Topological phases of quantized light

TL;DR

This paper explores the intrinsic topological phases of quantized light, revealing how Fock states and inhomogeneous couplings create novel topological phenomena, including phase transitions and quantum Hall effects in photonic systems.

Contribution

It introduces a new framework for topological phases based on the particle nature of light, extending topological photonics beyond classical regimes and higher dimensions.

Findings

Fock state Hamiltonian maps to a 1D Su-Schrieffer-Heeger model.

Strain induces a Lifshitz topological phase transition in a 2D Fock-state lattice.

Topological markers characterize phases in the constructed Haldane model.

Abstract

Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the particle nature of light, i.e., solely related to the quantized Fock states and the inhomogeneous coupling between them. The Hamiltonian of two cavities coupled with a two-level atom is an intrinsic one-dimensional Su-Schriefer-Heeger model of Fock states. By adding another cavity, the Fock-state lattice is extended to two dimensions with a honeycomb structure, where the strain due to the inhomogeneity of the coupling strengths induces a Lifshitz topological phase transition between a semimetal and a band insulator. In the semimetallic phase, the strain is equivalent to a pseudomagnetic field, which results in the quantization of the Landau levels and the valley Hall effect. We further construct a Haldane model where the topological phases can be characterized by the topological markers. This study demonstrates a fundamental distinction between the topological phases of bosons and fermions and provides a novel platform for studying topological physics in dimensions higher than three.