High Harmonic Spectroscopy of the Cooper Minimum in Molecules

The Cooper minimum (CM) has been studied using high harmonic generation solely in atoms. Here, we present detailed experimental and theoretical studies on the CM in molecules probed by high harmonic generation using a range of near-infrared light pulses from $\lambda =1.3$ to $1.8\mu \mathrm{m}$. We demonstrate the CM to occur in ${\mathrm{CS}}_2$ and ${\mathrm{CCl}}_4$ at $\sim 42$ and $\sim 40\mathrm{eV}$, respectively, by comparing the high harmonic spectra with the known partial photoionization cross sections of different molecular orbitals, confirmed by theoretical calculations of harmonic spectra. We use CM to probe electron localization in Cl-containing molecules (${\mathrm{CCl}}_4$, ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, and trans-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$) and show that the position of the minimum is influenced by the molecular environment.

Figure 1

Top (bottom) panels are experimental (theoretical) HHG spectra using $\lambda =1.8\mu \mathrm{m}$ wavelength light with intensity $\sim 9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ ($\sim 6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) along with experimental and theoretical (open symbols) partial PICS for (a) ${\mathrm{CS}}_2$ and (b) ${\mathrm{CCl}}_4$. Only the envelopes are shown in theoretical HHG spectra.

Figure 2

Position of the Cooper minimum in HHG spectra for Ar as a function of intensity for different wavelengths $\lambda =1.3–1.8\mu \mathrm{m}$. At each wavelength, we show the position for two different pressures (closed shapes, 45 Torr; open shapes, 25 Torr) in the finite gas cell. The dotted line at 48 eV corresponds to the position of the minimum in the experimental and theoretical PICS [23, 24].

Figure 3

(a) Harmonic spectra generated in ${\mathrm{CCl}}_4$, ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, and trans-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$ using $\lambda =1.8\mu \mathrm{m}$ and intensity $\sim 9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The dashed line emphasizes the shift of the minimum between different molecules. [(b)–(d)] Position of minimum in harmonic spectra as a function of intensity for (b) ${\mathrm{CCl}}_4$ and (c) ${\mathrm{CH}}_2{\mathrm{Cl}}_2$ with $P=10\mathrm{Torr}$ and $\lambda =1.3\mu \mathrm{m}$ (filled squares), $1.5\mu \mathrm{m}$ (filled circles), $1.8\mu \mathrm{m}$ (filled triangles) as well as (d) trans-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$ where $\lambda =1.8\mu \mathrm{m}$ and $P=10\mathrm{Torr}$ (filled triangles), 3 Torr (hollow triangles). (e) Position of minimum as a function of pressure for ${\mathrm{CCl}}_4$ (left hand side filled triangles) and ${\mathrm{CH}}_2{\mathrm{Cl}}_2$ (right hand side filled triangles) using $\lambda =1.8\mu \mathrm{m}$ light with intensity $\sim 9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

(a) Binding energies and corresponding Mulliken atomic populations on Cl for molecular orbitals of ${\mathrm{CCl}}_4$, ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, and trans-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$ as well as atomic Cl [2, 33, 34]. [(b)–(d)] Highest occupied molecular orbitals of (b) ${\mathrm{CCl}}_4$, (c) ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, and (d) trans-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$.