Dynamic Polarization in the Strong-Field Ionization of Small Metal Clusters

We report on the strong field ionization of small transition metal clusters (nickel, ${\mathrm{N}\mathrm{i}}_n$ $n=1–36$) within the quasistatic regime at an infrared wavelength of $1.5\mu \mathrm{m}$ and at intensities up to $2\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. From ion yields in a constant axial intensity beam, we obtained saturation intensities for the individual ${\mathrm{N}\mathrm{i}}_n$ clusters. As compared to quasistatic, single active electron calculations, a dramatic suppression of ionization was observed. Dynamic polarization in the laser field likely leads to strong multielectron screening of the “active” electron. Representing the metal clusters as classical conducting spheres, we obtained, via a barrier suppression calculation, the classical ionization rates. Agreement was obtained for larger clusters with $n>10$ when the dynamic polarization was taken into account, emphasizing the multielectron nature of the ionization suppression.

Figure 1

A mass spectrum of nickel clusters, obtained via strong-field ionization at $1.5\mu \mathrm{m}$ with an intensity $\sim {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$, plotted as a function of the number of nickel atoms, $n$, divided by the charge state $z$ of the ion. Peaks at half-integer $n/z$ correspond to doubly charged clusters. Peaks at integer $n/z$ can have contributions from both singly and doubly charged ions. The singly charged contribution can be estimated by subtracting the average of the neighboring half-integer peaks.

Figure 2

An example of an intensity dependence study of the ion yield of $\mathrm{N}\mathrm{i}_7{}^{+}$ and the calibration standard, Xe. A straight line is fitted to the signal at high intensity. The saturation intensity, $I_{\mathrm{s}\mathrm{a}\mathrm{t}}$, is defined as the intercept with the intensity axis. The dashed lines indicate the “worst-case” fits, used to obtain error estimates for the $I_{\mathrm{s}\mathrm{a}\mathrm{t}}$. Using an established method, absolute intensities (to within 20%) were determined using atomic xenon as a reference standard, as described in the text. Analogous plots were obtained for all other cluster masses.

Figure 3

Cluster size dependence of the ionization saturation intensity, $I_{\mathrm{s}\mathrm{a}\mathrm{t}}$, for (a) $\mathrm{N}\mathrm{i}_n{}^{+}$ and (b) $\mathrm{N}\mathrm{i}_n{}^{2+}$. The error bars were determined as indicated in Fig. 2. Metal clusters have dramatically higher $I_{\mathrm{s}\mathrm{a}\mathrm{t}}$ than predicted by simple QS-SAE models. The open circle shows the ADK prediction for the Ni atom. The solid line shows the result of a simple classical conducting sphere, barrier suppression ionization model. The dashed lines show the result of omitting the dynamic polarization term from this simple model. For details, see the text.