Cesium Rydberg-state ionization study by three-dimensional ion-electron correlation: Toward a monochromatic electron source

We study the excitation and ionization of cesium Rydberg states in an electric field ($\approx 2200\mathrm{V}/\mathrm{cm}$) near the classical field-ionization threshold ($\approx -280{\mathrm{cm}}^{-1}$ binding energy) by three-dimensional (3D) ion-electron coincidence spectroscopy. Cesium atoms are produced by an effusive oven and excited with lasers to Stark-shifted Rydberg states or directly ionized. Using a double time-of-flight setup we record 3D ($X, Y$, time of flight) coincidence imaging of electrons and ions. Above-threshold photoionization creates broad images with poor electron-ion spatial correlation. Fast ionizing states produce very good correlations and the images reveal the electric-field map of the ionization region. Slow ionizing states show that the relatively high atomic velocity is detrimental to the correlations. Experimental data are accurately reproduced by detailed Monte Carlo excitation and ionization simulations based on Stark maps obtained with local-frame transformation (LFT) theory. Agreement between our spectroscopic experiment and LFT theory is very good, with better that hundreds of megahertz accuracy. But, on rare particular states, several gigahertz discrepancy is found. This study can be used to select appropriate states for the creation of ion and electron beams with high brightness, good correlation, and low energy dispersion.

Figure 1

3D view of the apparatus showing the cesium oven, the neutral cesium beam, the three lasers, time-and-position-sensitive detectors (TPSD) and electron and cesium ions beams. The drift equipotential tubes between the electrodes and the detectors are not shown. The optical axis corresponds to the $z$ axis.

Figure 2

Stark map of Rydberg states in cesium, from $-400{\mathrm{cm}}^{-1}$ up to $100{\mathrm{cm}}^{-1}$ above the classical ionization threshold (shown in blue (dark gray) dashed line), from 0 to $3000\mathrm{V}/\mathrm{cm}$, with the ionization path at $2170\mathrm{V}/\mathrm{cm}$ used in this work. It is constructed from individual calculations using LFT theory at a given electric field. The three low energy electronic states ($6S_{1/2}, 6P_{3/2}$, and $7S_{1/2}$) have negligible Stark shift at this representation scale. Arrows represent one photon absorption. The inset is a zoom on the Stark map, showing in detail the region of the investigated Rydberg states.

Figure 3

Comparison between experimental (black) and theoretical (LFT) [red (dark gray)] photoionization scans. The classical ionization field threshold is indicated by a blue (dark gray) dashed line. Intensity scales are arbitrary, and both spectra are cut from the top in order to better see the low intensity lines.

Figure 4

Experimental and simulated results for the excitation of a fast-ionizing Stark-shifted Rydberg state. The ionizing laser is set at $\lambda =794.24165\mathrm{nm}$ and the resonant electric field is $2169.35\mathrm{V}/\mathrm{cm}$. Electrode potentials are chosen to locate this field value off axis. (a) Stark map showing the studied Rydberg state. The red (dark gray) line corresponds to the value of the Ti:sapphire wavelength and the gray circle shows the resonant state. (b) Planar cut of the electrodes simulated in simion. The field line is taken at $2169.35\mathrm{V}/\mathrm{cm}$. (c) 3D representation of the initial ionizing point for the excited Rydberg states. (d) Experimental (top line) and simulated (bottom line) images, from left to right are shown the electron image, the electron-ion ($Y$) correlation image, and the time of flight (ToF) between correlated ions and electrons.

Figure 5

Same as Fig. 4 but after the excitation of a fast-ionizing Rydberg state resonant on electric-field lines at the center of the electrodes. The field line of panel (b) is taken at $2165.6\mathrm{V}/\mathrm{cm}$. The axes for the 3D representation in panel (c) have been modified to obtain a better view.

Figure 6

Experimental and simulations results after the excitation of a long-lived Rydberg state excited on the one-sheet hyperboloid. Upper (experimental results) and lower (simulation) parts: from left to right the electron image, the $X$ and $Y$ electron-ion correlation images.

Figure 7

Results after the excitation of a “double” state on the one-sheet field hyperboloid. Left panel shows experiment (top) and simulation (bottom). Right panel shows rate equation simulation for a traveling (along the $X$ axis) excited atom. R1 and R2 are Rydberg states (see text for details) and Ion1 and Ion2 are the respective ionized form of the states.

Figure 8

(a) Histogram of the starting field of particles in the laser spot, corresponding to a normal distribution with $30\mu \mathrm{m}$ spread in all three axis. (b) Comparison of computed [red (dark gray) and yellow (light gray)] and experimentally acquired (black) photoabsorption spectra at $F=2172.5\mathrm{V}/\mathrm{cm}$. The yellow (light gray) spectra is the direct output of the LFT code at $F=2172.5\mathrm{V}/\mathrm{cm}$. The red (dark gray) theoretical spectrum (“convoluted”) is a weighted sum of spectra over the electric-field inhomogeneity shown in panel (a) to take into account the finite extension of the ionization zone.