Simulation of wave-function microscopy images of Stark resonances

Wave-function microscopy images for Stark resonance states of H atoms are simulated using the quantum-mechanical formalism developed previously. Spatial distributions of ejected electron current densities are compared with experiment, and a good agreement is shown. The nonzero values of minima in the experimentally observed electron current distributions are reproduced by convoluting the theoretical current distribution with an instrumental function representing uncertainties in the position. Our relative strengths of the ejected electron current densities differ from those calculated with the wave packet propagation technique. We show that for the full convergence of the calculation, the distance between the ionized atom and the detector should exceed $10\mu \mathrm{m}$.

Figure 1

Differential cross sections or radial distributions of ejected electron currents in photoionization into four given resonance states $(0,29,0)$, $(1,28,0)$, $(2,27,0)$, and $(3,26,0)$ of H atoms from a mixture of $2s$ and $2p$ states at an electric field 808 V/cm. The four resonance states are located at $-172.809$ ${\mathrm{cm}}^{-1}$, $-169.617$ ${\mathrm{cm}}^{-1}$, $-166.427$ ${\mathrm{cm}}^{-1}$, and $-187.029$ ${\mathrm{cm}}^{-1}$, respectively. The simulated photoelectron images are shown in the left panels, while the experimental and computational electron currents are compared in the right panels. The blue dots, red dashed curves, and solid green curves represent the experimental measurements, the calculated electron current densities and these current densities convolved with the experimental resolution of the detector. Note that for the purpose of comparison, the calculated results in the right panel are scaled to the macroscopic dimensions of the experiment.

Figure 2

Comparison of the computed electron current densities in photoionization into the resonance state $(0,29,0)$, $(1,28,0)$, $(2,27,0)$, and $(3,26,0)$ of H atoms from a mixture state of $2s$ and $2p$ at an electric field 808 V/cm. The cyan solid curves and dashed magenta curves denote the present results and those from the wave packet propagation technique [16].

Figure 3

The change of spatial electron current distributions with distances $z_{\det }$ of the atomic sources for the resonance state $(3,26,0)$ of H atoms in an electric field 808 V/cm. The resonance state is located at $-163.240$ ${\mathrm{cm}}^{-1}$. The cyan solid curves represent the electron current density distributions at $z_{\det }=-1000\mu \mathrm{m}$, while the red dashed curves denote those at $z_{\det }=-0.4\mu \mathrm{m}$, $-1.0\mu \mathrm{m}$, $-10\mu \mathrm{m}$, and $-100\mu \mathrm{m}$. Note: the electron current distributions spread out with increasing $z_{\det }$, and therefore $\rho$ of the red dash curve in each panel is multiplied by a factor denoted.

Figure 4

Comparison of electron current distributions for off-resonance states of Stark H atoms in an electric field 808 V/cm. The two off-resonance states are located at $\epsilon =-165.347{\mathrm{cm}}^{-1}$ and $-168.257{\mathrm{cm}}^{-1}$. Experiment: $•$ Stodolna et al. [16] (Expt.). Theory: —– present quantum mechanical calculation (QM); - - - - present semiclassical calculation (SC) using open-orbit theory; $-·-·$ present calculation using the uniform approximation. Note: the semiclassical electron currents diverge at caustics corresponding to the red dashed vertical lines.