Claudio Cirelli

Attosecond Science: Recent Highlights and Future Trends

We review the first ten years of attosecond science with a selection of recent highlights and trends and give an outlook on future directions. After introducing the main spectroscopic tools, we give recent examples of representative experiments employing them. Some of the most fundamental processes in nature have been studied with some results initiating controversial discussions. Experiments on the dynamics of single-photon ionization illustrate the importance of subtle effects on such extreme timescales and lead us to question some of the well-established assumptions in this field. Attosecond transient absorption, as the first all-optical approach to resolve attosecond dynamics, has been used to study electron wave packet interferences in helium. The attoclock, a recent method providing attosecond time resolution without the explicit need for attosecond pulses, has been used to investigate electron tunneling dynamics and geometry. Pushing the frontiers in attosecond quantum mechanics with increasing temporal and spatial resolution and often limited theoretical models results in unexpected observations. At the same time, attosecond science continues to expand into more complex solid-state and molecular systems, where it starts to have impact beyond its traditional grounds.

Ultrafast resolution of tunneling delay time

The question of how long a tunneling particle spends inside the barrier region has remained unresolved since the early days of quantum mechanics. The main theoretical contenders, such as the Buttiker–Landauer, Eisenbud–Wigner, and Larmor time, give contradictory answers. On the other hand, recent attempts at reconstructing valence electron dynamics in atoms and molecules have entered a regime where the tunneling time genuinely matters. Here, we compare the main competing theories of tunneling time against experimental measurements using the attoclock in strong laser field ionization of helium atoms. The attoclock uses a close to circularly polarized femtosecond laser pulse, mapping the angle of rotation of the laser field vector to time similar to the hand of a watch. Refined attoclock measurements reveal a real (not instantaneous) tunneling delay time over a large intensity regime, using two independent experimental apparatus. Only two theoretical predictions are compatible within our experimental error: the Larmor time and the probability distribution of tunneling times constructed using a Feynman Path Integral formulation. The latter better matches the observed qualitative change in tunneling time over a wide intensity range, and predicts a broad tunneling time distribution with a long tail. The implication of such a probability distribution of tunneling times, as opposed to a distinct tunneling time, would imply that one must account for a significant, though bounded and measurable, uncertainty as to when the hole dynamics begin to evolve. We therefore expect our results to impact the reconstruction of attosecond electron dynamics following tunnel ionization.Summary form only given. We present approach and results of an angular streaking experiment with the attoclock method [1] that suggest the existence of a real tunneling time in strong field ionization of Helium. The results are compared with competing theories of tunneling time and show that the only theories that are compatible with the experimental results are the L armor time and a distribution of tunneling times with a long tail constructed using a Feynman Path Integral formulation. We find that the latter matches the experimental data the best. Our results have strong implications on investigations of the electron dynamics in attosecond science since a significant uncertainty must be taken into account about when the electron hole dynamics begins to evolve.The attoclock method is based on the angular streaking of the photoelectron that was released from the atom by tunnel ionization. The angular distribution of the photoelectron momentum distribution contains the timing of the ionization process via an offset of the maximum of the angular distribution from the theoretically predicted value assuming instantaneous tunneling. Our results indicate the existence of a real tunneling time through this angular offset. The attoclock technique was transferred to a velocity map imaging setup (VMIS) in combination with tomographic reconstruction. The gas nozzle was integrated in the repeller plate, a configuration that allows one to achieve target gas densities that are significantly higher compared to setups employing cold atomic beams [2], leading to higher statistics and smaller error bars compared to previous measurements [1, 3]. Helium was leaked into the ultra high vacuum chamber and tunnel ionized by an elliptically polarized sub-10fs few-cycle pulse with a central wavelength of 735 nm and an ellipticity of 0.87. For the tomographic reconstruction, two-dimensional momentum space electron images are recorded in steps of two degrees covering a range of 180 degrees. The three-dimensional momentum distribution and thus the electron momentum distribution in the polarization plane is retrieved by tomographic reconstruction with a filtered backprojection algorithm [4, 5]. The results from the VMIS are confirmed with accurate measurements using a cold target recoil ion momentum spectrometer (COLTRIMS).

Resonance Effects in Photoemission Time Delays

We present measurements of single-photon ionization time delays between the outermost valence electrons of argon and neon using a coincidence detection technique that allows for the simultaneous measurement of both species under identical conditions. The analysis of the measured traces reveals energy-dependent time delays of a few tens of attoseconds with high energy resolution. In contrast to photoelectrons ejected through tunneling, single-photon ionization can be well described in the framework of Wigner time delays. Accordingly, the overall trend of our data is reproduced by recent Wigner time delay calculations. However, besides the general trend we observe resonance features occurring at specific photon energies. These features have been qualitatively reproduced and identified by a calculation using the multiconfigurational Hartree-Fock method, including the influence of doubly excited states and ionization thresholds.

Probing the longitudinal momentum spread of the electron wave packet at the tunnel exit.

We present an ellipticity resolved study of momentum distribution arising from strong-field ionization of helium. The influence of the ion potential on the departing electron is considered within a semi-classical model consisting of an initial tunneling step and subsequent classical propagation. We find that the momentum distribution can be explained by including the longitudinal momentum spread of the electron at the exit from the tunnel. Our combined experimental and theoretical study provides an estimate of this momentum spread.

Rydberg state creation by tunnel ionization

It is well known from numerical and experimental results that the fraction of Rydberg states (excited neutral atoms) created by tunnel ionization declines dramatically with increasing ellipticity of laser light, in a way that is similar to high harmonic generation (HHG). We present a method to analyze this dependence on ellipticity, deriving a probability distribution of Rydberg states that agrees closely with experimental (Nubbemeyer et al 2008 Phys. Rev. Lett. 101 233001) and numerical results. We show using analysis and numerics that most Rydberg electrons are ionized before the peak of the electric field and therefore do not come back to the parent ion. Our work shows, for the first time, the similarities and differences in the process that distinguishes formation of Rydberg electrons from electrons involved in HHG: ionization occurs in a different part of the laser cycle, but the post-ionization dynamics are very similar in both cases, explaining why the same dependence on ellipticity is observed.

Combining attosecond XUV pulses with coincidence spectroscopy

Here we present a successful combination of an attosecond beamline with a COLTRIMS apparatus, which we refer to as AttoCOLTRIMS. The setup provides either single attosecond pulses or attosecond pulse trains for extreme ultraviolet-infrared pump-probe experiments. We achieve full attosecond stability by using an active interferometer stabilization. The capability of the setup is demonstrated by means of two measurements, which lie at the heart of the COLTRIMS detector: firstly, we resolve the rotating electric field vector of an elliptically polarized few-cycle infrared laser field by attosecond streaking exploiting the access to the 3D momentum space of the charged particles. Secondly, we show streaking measurements on different atomic species obtained simultaneously in a single measurement making use of the advantage of measuring ions and electrons in coincidence. Both of these studies demonstrate the potential of the AttoCOLTRIMS for attosecond science.

Recent attoclock measurements of strong field ionization

Abstract The attoclock is a powerful, new, and unconventional experimental tool to study fundamental attosecond dynamics on an atomic scale. We have demonstrated the first attoclock with the goal to measure the tunneling delay time in laser-induced ionization of helium and argon atoms, with surprising results. It was found that the time delay in tunneling is zero for helium and argon atoms within the experimental uncertainties of a few 10’s of attoseconds. Furthermore we showed that the single active electron approximation is not sufficient even for atoms such as argon and the parent-ion interaction is much more complex than normally assumed. For double ionization of argon we found again surprising results because the ionization time of the first electron is in good agreement with the predictions, whereas the ionization of the second electron occurs significantly earlier than predicted and the two electrons exhibit some unexpected correlation.We present an ellipticity-resolved study of momentum distributions arising from strong-field ionization of helium. The influence of the ion potential on the departing electron is considered within a semiclassical model consisting of an initial tunneling step and subsequent classical propagation. We find that the momentum distribution can be explained by including the longitudinal momentum spread of the electron at the exit from the tunnel. Our combined experimental and theoretical study provides an estimate of this momentum spread.

Comparison of different approaches to the longitudinal momentum spread after tunnel ionization

We introduce a method to investigate the longitudinal momentum spread resulting from strong-field tunnel ionization of helium which, unlike other methods, is valid for all ellipticities of laser pulse. Semiclassical models consisting of tunnel ionization followed by classical propagation in the combined ion and laser field reproduce the experimental results if an initial longitudinal spread at the tunnel exit is included. The values for this spread are found to be of the order of twice the transverse momentum spread.

Comparison of attosecond streaking and RABBITT

Recent progress in the generation of ultra-short laser pulses has enabled the measurement of photoionization time delays with attosecond precision. For single photoemission time delays the most common techniques are based on attosecond streaking and the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT). These are pump-probe techniques employing an extreme-ultraviolet (XUV) single attosecond pump pulse for streaking or an attosecond pump pulse train for RABBITT, and a phase-locked infrared (IR) probe pulse. These techniques can only extract relative timing information between electrons originating from different initial states within the same atom or different atoms. Here we address the question whether the two techniques give identical timing information. We present a complete study, supported by both experiments and simulations, comparing these two techniques for the measurement of the photoemission time delay difference between valence electrons emitted from the Ne 2p and Ar 3p ground states. We highlight not only the differences and similarities between the two techniques, but also critically investigate the reliability of the methods used to extract the timing information.

Energy-Dependent Photoemission Time Delays of Noble Gas Atoms Using Coincidence Attosecond Streaking

We present photoemission time-delay measurements between electrons originating from the valence shells of neon and argon obtained by attosecond streaking. After giving a brief review of the different techniques, we focus on more detailed analysis using the attosecond streaking technique. We show that the temporal structure of the ionizing single attosecond pulse may significantly affect the obtained time delays, and we propose a procedure how to take this contribution properly into account. Our analysis reveals a delay of a few tens of attoseconds in a photon energy range between 28 and 40 eV in the emission of electrons ionized from argon with respect to those liberated from neon.