Core-resonant ionization of helium by intense XUV pulses: Analytical and numerical studies on channel-resolved spectral features

Channel-resolved ionization of helium by laser pulses with a photon energy equal to the energy difference between the ionic ground- and first-excited states, i.e., in the core-resonant scenario, is investigated theoretically for a considered peak intensity of $\sim {10}^{14}$ W/${\mathrm{cm}}^2$. By using the essential-states formalism, we derive analytical expressions for the channel-resolved photoelectron spectra, with the pulse-envelope effects taken into account. To examine the validity of the essential-states approach, we numerically solve the time-dependent Schrödinger equation of a model helium and use the corresponding results as references. The justified analytical estimation of the channel-resolved photoelectron spectra serves as a convenient approach to explore the effects of pulse durations and envelopes. It requires a longer pulse duration to observe the spectral peak splitting in the ionic first-excited-state channel than in the ionic ground-state channel. Ionization by two sequent pulses produces more complicated multipeak structures in the channel-resolved photoelectron spectra than ionization by a single pulse. Studies for the nonzero-detuning cases are also presented, where we propose a general procedure for understanding how the photoelectron spectra are built up.

Figure 1

Illustration for core-resonant ionization of He. As indicated by arrows, there are two dominant processes: (1) one-photon ionization from the ground-state He to the singly ionized continuum corresponding to the ground-state ${\mathrm{He}}^{+}$, and (2) resonant transitions between the two coupled continua.

Figure 2

Time-dependent ground-state probability obtained by the essential-states (labeled as ESSS) and the TDSE calculations for a fixed laser frequency $\omega =1.50$ and different pulse durations.

Figure 3

Channel-resolved PES obtained by the essential-states (labeled as ESSS) and the TDSE calculations for a fixed frequency $\omega =1.50$. Channel 1 (channel 2) denotes ionization into the ionic ground-state (first-excited-state) channel and its vertical axis is to the left (right). The four selected pulse durations are the same as in Fig. 2.

Figure 4

Normalized channel-resolved PES for a series of different number of cycles (from 40 to 400), obtained by the essential-states calculations for a fixed laser frequency $\omega =1.50$. Channel 1 (channel 2) denotes ionization into the ionic ground-state (first-excited-state) channel. The solid black curves indicate the minimum pulse duration for which one can visually observe two peaks in the spectra.

Figure 5

Channel-resolved PES obtained by the essential-states (labeled as ESSS) and the TDSE calculations for two sequent pulses with frequency $\omega =1.50$. Channel 1 (channel 2) denotes ionization into the ionic ground-state (first-excited-state) channel and its vertical axis is to the left (right).

Figure 6

Dynamics of the coupled continua for the nonzero-detuning cases, illustrated with the field-dressed energy levels of the Hamiltonian $\underline{\underline{\mathbf{H}}}$ given by Eq. (30). The time-dependent eigenenergies of $\underline{\underline{\mathbf{H}}}$ are displayed by red and blue curves, which respectively correspond to channel 1 (the ground-state ${\mathrm{He}}^{+}$) and channel 2 (the first-excited state ${\mathrm{He}}^{+}$) when the pulse is off. In this field-dressed picture, the free electron born at time ($t_p-s$) will undergoes adiabatic and nonadiabatic processes indicated by solid and dotted lines with arrows, respectively.

Figure 7

Channel-resolved PES obtained by the essential-states (labeled as ESSS) and the TDSE calculations for slightly different laser frequencies (a) $\omega =1.49$ and (b) $\omega =1.51$. Channel 1 (channel 2) denotes ionization into the ionic ground-state (first-excited-state) channel and its vertical axis is to the left (right). Dashed curves (labeled as ESSSA) are obtained by neglecting nonadiabatic processes of the field-dressed continua in the essential-states calculations.