Amplitude and Phase Reconstruction of Electron Wave Packets for Probing Ultrafast Photoionization Dynamics

Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the $1s3p$ state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.

Figure 1

(a) Illustration of the excitation and the ionization processes of He by attosecond high-harmonic pulses superposed with time-delayed IR femtosecond laser pulses. The 17th harmonic directly generates the reference wave packet from the ground state to the continuum. At the same time, the 15th harmonic can excite a ground state electron to the $1s3p$ state of He. The excited electron is, then, ionized by the probe laser pulse shown in red dotted line. (b) Photoelectron spectrum measured by applying the attosecond pulse train, generated from Ar with the laser intensity of $7\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, in the presence of a dressed IR laser pulse. The shown spectrum was taken with a time delay $\tau =50\mathrm{fs}$.

Figure 2

Holographic reconstruction of the two EWPs liberated from the ground state and the $1s3p$ state of He. (a) Photoelectron spectra generated by high-harmonic and time-delayed IR laser pulses. Photoelectrons corresponding to the energy range of the 17th harmonic are shown. (b) Photoelectron spectra obtained in the experiment. The photoelectron peaks at 1.6, 4.7, and 7.8 eV represent the photoelectron produced by 17th, 19th, and 21st harmonics. (c) Reference EWP, $p|b_R(\mathbf{p}){|}^2$. (d) Phase of the reference EWP. (e) Signal EWPs, $p|b_S(\mathbf{p}){|}^2$. (f) Phase of the signal EWP, reconstructed by applying the holographic technique for the direction of the laser polarization. The phase of the signal wave packet was drawn after subtracting $2{\omega }_0\tau$ for better visualization. The same color code was used for the number density of photoelectrons in (a), (b), (c), and (e). The number density in (e) was multiplied by 40.

Figure 3

Ionization dynamics of the $1s3p$ state of He. The population amplitude of the $1s3p$ state $|a_{1s3p}(t;\tau ){|}^2$, black dashed line, the instantaneous ionization rate for the two-photon ionization $d{N}_{2{\omega }_0}(t;\tau )/dt$, green thick solid line, the intensity profile of the attosecond pulse train $|E_X(t){|}^2$, blue thin solid line, the electric field of the probe laser pulse $E_{\mathrm{IR}}(t-\tau )$, red dash-dotted line are shown for the time delays of 0, 15, 30, and 45 fs. The group delay $t_S$ of the signal EWPs, obtained from Fig. 2f, is indicated with an arrow for each time delay. $|a_{1s3p}(t;\tau ){|}^2$ is shown only for the range where the electric field is strong so that the calculation error should not be large. All quantities are in arbitrary units.