Alexandra S. Landsman

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

Disease Extinction in the Presence of Random Vaccination

We investigate disease extinction in an epidemic model described by a birth-death process. We show that, in the absence of vaccination, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed random vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.

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).

Predicting extinction rates in stochastic epidemic models

We investigate the stochastic extinction processes in a class of epidemic models. Motivated by the process of natural disease extinction in epidemics, we examine the rate of extinction as a function of disease spread. We show that the effective entropic barrier for extinction in a susceptible?infected?susceptible epidemic model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. We make a direct comparison between predictions and numerical simulations. We also consider the effect of non-Gaussian vaccine schedules, and show numerically how the extinction process may be enhanced when the vaccine schedules are Poisson distributed.

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.

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.

Tunneling Time and Weak Measurement in Strong Field Ionization

Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.

Tunnelling time in strong field ionisation

We revisit the common approaches to tunnelling time in the context of attoclock experiments. These experiments measure tunnelling time using close-to-circularly polarised light of the infrared ultrashort laser pulse. We test the sensitivity of the attoclock measurements of tunnelling time to non-adiabatic effects, as described by a well-known theoretical model first developed by Perelomov, Popov, and Terent?ev. We find that in the case of ionisation of helium, both adiabatic and non-adiabatic theories give very similar predictions for ionisations times over a wide intensity range typical of ultrafast experiments.

Non-adiabatic imprints on the electron wave packet in strong field ionization with circular polarization

The validity of the adiabatic approximation in strong field ionization under typical experimental conditions has recently become a topic of great interest. Experimental results have been inconclusive, in part, due to the uncertainty in experimental calibration of intensity. Here we turn to the time dependent Schrodinger equation, where all the laser parameters are known exactly. We find that the centre of the electron momentum distribution (typically used for calibration of elliptically and circularly polarized light) is sensitive to non-adiabatic effects, leading to intensity shifts in experimental data that can significantly affect the interpretation of results. On the other hand, the transverse momentum spread in the plane of polarization is relatively insensitive to such effects, even in the Keldysh parameter regime approaching gamma approximate to 3. This suggests the transverse momentum spread in the plane of polarization as a good alternative to the usual calibration method, particularly for experimental investigation of non-adiabatic effects using circularly polarized light.