Crossed Beam Pump and Probe Dynamics in Metal Clusters

We investigate theoretically pump and probe dynamics in metal clusters with crossed-polarization laser beams. We explore the relation between the pronounced Mie plasmon resonance and the laser frequency. The resonance moves with the cluster radius and splits according to the actual deformation. We demonstrate that probe pulses with different (linear) polarization axes allow one to resolve the global shape oscillations of the cluster in monopole and quadrupole degrees of freedom.

Figure 1

Demonstration of pump and probe analysis for $\mathrm{Na}_9{}^{+}$. The laser parameters are as follows: frequency $\omega =2.3\mathrm{eV}$; intensity $1.3\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$; the profile is a ${sin}^2$ pulse with $\mathrm{FWHM}=24\mathrm{fs}$; polarization is in the $x$ direction (orthogonal to symmetry axis). The pump pulse was active in the first time bin 0–48 fs. Panel (a) shows the ionic rms radius for free evolution after pump. Panels (b) and (c) show the effect of a three probe pulse applied at different delay times, with (b) the envelope of dipole momentum in the $x$ direction and (c) the number of emitted electrons in the course of time.

Figure 2

Time evolution of key observables in a pump and probe analysis of $\mathrm{Na}_9{}^{+}$. The laser parameters are as given in Fig. 1. The pump pulse was active in the first time bin 0–48 fs. Panels (a) and (b) show features of the free evolution after pump, with (a) the rms extensions in the $x$, $y$, and $z$ directions and (b) the estimated plasmon peak frequency for modes in the $x$, $y$, and $z$ directions plus a horizontal dashed line to indicate the laser frequency. The probe pulses are applied in successive time bins of 48 fs. Panels (c) and (d) show features of the probe, with (c) the maximum amplitude of dipole response and (d) the number of emitted electrons after probe (fine dotted line without probe).

Figure 3

Complementing information for pump and probe analysis of $\mathrm{Na}_9{}^{+}$. Panel (a) shows the number of emitted electrons after probe averaged over all three polarization directions, (b) the ionic rms radius for free evolution after pump, (c) the electronic rms radius for free evolution, and (d) the separate electronic $x$, $y$, and $z$ extensions for free evolution after pump. The laser parameters are as given in Fig. 1.