Buildup and transient oscillations of Andreev quasiparticles

We study transient effects in a setup where the quantum dot is abruptly sandwiched between the metallic and superconducting leads. Focusing on the proximity-induced electron pairing manifested by the in-gap bound states, we determine characteristic timescales needed for these quasiparticles to develop. In particular, we derive analytic expressions for (i) charge occupancy of the quantum dot, (ii) amplitude of the induced electron pairing, and (iii) the transient currents under equilibrium and nonequilibrium conditions. We also investigate the correlation effects within the Hartree-Fock-Bogolubov approximation, revealing a competition between the Coulomb interactions and electron pairing.