Orientation dependence of energy absorption and relaxation dynamics of C${}_{60}$ in fs-laser pulses

By means of nonadiabatic quantum molecular dynamics it is shown that the amount of energy deposited into ${\mathrm{C}}_{60}$ by a short laser field strongly depends on the molecular orientation with respect to the laser polarization direction. In consequence, subsequent electron-vibration coupling leads to different nuclear relaxation mechanisms with mainly three pathways: (1) excitation of giant $A_g\left(1\right)$ modes (“breathing”), (2) formation of deformed cagelike complexes (“isomers”), and (3) fragmentation predominantly into two large pieces (“fission”). The results are in accord with and nicely explain already existing experimental data. Future experiments are proposed to confirm the detailed predictions.

Figure 1

Orientation dependence of the absorbed energy $E_{\mathrm{abs}}$ normalized to its maximum value $E_{\mathrm{abs}}^{\max }$ (given in each figure) in a linearly polarized laser field $black\mathbf{E}(t;\theta ,\varphi )$ with different laser parameters ($T=10\mathrm{fs}$ in all cases). Left column [(a),(c)]: $\lambda =800\mathrm{nm}$ (nonresonant). Right column [(b),(d)]: $\lambda =400\mathrm{nm}$ (resonant); first row [(a),(b)]: $I=1.0\times {10}^{13}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$; second row [(c),(d)]: $I=1.2\times {10}^{14}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$. The black dots indicate the positions of the carbon atoms (view on $yz$ plane; cf. sketch at the top of the figure, where we have slightly rotated the molecule for a complete definition of the polarization, respectively, orientation angles). The results have been calculated using the fixed-nuclei approximation.

Figure 2

Same as in Fig. 1 but for a long ($T=54\mathrm{fs}$), strong ($I=6.2\times {10}^{14}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$) and nonresonant ($\lambda =800\mathrm{nm}$) laser pulse: (a) fixed-nuclei approximation; (b) full-dynamical calculations.

Figure 3

${\mathrm{C}}_{60}$ radius $R$ as a function of time $t$ for different molecular orientations (dotted lines) in the same laser field ($T=54\mathrm{fs}$, $I=6.2\times {10}^{14}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$, $\lambda =800\mathrm{nm}$) as used before (cf. Fig. 2). The colors [blue (lower dark gray lines), green (lower light gray lines), and red (upper dark gray lines)] correspond to typical orientations within the same colored regions of Fig. 2b and, thus, belong to different energy absorption intervals given in the figure. The full lines are the corresponding mean values of $R\left(t\right)$ and summarize the three different relaxation channels: (1) excitation of breathing modes (blue squares), (2) formation of nonbreathing isomeric states (green circles), and (3) ultrafast almost symmetric fission (red triangles). Typical snapshots of the dynamics at $t\approx 240\mathrm{fs}$ corresponding to the three relaxation channels are shown at the top of the figure using the same colors. The black arrows indicate the laser polarization axis [cf. Fig. 2b]. Note, the fission process proceeds along the laser polarization direction.