Probing isotope effects of oriented molecules with odd-even high-order harmonics

We study high-order harmonic generation (HHG) from oriented isotope molecules beyond the Born-Oppenheimer approximation numerically and analytically. We compare the symmetric cases of ${\mathrm{H}}_{2}$ and its isotopic variant ${\mathrm{T}}_{2}$ to the asymmetric ones of ${\mathrm{HeH}}^{+}$ and ${\mathrm{HeT}}^{+}$. Different from symmetric molecules, the laser-induced stretching for asymmetric molecules depends strongly on the molecular orientation. In addition, the structures of the HHG spectra for oriented ${\mathrm{H}}_{2}$ versus ${\mathrm{T}}_{2}$ differ remarkably from each other, and one can trace the stretching of these symmetric isotope molecules directly from the spectra. However, the spectral structures for oriented ${\mathrm{HeH}}^{+}$ versus ${\mathrm{HeT}}^{+}$ are basically the same. In this situation, we propose a procedure for probing the stretching of these asymmetric isotope molecules using odd-even HHG, with a high time-space resolution.