Attosecond delays in laser-assisted photodetachment from closed-shell negative ions

We study laser-assisted photodetachment time delays by attosecond pulse trains from the closed-shell negative ions ${\mathrm{F}}^{-}$ and ${\mathrm{Cl}}^{-}$. We investigate the separability of the delay into two contributions: (i) the Wigner-like delay associated with one-photon ionization by the attosecond pulse train and (ii) the delay associated with the exchange of an additional laser photon in the presence of the potential of the remaining target. Based on the asymptotic form of the wave packet, the latter term is expected to be negligible because the ion is neutralized, leading to a vanishing laser-ion interaction with increasing electron-atom separation. While this asymptotic behavior is verified at high photoelectron energies, we also quantify sharp deviations at low photoelectron energies. Further, these low-energy delays are clearly different for the two studied anions, indicating a breakdown of the universality of laser-ion-induced delays. The fact that the short-range potential can induce a delay of as much as 50 as can have implications for the interpretation of delay measurements also in other systems that lack long-range potential.

Figure 1

The energy levels [37] in the Ne-like, F-like, and O-like systems, with $Z=9$ (top) and $Z=10$ (bottom).

Figure 2

The energy levels [37] in the Ar-like, Cl-like, and S-like systems, with $Z=17$ (top) and $Z=18$ (bottom).

Figure 3

RPAE for the many-body screening of the photon interaction. Panels (a) and (g) are forward and backward propagation, respectively, where the circle indicates the correlated interaction to infinite order.

Figure 4

The two left panels show the perturbed wave function $\rho \left(2p\to d\right)$ for Ne (a) and ${\mathrm{F}}^{-}$ (b) after absorption of a photon with an energy resulting in a photoelectron of 4.3 eV. The real part is shown with thin red lines, and the imaginary part with thick blue lines. The radial coordinate is complex rotated from $r=100a_0$, which is the reason for the damping of the perturbed wave function outside this distance. The two right panels show the perturbed wave function after absorption of a laser photon of 1.55 eV (red solid line). The photon energy is below the ionization limit and results in a localized real correction to the wave function. The wave function for the initial state of the electron (the $2p$ orbital) is shown for comparison (dot-dashed gray line). In neon also the first excited state with $d$ character is shown.

Figure 5

(a) First time-order process (TO1) where the XUV photon, $\mathrm{\Omega }$, is absorbed before interaction with the laser field, $\pm \omega$. (b) Second time-order process (TO2) where the interaction with the laser occurs before absorption of the XUV photon.

Figure 6

The one-photon Wigner delay and the two-photon atomic delay for electron emission from the $2p$ orbital in Ne and ${\mathrm{F}}^{-}$, as well as from the $3p$ orbital in Ar and ${\mathrm{Cl}}^{-}$.

Figure 7

The difference between the two-photon atomic delay and the one-photon Wigner delay for Ne, Ar, ${\mathrm{F}}^{-}$, and ${\mathrm{Cl}}^{-}$.

Figure 8

The effect on ${\tau }_a-{\tau }_W$ from the second photon time order. The plots show the difference between the difference delay with both time orders and that with only the dominating time order (i.e., with the XUV photon being absorbed first) for negative ions ${\mathrm{F}}^{-}$ and ${\mathrm{Cl}}^{-}$ (a) and atoms Ne and Ar (b).

Figure 9

(a) Absolute value of two-photon matrix elements with XUV photon absorbed before the laser interaction (process denoted TO1 in main text). The contributions on final $p$ and $f$ waves are shown separately with both absorption and emission of laser photon. (b) Same as (a), except that the XUV photon is absorbed after the laser interaction (TO2).