Attosecond Correlated Dynamics of Two Electrons Passing through a Transition State

The strong-field induced decay of a doubly excited, transient Coulomb complex ${\mathrm{Ar}}^{**}\to {\mathrm{Ar}}^{2+}+2e^{-}$ is explored by tracing correlated two-electron emission in nonsequential double ionization of Ar as a function of the carrier-envelope phase. Using $<6\mathrm{fs}$ pulses, electron emission is essentially confined to one optical cycle. Classical model calculations support that the intermediate Coulomb complex has lost memory of its formation dynamics and allows for a consistent, though model-dependent definition of “emission time,” empowering us to trace transition-state two-electron decay dynamics with sub-fs resolution. We find a most likely emission time difference of $\sim 200\pm 100$ as.

Figure 1

Longitudinal momentum of electron 1 ($P_{||e1}$) versus that of electron 2 ($P_{||e2}$). Top row: experiment. Middle row: full classical-trajectory Monte Carlo calculation. Bottom row: compound-state model simulation (see text). Columns for CEP values as indicated.

Figure 2

Energy of electron 1 and 2 versus time for two sample trajectories (solid and dashed lines) of the full calculation. Electron 1 tunnels close to a maximum of the electric field and excites the second electron during recollision about 1.5 half cycles later (gray shaded areas). Because of its low recollision energy electron 1 becomes bound during this process and a doubly exited complex (DEC) is created. The electrons are released into the continuum at one of the next electric field maxima via classical “over the barrier ionization.” For each event $i$ the ionization times $t_1^i$ and $t_2^i$ of electrons 1 and 2, respectively, are defined as the instants when their energy (ion potential plus kinetic) becomes positive.

Figure 3

Distribution of the ionization time difference $\Delta T=|t_2^i-t_1^i|$ for the DEC calculation (averaged over all CEPs). Insets: correlation maps (the momentum scale ranges from $-1.5$ to 1.5 au) obtained when selecting specific time differences $\Delta T$ as indicated.

Figure 4

(a) Ionization time difference $\Delta T$ as a function of momentum difference $\Delta P_{||}$ (see also Fig. 3) for the case of the DEC as well as the full calculation. (b) Experimental distribution of the electron momentum difference $\Delta P_{||}$ averaged over all CEPs. (c) Same as (b) obtained with the DEC calculation without any restriction on $\Delta T$ and for selected values of $\Delta T$ (according to the correlation maps shown in Fig. 3). On the upper ordinate the time scale $\Delta T$ is provided as extracted from the simulation.