Phase transition of light on complex quantum networks

TL;DR

This paper investigates how the topology of complex quantum networks influences the phase transition of light, revealing conditions under which quantum phase transitions can occur even with minimal coupling.

Contribution

It introduces a mean-field analysis of the Jaynes-Cummings-Hubbard model on complex networks, highlighting the impact of network eigenvalues on phase diagrams and transition conditions.

Findings

Phase diagram is non-trivial for complex topologies.

Scaling of hopping coefficient is crucial for phase transition.

Quantum phase transitions may occur at very small couplings.

Abstract

Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is non-trivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.