Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal reflections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic
analytical framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even
negative conductance at specific voltages.
Quasiparticle dynamics have been identified as an important factor in the operational performance of superconductors in quantum computing and sensing applications. In order to study such dynamics, we performed measurements of quasiparticle transport in a superconductor engineered to enhance quasiparticle relaxation. We found that a thin, highly disordered normal metal layer can be used to greatly reduce the relaxation time of quasiparticles in a superconductor, as seen by a large reduction in the quasiparticle charge imbalance in a fully proximitized Cu/Al bilayer wire, without significantly affecting the properties of the superconductor. The enhanced relaxation is likely due to an increased electron–electron scattering rate in the disordered normal metal. Our results provide a positive indication that quasiparticle relaxation can be substantially enhanced via a simple and technologically viable method, and demonstrate that direct measurement of quasiparticle imbalance can be a useful tool for the assessment and engineering of superconductors in various applications at mK temperatures.