Phase-Space Topology in a Single-Atom Synthetic Dimension

• URL: http://arxiv.org/abs/2506.24020v2
• Date: Tue, 01 Jul 2025 16:01:54 GMT
• Title: Phase-Space Topology in a Single-Atom Synthetic Dimension
• Authors: Kyungmin Lee, Sunkyu Yu, Seungwoo Yu, Jiyong Kang, Wonhyeong Choi, Daun Chung, Sumin Park, Taehyun Kim,
• Abstract summary: We investigate topological features in the synthetic Fock-state lattice of a single-atom system described by the quantum Rabi model.<n>By diagonalizing the Hamiltonian, we identify a zero-energy defect state localized at a domain wall of the synthetic lattice.<n>To address the challenge of applying band topology to the Fock-state lattice, we introduce a topological invariant based on phase-space geometry.
• Score: 14.613175676004728
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate topological features in the synthetic Fock-state lattice 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 synthetic lattice, whose spin polarization is topologically protected. To address the challenge of applying band topology to the Fock-state lattice, we introduce a topological invariant based on phase-space geometry-the phase-space winding number. We show that the Zak phase, representing the geometric phase difference between two sublattices, can also be computed using a phase-space parameter and corresponds directly to the phase-space winding number. 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 fermionic 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.

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