Disentangling Spectral Phases of Interfering Autoionizing States from Attosecond Interferometric Measurements

We have determined spectral phases of Ne autoionizing states from extreme ultraviolet and midinfrared attosecond interferometric measurements and ab initio full-electron time-dependent theoretical calculations in an energy interval where several of these states are coherently populated. The retrieved phases exhibit a complex behavior as a function of photon energy, which is the consequence of the interference between paths involving various resonances. In spite of this complexity, we show that phases for individual resonances can still be obtained from experiment by using an extension of the Fano model of atomic resonances. As simultaneous excitation of several resonances is a common scenario in many-electron systems, the present work paves the way to reconstruct electron wave packets coherently generated by attosecond pulses in systems larger than helium.

Figure 1

Measured (upper panel) and TD-XCHEM calculated (central panel) RABBIT spectrograms obtained by using a 1718 nm driving wavelength. In the experiment, $10^4$ laser shots are averaged for each delay. The lower panel shows the contributions of states of different symmetries to the calculated photoelectron spectrum for a time delay $\tau =2.5\mathrm{fs}$. The positions of the Ne resonances are indicated by blue (${{}^{1}P}^o$ symmetry) and red (${{}^{1}S}^e$ and ${{}^{1}D}^e$ symmetries) vertical lines.

Figure 2

Energy diagram showing the six lowest resonances of Ne and the relevant ionization channels. Sidebands ${\mathrm{SB}}_{62}$ and ${\mathrm{SB}}_{64}$ result from two-photon interfering paths involving an XUV and a MIR photon (blue and red dashed arrows). Regions scanned in photon energy are shown by shaded areas. The $2s2p^{6}3p$ ${{}^{1}P}^o$ and $2s2p^{6}4p$ ${{}^{1}P}^o$ resonances (denoted $3p$ and $4p$) are populated by harmonics $H_{63}$ and $H_{65}$, respectively, and can thus interfere through paths ① and ② leading to ${\mathrm{SB}}_{64}$. The $2s2p^{6}4s$ ${{}^{1}S}^e$ resonance ($4s$) can be populated at the end of these paths. The energy positions and widths of these resonances are $E_{3p}=45.54\mathrm{eV}$ and ${\mathrm{\Gamma }}_{3p}=16\mathrm{meV}$ [25], $E_{4p}=47.12\mathrm{eV}$ and ${\mathrm{\Gamma }}_{4p}=5\mathrm{meV}$ [25], and $E_{4s}=46.613\mathrm{eV}$ [31] and ${\mathrm{\Gamma }}_{4s}=18\mathrm{meV}$. Values for the other resonances can be found in Ref. [31].

Figure 3

Measured (full circles) and TD-XCHEM calculated (thick continuous line) atomic phase differences $\mathrm{\Delta }{\overline{\theta }}^{\text{at}}$ for ${\mathrm{SB}}_{62}$ (left panel) and ${\mathrm{SB}}_{64}$ (center panel), and normalized $H_{63}$ photoelectron yield (right panel) as a function of the central $H_{63}$ energy. Results of the single-resonance model of Ref. [30] and its generalization to the case of more resonances [Eq. (2)] are shown by dashed and dotted lines, respectively. The curves resulting from our TDSE calculations have been shifted up in energy by 0.125 eV to match the position of the $2s2p^{6}3p$ ${{}^{1}P}^o$ found experimentally [25]. All shown phases result from spectral integration of the sideband signal.