Microscopic theory of photoassisted electronic transport in normal-metal/BCS-superconductor junctions

We investigate photo assisted electronic transport in a\nnormal-metal/BCS-superconductor junction with a microscopic Hamiltonian\napproach, for several types of periodic voltage drives applied on the\nnormal-metal side. The time-dependent current and the photo-assisted noise are\ncomputed to all orders of the tunneling Hamiltonian using a\nKeldysh-Nambu-Floquet approach. An excess noise analysis allows one to\ndetermine to what extent pure electronic excitations with a small number of\nelectrons per period can be generated by the different drives. When the\nsuperconducting gap is small compared to the drive frequency, the junction\nbehaves like a normal-metal junction and minimal excess noise is reached for\nLorentzian voltage drives carrying an integer charge (levitons). In the\nopposite regime of a large-gap, the excess noise vanishes for half-quantized\nlevitons, giving rise to the perfect transmission of a Cooper pair on the\nsuperconducting side. This microscopic approach also allows us to address the\nintermediate regime, when the drive frequency is comparable to the gap,\nallowing us to study the non-trivial interplay between Andreev reflection and\nquasiparticle-transfer processes. Our analysis also shows the appearance of\nTien-Gordon-type relations connecting the current and noise in the AC-driven\njunction to their DC counterpart, which we investigate in details. Finally, the\npossibility to build a reliable on-demand source of Cooper pairs with this\nsetup is examined using realistic experimental parameters.\n