Quantum memory effects in the dynamics of electrons in gold clusters

Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a “memory term,” i.e., attempts to describe temporal nonlocal correlations. Using the Iwamoto, Gross, and Kohn exchange-correlation (XC) kernel, we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical jellium gold clusters. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the jellium model. Memory effects on nonlinear spectroscopy are studied as well: a real-time pump-probe setup is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail; and in high harmonic generation, we show that memory narrows and redshifts emission lines.

Figure 1

(Color online) The $Z\text{−}Z$ correlation function vs time for the finite HEG slab (top); the corresponding plasmon absorption cross-section line shape (bottom). This figure compares ALDA with $\mathrm{ALDA}+M$.

Figure 2

(Color online) The polarization vs time for the ${\mathrm{Au}}_{18}$ spherical jellium cluster (top panel) after the short pulse excitation. The corresponding absorption cross sections are shown in the bottom panel.

Figure 3

(Color online) Memory effects on the real-time (top) and frequency (bottom) two-photon response $L_{01}$ for ${\mathrm{Au}}_8$ spherical jellium cluster at $\tau =25\mathrm{fs}$.

Figure 4

(Color online) The ALDA and $\mathrm{ALDA}+M$ pump-probe $L_{01}$ two-photon absorption signals in ${\mathrm{Au}}_8$. The first photon is a 3.6 (plasmon) frequency and absorbed from the pump while the second is photon is obtained from the probe, $0.9\mathrm{eV}$ (top) and $1.7\mathrm{eV}$ (bottom).

Figure 5

(Color online) The ALDA and $\mathrm{ALDA}+M$ pump-probe $L_{01}$ two-photon absorption-emission signals in ${\mathrm{Au}}_8$. Absorption of the pump photon excites the plasmon at $3.5\mathrm{eV}$. The probe stimulates emission of a second photon at $3.6\mathrm{eV}$ (top) and $2.5\mathrm{eV}$ (bottom).

Figure 6

(Color online) Memory effects in the transient ionization rate for the ${\mathrm{Au}}_{18}$ spherical jellium cluster during a short and intense laser pulse.

Figure 7

(Color online) Memory effects on the HHG spectra for the ${\mathrm{Au}}_{18}$ spherical jellium cluster. The top panel shows the spectrum on a logarithmic scale. Close ups on the line shapes in linear scale of harmonics 3, 5, 7, and 9 are shown in the bottom panels.

Figure 8

(Color online) The reduced kernel ${\varphi }_{3∕4}\left(x\right)$.