Multiphoton excitation and ionization by elliptically polarized, intense short laser pulses: Recognizing multielectron dynamics and doorway states in ${\text{C}}_{60}$ vs Xe

Ionization and fragmentation of ${\text{C}}_{60}$ fullerenes are studied by time-of-flight mass spectrometry, in elliptically polarized femtosecond laser fields at 797 nm of intensities $I_0=\left(0.5–4.3\right)\times {10}^{14}\text{W}{\text{cm}}^{-2}$. Xe atoms serve as a test case. We derive a qualitative theory describing such polarization studies. It turns out that polarization dependence can very sensitively distinguish single active electron (SAE) and multiple active electrons dynamics. In the case of Xe a clear signature of SAE dynamics is observed, with very pronounced changes in the ion yield as a function of ellipticity, indicative of $\mathcal{N}=5–8$ and 18–22 photon processes for ${\text{Xe}}^{+}$ and ${\text{Xe}}^{2+}$, respectively. In contrast, only a moderate polarization dependence is observed in the ${\text{C}}_{60}$ case, although at least 5 $h\nu$ photons at 797 nm are needed to generate $\text{C}_{60}{}^{+}$ and additional 11 for $\text{C}_{60}{}^{2+}$. At lower intensities, a moderate reduction in the ion yield for circular polarization establishes a two-photon SAE absorption process, connected with the key role of the lowest unoccupied molecular orbital $\left(\text{LUMO}\right)+1\left(t_{1g}\right)$ as “doorway state.” The absence of any polarization effect at 399 nm corroborates this finding. At high intensities enhanced fragmentation is observed, which is tentatively attributed to returning loops of electron trajectories by the combined action of the $\text{C}_{60}{}^{+}$ field and the circularly polarized laser field—in contrast to conventional wisdom that linear polarization should lead to an enhanced recolliding electron yield. No sign of a pronounced multiphoton polarization signature with five and more photons is seen for ${\text{C}}_{60}$ which would be predicted by the SAE picture—although the slopes of the ion yield as a function of intensity are given by the corresponding power laws $\propto I_0^{\mathcal{N}}$. This is taken as clear evidence of multielectron dynamics after reaching the doorway state.

Figure 1

(Color online) Examples of mass spectra from ${\text{C}}_{60}$ after excitation with 27 fs pulses at 797 nm. (a) and (b) originate from linearly polarized light; (c) and (d) from circularly polarized light. The low-intensity mass spectra [(a) and (c)] have been taken at $I_0=0.94\times {10}^{14}\text{W}{\text{cm}}^{-2}$; the high-intensity ones [(b) and (d)], at $4.08\times {10}^{14}\text{W}{\text{cm}}^{-2}$. The small horizontal lines in (c) and (d) indicate the peak maxima in (a) and (b), respectively.

Figure 2

(Color online) ${\text{Xe}}^{+}$ and ${\text{Xe}}^{2+}$ ion yields as functions of ellipticity angle $\beta$ obtained with 27 fs laser pulses at 797 nm. The polarization changes from linear $\left(\beta =45°\right)$ to circular $\left(\beta =0°\right)$. The ion yield is normalized at each intensity $\left[I_0=\left(0.65–4.3\right)\times {10}^{14}\text{W}{\text{cm}}^{-2}\right]$ to its value for linear polarization. Note the dramatic reduction in ion signal, especially for ${\text{Xe}}^{2+}$, when the polarization changes from linear to circular.

Figure 3

(Color online) Dependence of the generalized relative $\mathcal{N}$-photon cross section on the ellipticity angle $\beta$ for different numbers of $\mathcal{N}$, normalized to its value for linearly polarized light, $\beta =\pi /4$.

Figure 4

(Color online) Schematic of multiphoton transitions (here $\mathcal{N}=4$) composed by one-photon amplitudes, which are $\propto \text{cos}\beta$ for LHC polarized excitation $\left(\Delta m=+1\right)$ and $\propto -\text{sin}\beta$ for RHC polarized excitation $\left(\Delta m=-1\right)$. Starting point is a ground state $|l_a{m}_a⟩$. Note that the dashed horizontal lines just indicate intermediate total photon energies and do not necessarily coincide with real levels of the system.

Figure 5

(Color online) Schematic illustration of interference between different order amplitudes. (a) Hypothetical term scheme for combined action of a three- and a one-photon amplitude ($c^{\left(2\right)\text{−}\left(1\right)}$ and $c^{\left(1\right)}$, respectively) inducing transitions into the ionization continuum from high-lying Rydberg states. (b) Ionization probabilities modeled for the situation shown in (a) with different relative contributions $w$ (%) from $c^{\left(2\right)\text{−}\left(1\right)}$.

Figure 6

(Color online) Energy levels and states ${|l_1{m}_1{l}_2{m}_2⟩}^{\pm ,0}$ of the two combined chromophore electrons with the relevant dipole-allowed transition amplitudes for the LHC and RHC polarized components of the radiation field. (Note that the arrows indicate amplitudes, not energy resonance or population transfer.) All levels with $l_1\equiv l_2=1$ are degenerate; they are drawn, however, as split for clarity.

Figure 7

(Color online) Yield of ${\text{Xe}}^{+}$ ions for different intensities as a function of the ellipticity angle $\beta$. The signals can be compared to each other (right scale for $I_0=1.65\times {10}^{14}\text{W}{\text{cm}}^{-2}$ and left scale for $1.15\times {10}^{14}$ and $0.65\times {10}^{14}\text{W}{\text{cm}}^{-2}$; the latter signal is plotted $\times 10$). The smooth lines represent theoretical model (10) with $\mathcal{N}$ given at the curves. The maximum has been normalized to linear polarization $\left(\beta =\pi /4\right)$.

Figure 8

(Color online) Yield of ${\text{Xe}}^{2+}$ ions as a function of the ellipticity angle $\beta$. Scales only on the left; the signal for $1.15\times {10}^{14}\text{W}{\text{cm}}^{-2}$ is plotted $\times 10$. Otherwise same as Fig. 7.

Figure 9

(Color online) Double-logarithmic plot of ion yields as functions of laser pulse intensity $I_0$ at 797 nm. The lines shown are spline fits to the experimental data points. Heavy lines (filled data points) and thin lines (empty data points) refer to “parent” and fragment ions, respectively. ◼ and ◻ (full lines) have been measured with linearly polarized light; ● and ○ (dashed lines), with circularly polarized light. The scales for all data are the same but have been shifted with respect to each other for clarity.

Figure 10

(Color online) Normalized ion yield as a function of ellipticity angle $\beta$ and laser intensity $I_0$ for 797 nm pulses. Top: $\text{C}_{60}{}^{+}$ parent ion; the full (red) line at the lowest intensity represents our model cross section (12) for a two-photon, one-chromophore transition. Bottom: ion yields of fragments $\text{C}_{60-2m}{}^{+}$ summed over all observed channels $m$ after $m$ units of ${\text{C}}_2$ have been evaporated. Note the different vertical scales. Since the fragment yield is very small at low intensities, we have indicated error bars.

Figure 11

(Color online) Normalized ion yield as a function of $\beta$ and laser intensity for 797 nm pulses. Top: $\text{C}_{60}{}^{2+}$ parent ion; bottom: fragments $\sum \text{C}_{60-2m}{}^{2+}$. Otherwise same as Fig. 10.

Figure 12

(Color online) Normalized ion yield as a function of ellipticity angle $\beta$ and laser pulse intensity $I_0$ for 797 nm pulses. Top: $\text{C}_{60}{}^{3+}$ parent ion; bottom: fragments $\sum \text{C}_{60-2m}{}^{3+}$. Otherwise same as Fig. 10.

Figure 13

(Color online) Normalized ion yield as a function of ellipticity angle $\beta$ and laser pulse intensity $I_0$ for 399 nm pulses for parent ions $\text{C}_{60}{}^{+}$ and $\text{C}_{60}{}^{2+}$, and fragments $\sum \text{C}_{60-2m}{}^{2+}$ of parent ions. No change in the yield with ellipticity angle $\beta$ is observed over the whole intensity range (single-photon absorption; black horizontal line at lowest intensities). Note the magnified vertical scale with respect to Figs. 10, 11, 12. For comparison, the two-photon, one-chromophore model (12) is also indicated at lowest intensities in red.

Figure 14

(Color online) Examples of classical electron trajectories in the combined field of $\text{C}_{60}{}^{+}$ and linearly (dashed lines) or circularly (full lines) polarized light. $I_0=4.3\times {10}^{14}\text{W}{\text{cm}}^{-2}$, 797 nm, initial kinetic energy is [(a) and (b)] 1 eV or [(c) and (d)] 10 eV, and starting point of the trajectory is [(b) and (d)] $0.65a$ or [(a) and (c)] $1a$. The initial field phase at $t=0$ is $\phi =162°$ in all cases shown, implying that the force on the electron at $t=0$ points into the direction of $-72°$ for circularly polarized light and into $+x$ direction as indicated by the vectors. All distances are given in units of the ${\text{C}}_{60}$ radius $a$. The thick gray full circles indicate the ${\text{C}}_{60}$ shell with the thickness of $0.35a$.

Figure 15

(Color online) Probabilities of finding different recollision energies for electrons emitted from the inner $\left(b\right)$ and outer radii $\left(a\right)$ of the ${\text{C}}_{60}$ molecule in linearly or circularly polarized light at $I_0=4.3\times {10}^{14}\text{W}{\text{cm}}^{-2}$, 797 nm. Initial conditions are taken statistically: kinetic energies of 0–10 eV (radial emission) at $0\le \Phi <2\pi$, laser field phase (at $t=0$) $0\le \phi <2\pi$, and starting radius of $0.65a$ or $a$.