Multiple Andreev-reflection in superconducting weak-links in the interaction with external microwave-fields

We present calculated current-voltage characteristics (CVCs) of NS- and SNS-contacts, where the carrier transport is characterised by single and multiple Andreev-reflection (AR) in the presence of an external microwave field. Based on the Tien-Gordon model of multiphoton- assisted electron tunneling [1] we describe the microwave field by an ac-voltage potential. This additional potential is added in the time-dependent Bogoliubov-de Gennes equations (BdGE) which describe inhomogeneous superconductors and in this way NS-phase boundaries. These modified BdGE are solved by single particle wave-functions, which contain the multiphoton emission and absorption processes of the quasi-particles (QPs). With this ansatz we obtain an extension of the BTK-theory for NS-contacts [2] and the OTBK-theory for SNS-contacts [3,4]. We show, that the calculated CVCs for NS-contacts are in the case of a vanishing probability for AR identical with the characteristics obtained with the Tien-Gordon model. For SNS-contacts we show theoretically that features in the CVCs appear at voltages $V = frac{{2Delta }} {{ne}} + frac{m} {n}frac{{hbar omega }} {e}$ (n,m integers). This equation was initially found experimentally by Hoffmann-Soerensen et al. [5]. We are now able to explain their results and show that investigations of the interaction of multiple AR with an external microwave field give clear evidence for the occurrence of multiple AR in the junction.