Tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors

TL;DR

This paper investigates the quantum tunneling behavior of Cooper pairs in asymmetric single-Cooper-pair transistors and coupled Cooper-pair boxes at subgap voltages, revealing band structures and multiphoton processes through theoretical and experimental analysis.

Contribution

It provides a detailed theoretical and experimental study of Cooper pair tunneling in complex superconducting circuits, highlighting new quantum phenomena such as band structures and multiphoton interactions.

Findings

Reproduced key features of experimental I-V curves

Identified traces of band structure in excited states

Observed multiphoton processes between Cooper-pair boxes

Abstract

We analyze tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors. Also tunneling of Cooper pairs across two capacitively coupled Cooper-pair boxes is considered, when the capacitive coupling and Cooper pair tunneling are provided by a small Josephson junction between the islands. The theoretical analysis is done at subgap voltages, where the current-voltage characteristics depend strongly on the macroscopic eigenstates of the island(s) and their coupling to the dissipative environment. As the environment we use an impedance which satisfies Re[Z]<<R_Q and a few LC-oscillators in series with Z. The numerically calculated I-V curves are compared with experiments where the quantum states of mesoscopic SQUIDs are probed with inelastic Cooper pair tunneling. The main features of the observed I-V data are reproduced. Especially, we find traces of band structure in the higher excited states of the Cooper-pair boxes as well as traces of multiphoton processes between two Cooper-pair boxes in the regime of large Josephson coupling.