Phase-Space Topology in a Single-Atom Synthetic Dimension

TL;DR

This paper explores topological properties in the phase space of a single-atom quantum system, revealing protected defect states and introducing a measurable topological invariant based on phase-space geometry.

Contribution

It introduces a novel phase-space topological invariant and demonstrates topologically protected states in a single-atom synthetic dimension, linking geometric phases to physical observables.

Findings

Identification of a zero-energy defect state localized at a domain wall

Introduction of a phase-space winding number as a topological invariant

Demonstration of bulk-boundary correspondence in phase-space topology

Abstract

We investigate topological features in the synthetic Fock-state lattice (FSL) of a single-atom system described by the quantum Rabi model. By diagonalizing the Hamiltonian, we identify a zero-energy defect state localized at a domain wall of the FSL, whose spin polarization is topologically protected. To address the challenge of applying band topology to the FSL, we introduce a physically motivated and directly measurable topological invariant based on phase-space geometry-the phase-space winding number. We show that the Zak phase, computed using a phase-space parameter, is related to the invariant. This quantized geometric phase reflects the spin polarization of the defect state, demonstrating a bulk-boundary correspondence. The resulting phase-space topology reveals the emergence of single-atom dressed states with contrasting properties-topologically protected spin states and driving-tunable bosonic states. Our results establish phase-space topology as a novel framework for exploring topological physics in single-atom synthetic dimensions, uncovering quantum-unique topological protection distinct from classical analogs.