Multiphoton interaction phase shifts in attosecond science

Ab initio simulations of a range of interferometric experiments are used to identify a strong dependence on multiphoton phase shifts in above-threshold ionization (ATI). A simple rule of thumb for interaction phase shifts is derived to explain both the conservation of photoelectron yield and its absolute CEP dependence. For instance, it is found that interferometric (ATI) experiments are shifted by $\pi /4$ relative to RABBIT experiments, and that there is no RABBIT term in a laser-assisted photoionization experiment with odd and even harmonics. Thus, our work helps to resolve the issues of interpretation of quantum dynamics in attosecond and free-electron laser sciences.

Figure 1

(a) Interactions in the rule of thumb for the experiment of Laurent et al. in Ref. [13]. (b) Photoelectron peaks corresponding to high-order harmonics 20–24 using KFR and TDCIS in Ne2p. The relative phase between even and odd harmonics is $\delta =-\pi /2$ and the photoelectrons are measured in the up direction. The lower part shows the lineout of the $21\mathrm{st}$ harmonic. (c) Yield of the $21\mathrm{st}$ harmonic peak resolved in emission angle, $\theta$, and CEP, $\phi$. The right side panel shows the lineout of the $21\mathrm{st}$ harmonic over emission angle for $\phi =0$. The TDCIS-lineouts are estimated as an average of calculations with $r_{\mathrm{surf}}=\{84,88,92,96\}$ in t-SURFF. The purple shaded area marks confidence up to one standard deviation in TDCIS.

Figure 2

(a) Interactions in the rule of thumb for the twin SB experiment by Maroju et al. in Ref. [22]. (b) Photoelectron peaks corresponding to FEL-generated harmonics 64 and 67 using KFR and TDCIS in Ne2p. The photoelectrons are measured in the up direction. (c) Yield of the high twin SB resolved in emission angle, $\theta$, and CEP, $\phi$.

Figure 3

(a) Interactions in the rule of thumb for the $2\omega /\omega$-ATI experiment by Zipp et al. in Ref. [21]. (b) Photoelectron SB and ATI peaks in Ne2p measured in the upper $z$-hemisphere using KFR. $2U_p$ is indicated by the black dashed line. Yield of the (c) third SB [6.8 eV in (b)] and (d) second ATI peak [5.3 eV in (b)] with resolved in emission angle, $\theta$, and CEP, $\phi$.