Resolving Ultrafast Spin-Orbit Dynamics in Heavy Many-Electron Atoms

We use $R$-matrix with time-dependence theory, with spin-orbit effects included, to study krypton irradiated by two time-delayed extreme ultraviolet ultrashort pulses. The first pulse excites the atom to $4s^{2}4p^{5}5s$. The second pulse then excites $4s4p^{6}5s$ autoionizing levels, whose population can be observed through their subsequent decay. By varying the time delay between the two pulses, we are able to control the excitation pathway to the autoionizing states. The use of cross-polarized light pulses allows us to isolate the two-photon pathway, with one photon taken from each pulse.

Figure 1

Energy levels of atomic krypton relevant to the autoionization process shown in Fig. 2 (not to scale).

Figure 2

Ejected electron spectra for delays of 4, 5, and 6 fs between the two pulses. We show results for when the pulses are parallel polarized (a) and cross-polarized (b). We also show the corresponding eigenphase sum calculated using the same Kr model using the rmatrixi time-independent codes. In the upper frame we plot the eigenphase sum for the $J=0$ even symmetry, and in the lower frame we show that for $J=1$ even symmetry, to indicate the position of the resonances for parallel- and cross-polarized pulses, respectively.

Figure 3

Measure of ionization resulting from the decay of the $4s4p^{6}5s$ state excited by a 6 cycle 10 eV pulse followed by a 6 cycle 15 eV pulse after a specified time delay. The population is calculated at a time of 47 fs after the start of the first pulse. We plot results for parallel-polarized cases where the spin-orbit interaction is omitted, and parallel-polarized and cross-polarized cases for when the spin-orbit interaction is included. We also plot a ${\sin }^2$ function (dashed gray line) of the frequency associated with the 0.615 eV splitting, of amplitude scaled to fit the cross-polarized dataset.

Figure 4

A schematic to demonstrate the electron dynamics displayed in Fig. 3 in an uncoupled electron basis, shown in three stages (large blue circles). In stage A, the ground state krypton atom is excited by a 10 eV pulse. Stage B shows the effect of the spin-orbit interaction upon the $4p$ hole, and stage C shows the effect of the second 15 eV pulse for parallel-polarized and cross-polarized pulses. See text for more detail.