Theory of attosecond transient-absorption spectroscopy of krypton for overlapping pump and probe pulses

We present a fully ab initio calculations for attosecond transient absorption spectroscopy of atomic krypton with overlapping pump and probe pulses. Within the time-dependent configuration interaction singles (TDCIS) approach, we describe the pump step (strong-field ionization using a near-infrared pulse) as well as the probe step (resonant electron excitation using an extreme-ultraviolet pulse) from first principles. We extend our TDCIS model and account for the spin-orbit splitting of the occupied orbitals. We discuss the spectral features seen in a recent attosecond transient absorption experiment [A. Wirth et al., Science 334, 195 (2011)]. Our results support the concept that the transient absorption signal can be directly related to the instantaneous hole population even during the ionizing pump pulse. Furthermore, we find strong deformations in the absorption lines when the overlap of pump and probe pulses is maximum. These deformations can be described by relative phase shifts in the oscillating ionic dipole. We discuss possible mechanisms contributing to these phase shifts. Our finding suggests that the nonperturbative laser dressing of the entire $N$-electron wave function is the main contributor.

Figure 1

Cross section $\sigma \left(\omega \right)$ of Eq. (17) for several values of $\varphi \left(\tau \right)$. The transition energy is ${\omega }_0=3$ a.u., $\Gamma =3.2\times {10}^{-3}$ a.u., and the transition strength is given by $z_0=0.01$.

Figure 2

NIR pump (solid red line) and XUV probe pulses (green dashed line) used for transient absorption spectroscopy are shown separately. The peaks of both pulses are centered at $t=0$.

Figure 3

Attosecond XUV transient absorption spectrum ${\sigma }_m(\omega ;\tau )$ [see Eq. (14)] of krypton as a function of energy $\omega$ and pump-probe delay $\tau$.

Figure 4

Transient absorption spectra for the pump-probe delay $\tau =0$ and $\tau =70(\approx 1.7\text{fs})$ are shown in panels (a) and (b), respectively. The atomic cross section ${\sigma }_a$ (solid red line), the measured cross section ${\sigma }_m$ (green dashed line), and ${\sigma }_{\mathrm{dipole}}$ (blue dotted line) are shown for each $\tau$.

Figure 5

Instantaneous hole population ${\rho }_{\mathrm{eff}}^{\mathrm{IDM}}\left(\tau \right)$ (solid red line) together with reconstructed populations ${\rho }_{\mathrm{eff}}^{\mathrm{dipole}}\left(\tau \right)$ (blue dotted line) and ${\rho }_{\mathrm{eff}}^{\mathrm{fit}}$ (green dashed line). The experimental population (grey dashed line) is taken from Ref. [35]. The reconstructed and experimental populations are scaled such that all have the same value at $t=2.4$ fs. The NIR pulse intensity is highlighted (gray area) in the background.

Figure 6

Phase shift ${\varphi }_{T_1}\left(\tau \right)$ of strongest transition line and phase shift ${\varphi }_{T_3}\left(\tau \right)$ of weakest transition line.

Figure 7

Apparent energy shifts of strongest transition line $T_1$ for calculated cross sections with (red line with crosses) and without (green line with asterisks) the $4s$ orbital active, and for the experimentally obtained cross sections (blue dotted line). The experimental values are taken from Ref. [35].

Figure 8

The phase shifts ${\varphi }_{T_1}\left(\tau \right)$ of the transition line $T_1(4p_{3/2}^{-1}\to 3d_{5/2}^{-1})$ are shown for TDCIS calculations with (solid red line) and without (green dashed line) the ionic state $4s^{-1}$. Additionally, the phase shift ${\varphi }_{T_1}^{\mathrm{ion}}\left(\tau \right)$ (blue dotted line) is shown for a Bloch model describing three ionic states (see text for details). Here, ${\varphi }_{T_1}^{\mathrm{ion}}\left(\tau \right)$ originates solely from the dressing of the ionic state ${\left[4p_{3/2}^{1/2}\right]}^{-1}$ through the coupling to $4s^{-1}$.

Figure 9

Phase shifts ${\varphi }_{T_1}\left(\tau \right)$. The TDCIS calculations were done on the one side (solid red line) with the full electron-ion interaction and all $3d^{-1},4s^{-1},4p^{-1}$ ionic states active, and on the other side (green dashed line) with a simplified two-level TDCIS model without residual Coulomb interaction (${\widehat{H}}_1=0$).

Figure 10

Phase shifts ${\varphi }_T\left(\tau \right)$ for transition $T={\left[4p_{3/2}^{1/2}\right]}^{-1}\to {\left[3d_{5/2}^{1/2}\right]}^{-1}$. The TDCIS calculations were done once with (solid red line) and once without (green dashed line) field-driving mixing with the neutral ground state ${\Phi }_0$ after the probe pulse. In both cases, no dressing of the ionic states can occur (see text for details).