Localization and delocalization in networks with varied connectivity

TL;DR

This paper explores how varying connectivity influences localization and delocalization phenomena in circuit-QED networks, revealing a complex interplay between interactions, connectivity, and disorder through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of localization behaviors across different network models with varied connectivity, including exact solutions and phase diagrams.

Findings

All-to-all harmonic networks exhibit self-trapping.

Finite-range harmonic networks show delocalization.

Interaction effects lead to rich phase diagrams with disorder considerations.

Abstract

We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) Harmonic (ii) Jaynes-Cummings and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of Harmonic networks, exact analytical results are obtained and we demonstrate that all-to-all connection shows self-trapping whereas the finite-ranged connectivity shows delocalization. The interacting cases (Jaynes-Cummings, Bose-Hubbard networks) are investigated both via exact quantum dynamics and semi-classical approach. We obtain an interesting phase diagram when one varies the range of connectivity and the strength of the interaction. We investigate the consequence of imperfections in the cavity/qubit and the role of inevitable disorder. Our results are relevant especially given recent experimental progress in engineering systems with long-range connectivity.