Quasiparticle trapping in quench dynamics of superconductor/quantum dot/ superconductor Josephson junctions

With the aid of Keldysh nonequilibrium Green's functions, we investigate the quench dynamics in a superconductor-quantum dot-superconductor (S-QD-S) Josephson junction during transient transport processes going beyond the wide-band limit. We calculate the transient current when the bias is suddenly turned off/on. We find that because of the distinct physical mechanisms that govern superconducting current in zero-bias and nonzero-bias scenarios, the quench dynamics of the "turning-off"and "turning-on"transient processes exhibit significant differences. When the bias is turned off, aided by quasiparticle bound states, electrons become trapped in the energy gap and oscillate between the bound states ±ϵb. Consequently, the turning-off transient current exhibits oscillations at a frequency of 2ϵb, which is dependent on φ. Because the bound states in a φ-driven Josephson junction have an infinite lifetime, the turning-off transient current exhibits perpetual oscillations and relaxes towards the steady state at an infinitely slow rate. In contrast, the turning-on transient current, which is underpinned by multiple Andreev reflections, quickly settles into a steady alternating state at a frequency of 2V. The infinite relaxation time of the turning-off transient current, in conjunction with the distinct quench dynamics observed during both "turning-off"and "turning-on"operations, reveals the unique role of quasiparticle trapping in superconducting transient transport processes.