Dynamic Two-Center Interference in High-Order Harmonic Generation from Molecules with Attosecond Nuclear Motion

We report a new dynamic two-center interference effect in high-harmonic generation from ${\mathrm{H}}_2$, in which the attosecond nuclear motion of ${\mathrm{H}}_2^{+}$ initiated at ionization causes interference to be observed at lower harmonic orders than would be the case for static nuclei. To enable this measurement we utilize a recently developed technique for probing the attosecond nuclear dynamics of small molecules. The experimental results are reproduced by a theoretical analysis based upon the strong-field approximation which incorporates the temporally dependent two-center interference term.

Figure 1

(a) Measured ratio of harmonic signals in ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ at driving field intensity $(3.0\pm 0.1)\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. Two independent data sets are shown. Black line shows prediction from SFA calculation [Eq. (2)]. Gray line shows SFA calculation in which the nuclear motion has been neglected. Dotted line shows SFA calculation in which two-center interference is neglected. Inset shows calculated alignment distribution $\sigma (\theta )$ [20] at the pulse peak in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ at this intensity. For comparison the dotted curve shows $\sigma (\theta )$ for the 8 fs case investigated in Ref. 6. (b) Same as (a), but for driving field intensity $(2.2\pm 0.2)\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$.

Figure 2

Data points show electron wavelength corresponding to the harmonic orders observed at driving field intensities of $(3.0\pm 0.1)\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ (black) and $(2.2\pm 0.2)\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ (gray), plotted against electron travel time. Solid lines show $2R(t)\cos ({\theta }_m)$ for $\mathrm{H}_2{}^{+}$ at the high (black) and low (gray) intensities. Dotted line shows $2R_{\mathrm{eq}}\cos ({\theta }_m)$ for ${\mathrm{H}}_2$ at an intensity $(3.0\pm 0.1)\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. Inset shows SFA calculation of signal ratio at $3.0\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ assuming a single alignment angle ${\theta }_m$.

Figure 3

Dynamic two-center interference in HHG, considering a chirped returning electron wave packet (${\lambda }_1>{\lambda }_2>{\lambda }_3$) and an evolving nuclear wave function. Red and blue represent opposite signs of the wave functions. At early times (A) and late times (C), the condition for two-center interference is not satisfied [$2R(t_1)\cos \theta \ll {\lambda }_1$, $2R(t_3)\cos \theta \gg {\lambda }_3$]. The corresponding low and high-order harmonics are therefore emitted without significant interference. At intermediate times (B), $2R(t_2)\cos \theta \approx {\lambda }_2$, and thus the emission of harmonics of photon energy $h/2m{\lambda }_2^2$ is suppressed.