Probing time delays and coherent imaging of multiphoton resonant ionization

We measure the laser-intensity-dependent photoelectron momentum and energy spectra and identify the emerged resonant $(4s,3d$, and $4f)$ states of multiphoton ionization of Ne at 400 nm. We employ parallelly polarized two-color fields involving a strong ionizing 400-nm field and a weak 800-nm field to probe the relative time delay of resonant states. By analyzing phase-resolved three-dimensional photoelectron momentum distributions, we find the time delay of resonant states has an anisotropic angle dependence. Using an intuitive model, we show that the angle-dependent time delay carries the information of subcycle evolution of quantum states and reflects the temporal coherent properties of multiphoton resonant states during absorption and emission of photons. We find that the relative time delays among the resonant ionization via $4s,3d$, and $4f$ states along the polarization depend on the number of photons absorbed. This study has implications for coherent imaging of electron wave packets in the multiphoton ionization regime.

Figure 1

The intensity-resolved photoelectron momentum distribution along the polarization direction (a) and energy distribution (b). The color scale is normalized to the maximum yield at each laser intensity. The arrows in (a),(b) represent ionization via resonant states. The dashed lines in (b) denote the $n$-photon ATI peaks and the vertical line indicates the intensity where the three resonant states coexist. (c) The scheme of the involved atomic states and their corresponding multiphoton resonant excitation paths. (d). A schematic illustration of our model. Here the $4f$ resonant ionization channel is taken for an example. The inset describes the electron yield oscillation versus the relative phase and the temporal evolution of quantum states in the PTC field.

Figure 2

The phase-integrated angle-resolved photoelectron energy distribution in the single 400-nm field (a) and the corresponding result in the PTC field (b). Three arrows in (a) denote the resonant ionization via the $4s,3d$, and $4f$ states. The dashed arrows in (b) represent the formation of sideband structures via absorption $(+)$ or emission $(-)$ of an 800-nm photon from the $4f$ resonant ionization channel, which is confined within a rectangle.

Figure 3

(a) The phase-resolved photoelectron energy distribution intergrated over the $-z$ half plane. (b) The phase-resolved angular distribution via the $4f$ resonant state with an energy interval of [1.9 eV, 2.25 eV] denoted by the rectangle in Fig. 2.

Figure 4

(a),(b) The angle-resolved photoelecton yield oscillations extracted from Fig. 3 for resonant ionization via the $4f$ and $3d$ states. The vertical lines located at the yield peaks are used to mark the position of the maximum. (c) The measured angle-resolved photoemission time delays relative to the polarization axis for $4f$ and $3d$ resonant ionization. (d) The constructed phase-resolved angular distribution via the $4f$ resonant state using the model.

Figure 5

The measured photoelectron yield oscillations of resonant ionization via $4s$ (circles), $3d$ (upward triangles), and $4f$ (downward triangles) states with their fittings (solid lines) along the $+z$ (a) and $-z$ axis (b). In addition, the yield oscillations of the sideband (squares) associated with emitting an 800-nm photon from $4f$ resonant ionization are plotted. All yield oscillations are extracted from the phase-resolved momentum distribution of $p_z$.