Collective modes in non-equilibrium in unconventional superconductors with competing ground states

Motivated by the recent development of terahertz pump-probe spectroscopy, we investigate the short-time dynamics and collective modes in superconductors with multiple attractive pairing chnnels. We consider a single-band square lattice model with nearest neighbor attraction. This interaction decouples into s-, d- and p-wave channels leading to strong competition between them for various band fillings. Driving the system out of equilibrium, we find signatures of collective modes of symmetries different from the ground state ( so-called Bardasis-Schrieffer modes) for the s-wave ground state. We show that polarizationcan be used to excite Bradsis-Schrieffer modes of a particular symmetry in a controlled way and discuss implications for the future pump probe experiments.