Topologically robust control of autoionizing state population

Attosecond technologies not only have made possible the study of electronic dynamics in atoms and molecules at their natural time-scale but have also offered the tools to steer them [1,2]. Ultrashort laser pulses can be tailored to facilitate the transfer of electronic population between molecular states through topologically robust processes. Such processes are particularly relevant when dealing with autoionizing states [3,4] and are predicated on the existence of an exceptional point (EP) — a condition where the energies of two states of a dissipative system merge under specific driving parameters [5]. The theoretical framework for understanding these phenomena involves an adiabatic model where the laser's parameter trajectory encircles the EP, resulting in the conversion of one state into another. The effectiveness of this model hinges on the adiabatic and rotating-wave approximations' (RWA) validity. To illustrate the EP model in a realistic system, we present a theoretical study of population transfers between autoionizing states of molecular oxygen near the a ⁴∏_u ionization threshold, within the fixed nuclei approximation. We simulate the interaction of ultrashort pulses with O₂ , tailoring the incoming pulse so that the trajectory of its parameters encircles an EP. To obtain the autoionizing states of the molecule, we diagonalize the close-coupling electronic Hamiltonian computed with the ASTRA molecular ionization code~[6], imposing outgoing boundary conditions. To identify the domain of applicability of the EP model, we compare the results of the time evolution computed by solving the time-dependent Schrödinger equation numerically, with those obtained applying the RWA and adiabatic approximations. We propose realistic control schemes in terms of feasible pulse intensities, duration and frequencies.