Steady state properties of open topological waveguides

doi:10.3969/j.issn.1007-5461.2025.06.008

Abstract

Abstract: Based on the Su-Schrieffer-Heeger (SSH) model, the steady-state properties of an open topological waveguide were investigated using the truncated Wigner approximation (TWA). The study demonstrates that by applying identical drive and dissipation to each cavity in the topological waveguide, two distinct skin effects emerge in the photon distribution upon reaching steady state: localization toward the edges and localization toward the sub-edges. As the dimerization parameter increases, the skin effect shifts from edge localization to sub-edge localization, eventually diminishing completely. This work offers new insights for exploring topological properties of many-body systems in open quantum systems.

Key words: quantum optics, Su-Shrieffer-Heeger model, quantum open system, truncated Wigner approximation, skin effect

CLC Number:

O431.2

CHI Xihao , GUO Xiang , YIN Dongmei , WANG Zhihai . Steady state properties of open topological waveguides[J]. Chinese Journal of Quantum Electronics, 2025, 42(6): 806-817.

References

[1] Hasan M Z, Kane C L.Colloquium: Topological Insulators. Reviews of Modern Physics, 2010, 82(4):3045–3067. [2]Qi X L, Zhang S C. Topological Insulators and Superconductors. Reviews of Modern Physics, 2011, 83(4), 1057–1110. [3] Kane C L, Mele E J.Quantum Spin Hall Effect in Graphene.Physical Review Letters, 2005, 95(22), 226801 [4] Wang Y, Lu Y H, Gao J, Chang Y J, Tang, H., Jin X M.Topological Phononic Insulators,Physical Review B, 2021, 103(1), 014110. [5] Cheng W J, Wang Z H, Liu Y X. Topology and retardation effect of a giant atom in a topological waveguide .Physical Review A, 2022, 106(3), 033522. [6] Su, W P, Schrieffer J R, Heeger A J.Solitons in Polyacetylene,Physical Review Letters, 1979, 42(25), 1698–1701. [7] Teo J C Y, Kane C L.Topological Defects and Gapless Modes in Insulators and Superconductors.Physical Review B, 2010, 82(11), 115120. [8] Ganeshan S, Sun K, Sarma S D.Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models.Physical Review Letters, 2013,110(18), 180403. [9] Andrea, B. R., et al.Topological Optical Waveguiding in Silicon and the Transition between Topological and Trivial Defect States.Physical Review Letters, 2016, 116(16), 163901. [10] Jukka I V, Teemu O. Chiral Topological Phases and Fractional Domain Wall Excitations in One-Dimensional Chains and Wires.Physical Review Letters, 2011, 107(16), 166804. [11] Kane C L, Lubensky T C.Topological Boundary Modes in Isostatic Lattices.Nature Physics, 2014, 10(1), 39–45. [12] Cheng Q,Pan Y, Wang Q, Li T, Zhu S. Topologically protected interface mode in plasmonic waveguide arrays[J]. Laser & Photonics Reviews, 2015, 9(4), 392–398. [13] Pearson C J, Barford W, Bursill R J.Topological Insulators in the Presence of Disorder.Physical Review B, 2011, 83(19), 195105. [14] Sattwik D M, Miguel F P, Rahul T.Decoherence-induced self-dual criticality in topological states of matter.PRX Quantum, 2024, 5(2), 020317. [15] Hao D D, Wang L, Lu X D, Cao X Z, Jia S T, Hu Y, Xiao Y H. Topological Atomic Spin Wave Lattices by Dissipative Couplings.Physical Review Letters, 2023, 130(15), 153602. [16]Chen J Z, Shi A Q, Peng Y C,Peng P, Liu J J.Hybrid Skin-Topological Effect Induced by Eight-Site Cells and Arbitrary Adjustment of the Localization of Topological Edge States.Chinese Physics Letters ,2024,41(5), 037103 [17]Zhu X L, Peng T, Lyu F, Cao W, Hou Y, Xiong R, Wang Z Y.Non-Hermitian quasicrystalline topological insulators.Physical Reveiew B,2025,111(3), 035305 [18]Peng Y C, Shi A Q,Peng P, Liu J J.Pseudospin-induced asymmetric field in non-Hermitian photonic crystals with multiple topological transitions. Physical Reveiew B,2025 111(8), 085148 [19]Shi A Q, Bao L S,Peng P, Ning J Y, Wang Z N, Liu J J.Non-Hermitian Floquet higher-order topological states in two-dimensional quasicrystals. Physical Reveiew B,2025,111(9), 094109 [20]Lin X D, Zhang L.Measuring non-Hermitian topological invariants directly from quench dynamics. Physical Reveiew Reseach ,2025,7(1), L012060 [21] Liu D Y,Peng P,Lu, X Y,Shi, A Q,Peng Y C,Wei Y Z,Liu J J,Multiple topological states within a common bandgap of two non-trivial photonic crystals. Optics Letters,2024,49(9) 2393-2396 [22]Cui S J,Geng Z J , Chen Z J, Shen Y X, Zhu X F.Dual-band higher-order topological states in composite square-lattice sonic crystals. Physical Reveiew Applied,2025,23(4), 044005 [23]Shi A Q, Peng Y C,Peng P, Chen J Z, Liu J J.Delocalization of higher-order topological states in higher-dimensional non-Hermitian quasicrystals. Physical Reveiew B,2024,110(1), 014106 [24]Liu T Y, Yan W, Qiu M.Bending immunity in valley edge states and non-Hermitian supercoupling effects. Physical Reveiew B,2024,110(1), L020101 [25] Feynman R P, Hibbs A R.Quantum Mechanics and Path Integrals, New York: McGraw-Hill, 1965. [26] Caldeira A O, Leggett A J.Quantum Tunneling in Dissipative Systems.Physica A, 1983, 121(3), 587–616. [27] Kazuyuki S, Yuan M, Hosho K. Quantum many-body scars in spin models with multibody interactionsPhysical Review B, 2023, 108(15), 155102. [28] Goldenfeld, N.Lectures on Phase Transitions and the Renormalization GroupWestview Press, Boulder, 1992. [29] Chandrasekhar S.Stochastic Problems in Physics and Astronomy.Reviews of Modern Physics, 1943, 15(1), 1–89. [30]Ford G W, Kac M, Mazur P.Statistical Mechanics of Assemblies of Coupled Oscillators.Journal of Mathematical Physics, 1965, 6(4), 504–515. [31] Haake F.Statistical Treatment of Open Systems by Generalized Master Equation.Berlin: Springer-Verlag, 1973. [32] Klauder J R, McKenna J,Currie D G.Some Aspects of the Rotation and Lorentz Groups.Journal of Mathematical Physics, 1965, 6(5), 734–739. [33Jarzynski C.Nonequilibrium Equality for Free Energy Differences.Physical Review E, 1997, 56(5), 5018–5035. [34] Gardiner C W, Collett M J.Input and Output in Damped Quantum Systems.Physical Review A, 1985, 31(6), 3761–3774. [35] Davies E B.Markovian Master Equations.Communications in Mathematical Physics, 1974, 39(2), 91–110. [36] Walls D, Milburn G J.Quantum Optics. Berlin: Springer-Verlag, 1994. [37] Breuer H P, Petruccione F.The Theory of Open Quantum Systems. Oxford :Oxford University Press, 2002. [38] Lindblad G.On the Generators of Quantum Dynamical Semigroups.Communications in Mathematical Physics, 1976, 48(2), 119–130. [39] Scully M O, Zubairy M S.Quantum Optics. Cambridge: Cambridge University Press, 1997. [40] Louisell W H.Quantum Statistical Properties of Radiation. New York: Wiley, 1973. [41] Wheeler J A, Zurek W H.Quantum Theory of Measurement. Princeton: Princeton University Press, 1983. [42]Zhang W, Zhou D L, Chang M S, Chapman M S, You L.Proposed Realization of the Einstein-Podolsky-Rosen Paradox with Ultracold Atoms.Physical Review A, 2005, 72(1), 013602. [43] Immanuel B, Jean D, Wilhelm Z. Many-body physics with ultracold gases[J].Reviews of Modern Physics, 2008, 80(3), 885–960. [44] Kawaguchi Y, Ueda M.Spinor Bose–Einstein Condensates.Physics Reports, 2012, 520(5), 253–381. [45] Zhai Q, Chang L, Lu R, You L.Quantum Phase Transitions of Spin-Orbit-Coupled Degenerate Fermi Gases.Physical Review A, 2009, 79(4), 043608. [46] Schachenmayer J, Pikovsky A, Rey A M.Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space.Physical Review X, 2015, 5(1), 011022. [47] Huber J, Kirton P, Rabl P. Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems.SciPost Physics, 2021, 10(3), 045.