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arXiv:2211.05660

Quantum phase slips in a resonant Josephson junction

Tereza Vakhtel, Bernard van Heck

Published Nov 10, 2022• 0 citations
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Abstract

Notebooks and python code that generate the figures in "Quantum phase slips in a resonant Josephson junction"
DOI
10.48550/arxiv.2211.05660

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We investigate the consequences of resonant tunneling of Cooper pairs on the quantum phase slips occurring in a Josephson junction. The amplitude for quantum tunneling under the Josephson potential barrier is modified by the Landau-Zener amplitude of adiabatic passage through an Andreev level crossing, resulting in the suppression of $2\ensuremath{\pi}$ phase slips. As a consequence, close to resonance, $4\ensuremath{\pi}$ phase slips become the dominant tunneling process. We illustrate this crossover by determining the energy spectrum of a transmon circuit, showing that a residual charge dispersion persists even at perfect transparency.
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, then $2\ensuremath{\pi}$ quantum phase slips are suppressed, and fluxons are predominantly coupled by $4\ensuremath{\pi}$ 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 $4\ensuremath{\pi}$-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, then 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.