Measurement of the Current-Phase Relation in Josephson Junctions Rhombi Chains

TL;DR

This study investigates the current-phase relation in one-dimensional Josephson junction rhombi chains at low temperatures, revealing a transition in supercurrent behavior and flux quantum periodicity depending on the Josephson to charging energy ratio.

Contribution

It provides the first detailed measurement of the current-phase relation in Josephson rhombi chains across different regimes, highlighting the transition from classical to quantum behavior.

Findings

Sawtooth-like supercurrent in the strong coupling regime

Abrupt change in supercurrent oscillation period near full frustration

Suppressed and rounded switching current in the quantum regime

Abstract

We present low temperature transport measurements in one dimensional Josephson junctions rhombi chains. We have measured the current phase relation of a chain of 8 rhombi. The junctions are either in the classical phase regime with the Josephson energy much larger than the charging energy, $E_{J}\gg E_{C}$, or in the quantum phase regime where $E_{J}/E_{C}\approx 2$. In the strong Josephson coupling regime ($E_{J}\gg E_{C} \gg k_{B}T$) we observe a sawtooth-like supercurrent as a function of the phase difference over the chain. The period of the supercurrent oscillations changes abruptly from one flux quantum $\Phi_{0}$ to half the flux quantum $\Phi_{0}/2$ as the rhombi are tuned in the vicinity of full frustration. The main observed features can be understood from the complex energy ground state of the chain. For $E_{J}/E_{C}\approx 2$ we do observe a dramatic suppression and rounding of the switching current dependence which we found to be consistent with the model developed by Matveev et al.(Phys. Rev. Lett. {\bf 89}, 096802(2002)) for long Josephson junctions chains.