Probing dynamical symmetries by bicircular high-order harmonic spectroscopy beyond the Born-Oppenheimer approximation

Abstract

We explore the possibility of bicircular high-order harmonic spectroscopy to probe the laser-induced dynamics of molecules in a non-Born-Oppenheimer treatment. The numerical solutions of the time-dependent Schr\odinger equation for aligned ${\mathrm{H}}_{2}$ and its isotopologs in $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ bicircular fields show that the intensity ratio between ${\mathrm{D}}_{2}$ and ${\mathrm{H}}_{2}$ for harmonic orders $3q$ is lower than that for orders $3q\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{4pt}{0ex}}(q\ensuremath{\in}\mathbb{N})$. Based on the strong-field approximation, we demonstrate that the interplay of vibrational wave-packet motion and dynamical-symmetry breaking leads to the different ratio. In general, the vibrational motion causes the ratio between isotopologs to increase with $q$ for both harmonic orders $3q$ and $3q\ifmmode\pm\else\textpm\fi{}1$. On the other hand, the emission of orders $3q$ is possible only because of the alignment-induced breaking of the dynamical symmetry. The faster nuclear motion in ${\mathrm{H}}_{2}$ enhances the symmetry breaking, resulting in the lower ${\mathrm{D}}_{2}$/${\mathrm{H}}_{2}$ ratio for the orders $3q$. Therefore, the harmonic orders $3q$ give access to the attosecond probing of dynamical symmetries in molecules.