Collective quantum phases in frustrated arrays of Josephson junctions

TL;DR

This paper investigates the rich variety of collective quantum phases and phase transitions in frustrated arrays of Josephson junctions, revealing how frustration and physical parameters influence the emergence of insulating, superconducting, and entangled vortex states.

Contribution

It introduces a detailed analysis of quantum phases in frustrated Josephson junction arrays, highlighting the role of frustration and mapping the phase diagram through quantum correlations.

Findings

Identification of disordered and ordered quantum phases in non-frustrated arrays.

Discovery of highly entangled vortex and anti-vortex patterns in frustrated arrays.

Mapping of the phase diagram using quantum correlation functions.

Abstract

We study collective quantum phases and quantum phase transitions occurring in frustrated sawtooth arrays of small quantum Josephson junctions. Frustration is introduced through the periodic arrangement of $0$- and $\pi$- Josephson junctions with the Josephson coupling energies $\alpha E_\mathrm{J}$ of different signs, $-1\leq \alpha \leq 1$. The complexity of the potential landscape of the system is controlled by the frustration parameter $f=(1-\alpha)/2$. The potential energy has a single global minimum in the non-frustrated regime ($f<f_\mathrm{cr}=0.75$) and a macroscopic number of equal minima in the frustrated regime ($f>f_\mathrm{cr}=0.75$). We address the coherent quantum regime and identify several collective quantum phases: disordered (insulating) and ordered (superconducting) phases in the non-frustrated regime, as well as highly entangled patterns of vortices and anti-vortices in the frustrated regime. These collective quantum phases are controlled by several physical parameters: the frustration $f$, the Josephson coupling, and the charging energies of junctions and islands. We map the control parameter phase diagram by characterizing the quantum dynamics of frustrated Josephson junction arrays by spatially and temporally resolved quantum-mechanical correlation function of the local magnetization.