Attosecond laser control of photoelectron angular distributions in XUV-induced ionization of H2

We investigate how attosecond XUV pump/IR probe schemes can be used to exert control on the ionization dynamics of the hydrogen molecule. The aim is to play with all available experimental parameters in the problem, namely the XUV pump-IR probe delay, the energy and emission direction of the produced photo-ions, as well as combinations of them, to uncover control strategies that can lead to preferential electron ejection directions. We do so by accurately solving the time-dependent Schrödinger equation, with inclusion of both electronic and nuclear motions, as well as the coupling between them. We show that both the IR pulse and the nuclear motion can be used to break the molecular inversion symmetry, thus leading to asymmetric molecular-frame photoelectron angular distributions. The preferential electron emission direction can thus be tuned by varying the pump-probe delay, by choosing specific ranges of proton kinetic energies, or both. We expect that similar control strategies could be used in more complex molecules containing light nuclei.

Controlling photoionization using attosecond time-slit interferences

When small quantum systems, atoms or molecules, absorb a high-energy photon, electrons are emitted with a well-defined energy and a highly symmetric angular distribution, ruled by energy quantization and parity conservation. These rules are based on approximations and symmetries which may break down when atoms are exposed to ultrashort and intense optical pulses. This raises the question of their universality for the simplest case of the photoelectric effect. Here we investigate photoionization of helium by a sequence of attosecond pulses in the presence of a weak infrared laser field. We continuously control the energy of the photoelectrons and introduce an asymmetry in their emission direction, at variance with the idealized rules mentioned above. This control, made possible by the extreme temporal confinement of the light-matter interaction, opens a road in attosecond science, namely, the manipulation of ultrafast processes with a tailored sequence of attosecond pulses.

Tunable high-order frequency mixing for XUV transient absorption and photoelectron spectroscopies

We generate tunable extreme ultraviolet emission through high-order frequency mixing between a strong near-infrared field and a weak shortwave-infrared pulse whose wavelength can be adjusted. In this two-color driving scheme, new harmonics appear in between the single-color harmonics at energies which are linear combinations of photons from the two pulses. We demonstrate the utility of tunable two-color harmonics by employing them for XUV transient absorption spectroscopy and time-resolved photoelectron spectroscopy. We show that the two-color harmonics can be used to address the dynamics associated with excited states in Helium and Oxygen which are inaccessible using single-color harmonics. Specifically, we show the ability to switch between excitation of 3p and 4p states in Helium, control of transitions to the light induced states, observe new four-wave-mixing emissions, and selectively address different principal and vibrational quantum numbers associated with Oxygen Rydberg states.

Design of an optically-locked interferometer for attosecond pump-probe setups

We present the design and performance of an active stabilization system for attosecond pump-probe setups based on a Mach-Zehnder interferometer configuration. The system employs a CW laser propagating coaxially with the pump and probe beams in the interferometer. The stabilization is achieved with a standalone feedback controller that adjusts the length of one of its arms to maintain a constant relative phase between the CW beams. With this system, the time delay between the pump and probe beams is stabilized within 10 as rms over several hours. The system is easy to operate and only requires a few minutes to set up before any pump/probe measurements.

Circular Holographic Ionization-Phase Meter

We propose an attosecond extreme ultraviolet pump IR-probe photoionization protocol that employs pairs of counterrotating consecutive harmonics and angularly resolved photoelectron detection, thereby providing a direct measurement of ionization phases. The present method, which we call circular holographic ionization-phase meter, gives also access to the phase of photoemission amplitudes of even-parity continuum states from a single time-delay measurement since the relative phase of one- and two-photon ionization pathways is imprinted in the photoemission anisotropy. The method is illustrated with ab initio simulations of photoionization via autoionizing resonances in helium. The rapid phase excursion in the transition amplitude to both the dipole-allowed (2s2p)^{1}P^{o} and the dipole-forbidden (2p^{2})^{1}D^{e} states are faithfully reproduced.

Anisotropic photoemission time delays close to a Fano resonance

Electron correlation and multielectron effects are fundamental interactions that govern many physical and chemical processes in atomic, molecular and solid state systems. The process of autoionization, induced by resonant excitation of electrons into discrete states present in the spectral continuum of atomic and molecular targets, is mediated by electron correlation. Here we investigate the attosecond photoemission dynamics in argon in the 20–40 eV spectral range, in the vicinity of the 3s⁻¹np autoionizing resonances. We present measurements of the differential photoionization cross section and extract energy and angle-dependent atomic time delays with an attosecond interferometric method. With the support of a theoretical model, we are able to attribute a large part of the measured time delay anisotropy to the presence of autoionizing resonances, which not only distort the phase of the emitted photoelectron wave packet but also introduce an angular dependence.

Ionization time delays are of interest in understanding the photoionization mechanism in atoms and molecules in ultra-short time scales. Here the authors investigate the angular dependence of photoionization time delays in the presence of an autoionizing resonance in argon atom using RABBITT technique.

Revealing the Sub-Barrier Phase using a Spatiotemporal Interferometer with Orthogonal Two-Color Laser Fields of Comparable Intensity

We measure photoelectron momentum distributions of Ar atoms in orthogonally polarized two-color laser fields with comparable intensities. The synthesized laser field is used to manipulate the oscillating tunneling barrier and the subsequent motion of electrons onto two spatial dimensions. The subcycle structures associated with the temporal double-slit interference are spatially separated and enhanced. We use such a spatiotemporal interferometer to reveal sub-barrier phase of strong-field tunneling ionization. This study shows that the tunneling process transfers the initial phase onto momentum distribution. Our work has the implication that the sub-barrier phase plays an indispensable role in photoelectron interference processes.

Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities

We theoretically investigate the nonadiabatic subcycle electron dynamics in orthogonally polarized two-color laser fields with comparable intensities. The photoelectron dynamics is simulated by exact solution to the 3D time-dependent Schrödinger equation, and also by two other semiclassical methods, i.e., the quantum trajectory Monte Carlo simulation and the Coulomb-corrected strong field approximation. Through these methods, we identify the underlying mechanisms of the subcycle electron dynamics and find that both the nonadiabatic effects and the Coulomb potential play very important roles. The contribution of the nonadiabatic effects manifest in two aspects, i.e., the nonadiabatic ionization rate and the nonzero initial velocities at the tunneling exit. The Coulomb potential has a different impact on the electrons' trajectories for different relative phases between the two pulses.

Modulation of attosecond beating in resonant two-photon ionization

We present a theoretical study of the photoelectron attosecond beating due to interference of two-photon transitions in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, both the phase shift and frequency of the sideband beating significantly vary with photon energy. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a nonholographic interferometric means to reconstruct coherent metastable wave packets. We characterize these phenomena by means of a general analytical model that accounts for the effect of both intermediate and final resonances on two-photon processes. The model predictions are in excellent agreement with those of accurate ab initio calculations for the helium atom in the region of the N=2 doubly excited states.

Attosecond pulse characterization

In this work we propose a novel procedure for the characterization of attosecond pulses. The method relies on the conversion of the attosecond pulse into electron wave-packets through photoionization of atoms in the presence of a weak IR field. It allows for the unique determination of the spectral phase making up the pulses by accurately taking into account the atomic physics of the photoionization process. The phases are evaluated by optimizing the fit of a perturbation theory calculation to the experimental result. The method has been called iPROOF (improved Phase Retrieval by Omega Oscillation Filtering) as it bears a similarity to the PROOF technique [Chini et al. Opt. Express 18, 13006 (2010)]. The procedure has been demonstrated for the characterization of an attosecond pulse train composed of odd and even harmonics. We observe a large phase shift between consecutive odd and even harmonics. The resulting attosecond pulse train has a complex structure not resembling a single attosecond pulse once per IR period, which is the case for zero phase. Finally, the retrieval procedure can be applied to the characterization of single attosecond pulses as well.