Transient effects in quantum dots contacted via topological superconductor

We investigate gradual development of the quasiparticle states in two quantum dots attached to opposite sides of the topological superconducting nanowire, hosting the boundary modes. Specifically, we explore the nonequilibrium cross-correlations transmitted between these quantum dots via the zero-energy Majorana modes. Our analytical and numerical results reveal the nonlocal features observable in the transient behavior of electron pairing, which subsequently cease while the hybrid structure evolves towards its asymptotic steady-state configuration. We estimate duration of these temporary phenomena. Using the nonperturbative scheme of the time-dependent numerical renormalization group technique we also analyze nonequilibrium signatures of the correlation effects competing with the proximity induced electron pairing. These dynamical processes could manifest themselves in braiding protocols imposed on the topological and/or conventional superconducting quantum bits, using superconducting hybrid nanostructures.