Momentum transfers in correlation-assisted tunneling

We consider correlation-assisted tunnel ionization of a small molecule by an intense low-frequency laser pulse. In this mechanism, the departing electron excites the state of the ion via a Coulomb interaction. We show that the wave packets emerging from this process can have nontrivial spatial structure and give a measurable indicator of correlated multielectron dynamics during the tunneling step. We also show that the saddle-point approximation requires special attention in this geometric analysis.

Figure 1

Three possible ionization processes which leave the core excited: (a) the ionized electron may depart from a sub-HOMO orbital, or it may interact with the core either (b) inside the tunneling barrier or (c) after the ionization step.

Figure 2

Correlation-assisted ionization of CO${}_2$. An electron (a) can ionize from HOMO and (b) change to an excited channel in (c) a midbarrier transition. This subjects it (c) to the dipole potential of the transition charge, (g), which changes the relative phase of the two lobes (d). This double-slit wave function then diffracts to multiple lobes (e). This contrasts with direct ionization on the excited $B$ channel, which has a single lobe (f).

Figure 3

Momentum-resolved ionization yield for the $X\to B$ perpendicular dipole transition in parallel-aligned CO${}_2$, with the corresponding direct amplitude in the inset. The dashed curve is the prediction from the spatial saddle-point approximation. The parameters used are $F=0.05$ and $\omega =0.055$ (so $I\approx 9\times {10}^{13}$ W/cm${}^2$ and $\lambda =800$ nm), $d_{\mathsf{m}\mathsf{n}}=0.175$, $\sigma =2.19$, $C_{0,X}=-0.23$, $C_{0,B}=0.18i$, $I_{p,X}=0.5064$, and $I_{p,B}=0.6644$. (All quantities are in atomic units unless noted.)

Figure 4

Ratio between the correlation-assisted and the direct signals for the $X\to B$ perpendicular dipole transition in parallel-aligned CO${}_2$, with the same parameters as Fig. 3. This contributes to the total amplitude in a heterodynelike scheme, as in Eq. (18).