Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules

We introduce bicircular high-harmonic spectroscopy as a new method to probe dynamical symmetries of atoms and molecules and their evolution in time. Our approach is based on combining a circularly polarized femtosecond fundamental field of frequency $\omega$ with its counterrotating second harmonic $2\omega$. We demonstrate the ability of bicircular high-harmonic spectroscopy to characterize the orbital angular momentum symmetry of atomic orbitals. We further show that breaking the threefold rotational symmetry of the generating medium—at the level of either the ensemble or that of a single molecule—results in the emission of the otherwise parity-forbidden frequencies $3q\omega (q\in \mathbb{N})$, which provide a background-free probe of dynamical molecular symmetries.