History-dependent effects in subcycle-waveform strong-field ionization

Recent developments in laser sources allow one to shape the precise electric-field waveform oscillation at the subcycle level. These waveforms may then be used to drive and control ultrafast nonlinear phenomena at the attosecond timescale. By utilizing numerical solutions of time-dependent Schrödinger equations and exact solutions of a simple quantum-mechanical system, we show that an atom driven by such sources exhibit coherent history-dependent effects. These manifest themselves in “macroscopic” quantities such as the yield in multicolor, strong-field ionization. We argue that weakly bound, metastable electronic states may enable the dependence on the system history even in long-duration, relatively weak driving waveforms.

Figure 1

Resonance states in Dirac-$\delta$ system. Two staggered sets of curves (red and black online) show the respective zero-contours of the real and imaginary parts of the resonance-eigenvalue equation, with the intersections showing the locations of complex resonance energies. States with energies close to the positive real axis (family one) are those in which the system can retain some information about its history.

Figure 2

Synthesized subcycle pulse trains. The left panel shows the intensity versus time (in femtoseconds). Only pulse train A is shown because, at this scale, waveform B looks the same. The right panel shows two fundamental periods in both pulse streams. Note that the strong unipolar impulses are the same in amplitude and only differ in their relative timing.

Figure 3

Survival probability (nonionization) of a model atom as calculated by the rate-ionization model (left panel) and according to the TDSE (right panel). The effective multiphoton order for the rate model is $K=6.5$ and the ionization cross section is chosen such that the final ionization probability in pulse train A is 1%. The fundamental excitation wavelength is $\lambda =800$ nm. The inset in the left panel shows a detail of the bound-state population vs time and illustrates that most of the ionization occurs during the strong electric-field impulses. These “steps” are smoothed out in the TDSE measurement due to the size of the computational domain.

Figure 4

Ionization in synthesized pulse trains for fundamental harmonic wavelengths $\lambda =1200$ nm (left panel) and $\lambda =2400$ nm (right panel).

Figure 5

Exactly solvable one-dimensional atom model exposed to a multicolor time-dependent driving field. The ground-state amplitude $\psi (x=0,t)$ is shown as a function of time. It exhibits adiabatic following of the driving field (large-scale variations) together with high-frequency oscillations due to interference between the ground and continuum states (causing, in particular, excursion exceeding unity). The final value after excitation reflects ionization (indicated by arrow) and shows that different pulse timings result in different effective ionization rates.

Figure 6

Resonance excitation as seen in a zoom-in on the same data as shown in the previous figure. Plots illustrate “shaking” of the electronic wave function in the external field. Note the increased amplitude of oscillation after the second impulse in pulse train A. These oscillations are due to excitation of low-lying resonance states labeled “family one” in Fig. 1.