Tunneling of fluxons via a Josephson resonant level

TL;DR

This paper investigates how fluxons in a superconducting loop are coupled via quantum phase slips, highlighting the dominance of 4π phase slips when tunneling occurs through a resonant level, with implications for qubit design.

Contribution

It demonstrates that resonant tunneling suppresses 2π phase slips, leading to a 4π-dominated regime observable in fluxonium qubits, and establishes a duality with topological superconducting islands.

Findings

4π quantum phase slips dominate fluxon coupling at resonance.

The 4π regime can be observed in fluxonium qubit spectra.

Low-energy Hamiltonian is dual to topological superconducting islands.

Abstract

Fluxons in a superconducting loop can be coherently coupled by quantum phase slips occurring at a weak link such as a Josephson junction. If Cooper pair tunneling at the junction occurs through a resonant level, $2\pi$ quantum phase slips are suppressed, and fluxons are predominantly coupled by $4\pi$ quantum phase slips. We analyze this scenario by computing the coupling between fluxons as the level is brought into resonance with the superconducting condensate. The results indicate that the $4\pi$-dominated regime can be observed directly in the transition spectrum for circuit parameters typical of a fluxonium qubit. We also show that, if the inductive energy of the loop is much smaller than the plasma frequency of the junction, the low-energy Hamiltonian of the circuit is dual to that of a topological superconducting island. These findings can inform experiments on bifluxon qubits as well as the design of novel types of protected qubits.