Direct extraction of intense-field-induced polarization in the continuum on the attosecond time scale from transient absorption

A procedure is suggested for using transient absorption spectroscopy above the ionization threshold to measure the polarization of the continuum induced by an intense optical pulse. In this way transient absorption measurement can be used to probe subfemtosecond intense field dynamics in atoms and molecules. The method is based on an approximation to the dependence of these spectra on time delay between an attosecond XUV probe pulse and an intense pump pulse that is tested over a wide range of intensities and time delays by all-electrons-active calculations using the multiconfiguration time-dependent Hartree-Fock method in the case of neon.

Figure 1

(a) Energy-resolved absorption signals for the probe-only (dash) and pump-probe cases with time delays of $-0.092$ fs (dash-dot line), 0 fs (solid line), and $+0.092$ fs (dash-dot-dot line). Inset: Schematic of timing of the associated electric fields of the 12-fs 266-nm pump and the delayed 1-fs XUV probe. Comparison of the extracted (dots) and the computed (solid) induced polarization by the pump field ($I_{\mathrm{pump}}=1\times {10}^{14}$ W/${\mathrm{cm}}^2$) in the continuum in the (b) frequency and (c) temporal domains. Inset: A schematic comparison of the field-induced polarization (solid line) and instantaneous electric field of the pump field (dashed line) and its envelope (dash-dot line).

Figure 2

(a) Energy-resolved absorption signals for the probe-only (dashed line) and pump-probe case with a time delay of $-17.74$ fs (solid line) with its Fourier-transform (FT) in the inset. (b) Comparison of the extracted polarization for two different time delays, $t_d=0$ fs (black solid line) and $t_d=-17.74$ fs (green dashed line), with the MCTDHF computed polarization in continuum (red dots).

Figure 3

Comparison of the extracted (dots) and the MCTDHF computed (solid) induced polarization by the pump field ($I_{\mathrm{pump}}=5\times {10}^{15}$ W/${\mathrm{cm}}^2$) in the continuum. Inset: The time-dependent population of the ground states for $I_{\mathrm{pump}}=1\times {10}^{14}$ W/${\mathrm{cm}}^2$ (green, top line), $1\times {10}^{15}$ W/${\mathrm{cm}}^2$ (orange, middle line), and $5\times {10}^{15}$ W/${\mathrm{cm}}^2$ (blue, bottom line).

Figure 4

Comparison of the extracted (dots) and the computed (solid) induced polarization by the pump field ($I_{\mathrm{pump}}=1\times {10}^{14}$ W/${\mathrm{cm}}^2$) in the continuum with a $30\%$ error in the measured spectra shown in the inset [cf. Fig. 1].

Figure 5

At $I_{\mathrm{pu}}=1\times {10}^{15}$ W/${\mathrm{cm}}^2$: (a) Comparison of the input electric field magnitude (black thin-solid line), $|{\tilde{\mathcal{E}}}_{\mathrm{in}}{\left(\omega \right)|}^2$, and the electric field magnitude for the generated harmonics (green thick-solid line), $|{\tilde{\mathcal{E}}}_{\mathrm{HG}}{\left(\omega \right)|}^2$. (b) Comparison of the input electric field magnitude (black thin-solid line), $|{\tilde{\mathcal{E}}}_{\mathrm{in}}{\left(\omega \right)|}^2$, output electric field magnitude (red dashed line), $|{\tilde{\mathcal{E}}}_{\mathrm{out}}{\left(\omega \right)|}^2$ as computed via Eq. (9), and the electric field magnitude for harmonics (green thick-solid line), $|{\tilde{\mathcal{E}}}_{\mathrm{HG}}{\left(\omega \right)|}^2$.