Small physical objects, such a quantum dots, attached to bulk superconductors are prone to absorb the electron pairs. Their signatures are manifested by in-gap bound states, which appear in pairs symmetrically around the Fermi level. Under appropriate conditions, these in-gap states can evolve into the Majorana type quasiparticles which are promising candidates for stable quantum bits and implementation of quantum computations.

I shall discuss the time-resolved development of both, the conventional and topological bound states in superconducting hybrid stuructures. In particular, for two quantum dots contacted through the topological superconducting nanowire, we predicted nonlocal cross-correlations evidenced solely under nonequilibrium conditions by the crossed Andreev reflections [1]. We also analyzed competition of the Coulomb interactions with the proximity induced electron pairing (by means of time-dependent NRG calculations), revealing unique features in ac conductance of the periodically driven setup [2]. Furtheremore, we determined molecular quasiparticle spectrum of the short-length topological superconducting nanostructure [3] and inspected the quantum entanglement transmitted through the Majorana modes [4].

[1] Transient effects in quantum dots contacted via topological superconductor,
R. Taranko, K. Wrześniewski, I. Weymann, T. Domański, Phys. Rev. B 110, 035413 (2024).

[2] Signatures of Kondo-Majorana interplay in ac response,
K.P. Wójcik, T. Domański, I. Weymann, Phys. Rev. B 109, 075432 (2024).

[3] Nonlocal correlations transmitted between quantum dots via short topological superconductor,
G. Górski, K.P. Wójcik, J. Barański, I. Weymann, T. Domański, Sci. Rep. 14, 13848 (2024).

[4] Entanglement transmitted via Majorana wire: Insights from fermionic negativity, concurence and quantum mutual information C. Jasiukiewicz, A. Sinner, I. Weymann, T. Domański,L. Chatorlishvilli, Phys. Rev. B 111, 075415 (2025).