  We explore the electron dynamics of a system composed of double quantum dot
embedded between metallic and superconducting leads in a T-shape geometry. In
nanoscopic systems, where electron transfer between electrodes can be realized
via different paths, interference effects play an important role. For double
quantum dot system in the chosen geometry, interference of electrons
transferred between electrodes via the interfacial quantum dot and electrons
scattered on the side dot gives rise to Fano-like interference. If such a
system is additionally coupled to a superconducting electrode, together with
the well-understood Fano resonance an additional resonance appears on the
opposite side of the Fermi level. In the recent work [Sci. Rep. 10, 2881
(2020)], we showed that this resonance occurs solely as a result of the local
pairing of non-scattered electrons with scattered ones. In this work,
considering the quench dynamics, we explore how much time is required for
formation of each of these resonances. In particular, (i) we analyze the charge
oscillations between subsystems; (ii) we estimate the time required for each
resonance to achieve stable equilibrium upon an abrupt change of interdot
connection; (iii) we discuss a typical energy and time scales for experiments
on similar architectures.
