Photoelectron angular distributions from the ionization of xenon Rydberg states by midinfrared radiation

Angle-resolved photoelectron spectra, resulting from the strong-field ionization of atoms or molecules, carry a rich amount of information on ionization pathways, electron dynamics, and the target structure. We have investigated angle-resolved photoelectron spectra arising from the nonresonant ionization of xenon Rydberg atoms in the multiphoton regime, using intense midinfrared radiation from a free-electron laser. The experimental data reveal a rich oscillatory structure in the low-order above-threshold ionization region. By performing quantum-mechanical and semiclassical calculations, the observed oscillations could be well reproduced and explained by both a multiphoton absorption picture as by a model invoking electron wave-packet interferences. Furthermore, we demonstrate that the shape and orientation of the initial Rydberg state leaves its own fingerprint on the final angular distribution.

Figure 1

Experimental setup. Xenon was injected into the vacuum chamber using a pulsed valve. In the metastable source [21], a significant fraction of the atoms was promoted into the metastable 5$p^5$(${}^2$$P_{3/2}$)6$s$[3/2]${}_2$ state by means of electron impact. In the interaction region, a tunable dye laser (in red, denoted with “$E_{\mathrm{Dye}}$”) excited the metastable xenon atoms to the Rydberg states of interest. Ionization of these states proceeded by interaction with the FELICE laser (in yellow, denoted with “$E_{\mathrm{FELICE}}$”) [15]. The photoelectrons were detected with a velocity map imaging (VMI) spectrometer [22], containing a set of electrodes (R, repeller; E, extractor; G, ground) and a position-sensitive detector consisting of a dual stack of microchannel plates (MCPs), a phosphor screen, and a CCD camera. To allow for the three-dimensional (3D) reconstruction of the photoelectron kinetic energy and angular distribution, an axis of cylindrical symmetry of the 3D distribution parallel to the detection plane is required, which was obtained by choosing the polarization of the FELICE laser parallel to the detector. The polarization of the dye laser was, however, orthogonal to the FELICE-laser polarization and the detection plane. Consequently, the prerequisite cylindrical symmetry was achieved only when the dye laser was used to excite fully symmetric atomic orbitals, i.e., $s$ orbitals. In this case, for the 3D reconstruction, an Abel inversion routine based on a Legendre polynomial expansion was used, similarly to the BASEX method [23]. For all the other orbitals, the measured 2D projections are presented throughout this paper.

Figure 2

Electron momentum distribution recorded after ionization of the xenon 10$s$[3/2]${}_2$ state as a function of the FEL wavelength. Each panel shows both the “inverted” experimental data (top) and the results of focal volume-averaged TDSE calculations carried out for a maximum value of the vector potential $A_{\max }$ $=$ 0.12 a.u. and considering a pulse duration of 16 full laser cycles (bottom). For a detailed discussion rationalizing these values of the intensity and the pulse duration, the reader is referred to the discussion in the text. The laser polarization direction is along the vertical axis.

Figure 3

Angular distributions of the first and second ATI ring observed after ionization of the xenon 10$s$[3/2]${}_2$ state, as a function of the FEL wavelength. The presented angular distributions for the experimental data [yellow (light gray)] and TDSE calculations [green (gray)] are derived from the momentum distributions presented in Fig. 2. SFA calculations [blue (black)] were performed for a single intensity of 1 × 10${}^8$ W/cm${}^2$, which is justified by the fact that the focal volume-averaged TDSE calculations show only minor differences in the angular distribution compared to the single intensity 1 × 10${}^8$ W/cm${}^2$ TDSE calculations. The $y$ axis represents the logarithmic signal strength in arbitrary units and the different angular distributions are shifted with respect to each other for clarity. The figures can be quantitatively interpreted by using the fact that relative vertical scales are identical and the signal strengths cover one to two orders of magnitude for, respectively, the smallest range signal (24.2 μm) and largest range signal (30.2 μm).

Figure 4

SFA calculations for the ionization of xenon 10$s$ using a few-cycle midinfrared laser pulse with λ${}_{\mathrm{laser}}$ $=$ 29 μm and $I$ $=$ 1 × 10${}^8$ W/cm${}^2$. The flat top pulse used in the calculations is shown in the lower panel and consists of 3.5 cycles, with a half cycle turn on and off. The electron momentum distribution is obtained for (a) a 3.5-cycle flat-top laser pulse, (b) considering only interference between trajectories from the first and third half-cycle of the laser pulse, (c) considering only interference between trajectories from the first and second half-cycle of the laser pulse, and (d) considering interference of all trajectories (1–4) that start during the first two laser cycles.

Figure 5

(a)–(d) Raw experimental photoelectron images for the ionization of the 12$s$[3/2]${}_2$, 11$p$[3/2]${}_2$, 11$d$[7/2]${}_4$, and 8$f$[3/2]${}_2$ Rydberg states by 31.2-μm FEL radiation. Because the experiment does not contain an axis of cylindrical symmetry, the images are not inverted. The laser polarization axis is the vertical axis. The momentum in the plane of the detector perpendicular to the laser polarization axis is labeled $p_{\mathrm{r}}$′ and is distinct from the actual momentum perpendicular to the laser polarization axis $p_{\mathrm{r}}$ in the 3D distribution. (e) Angular distributions of the first ATI ring.

Figure 6

Momentum maps resulting from the ionization of xenon 11$p$[3/2]${}_2$ state as a function of the FEL wavelength. The top rows in each panel are the inverted experimental data and bottom parts show focal volume averaged TDSE calculations carried out for a maximum field strength of $A_{\max }$ $=$ 0.10 a.u., a pulse duration of 16 full laser cycles, and a 1:2 mixture of $m_{\ell }$ $=$ 0 and $|m_{\ell }|$ $=$ 1. The laser polarization direction is along the $z$ axis.

Figure 7

Calculated photoelectron momentum maps for the ionization of xenon 11$p$ with 26-μm radiation and at an intensity of $1\times {10}^8$ W/cm${}^2$. (a) TDSE calculation for $m_{\ell }$ $=$ 0; (b) TDSE calculation for $|m_{\ell }|$ $=$ 1; (c) SFA calculation with a π shift for each positive laser field maximum; (d) SFA calculation without π shift. In the bottom two figures the laser field $F$ is plotted; the π-shifted trajectories are marked by red dots and normal trajectories by black dots. The right half of the figure shows the ionization of $p$ orbitals with $m_{\ell }$ $=$ 0 and $m_{\ell }$ $=$ 1. The color indicates the phase, where yellow (light gray) and blue (dark gray) have opposite phases. The arrows indicate the ionization direction.