Topological Invariants in Nonlinear Thouless Pumping of Solitons

• URL: http://arxiv.org/abs/2506.08502v1
• Date: Tue, 10 Jun 2025 06:58:15 GMT
• Title: Topological Invariants in Nonlinear Thouless Pumping of Solitons
• Authors: Fei-Fei Wu, Xian-Da Zuo, Qing-Qing Zhu, Tao Yuan, Yi-Yi Mao, Chao Zeng, Yi Jiang, Yu-Ao Chen, Jian-Wei Pan, Wei Zheng, Han-Ning Dai,
• Abstract summary: We introduce a unified topological invariant applicable across both weakly and strongly nonlinear regimes.<n>In the weak nonlinearity regime, where the nonlinear bands are wellseparated, the invariant reduces to the Abelian Chern number of the occupied nonlinear band.<n>As the nonlinearity increases, the nonlinear bands start to intertwine, leading to a situation where the invariant is expressed as the non-Abelian Chern number divided by the number of interacting bands.
• Score: 8.026610383567432
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Recent explorations of quantized solitons transport in optical waveguides have thrust nonlinear topological pumping into the spotlight. In this work, we introduce a unified topological invariant applicable across both weakly and strongly nonlinear regimes. In the weak nonlinearity regime, where the nonlinear bands are wellseparated, the invariant reduces to the Abelian Chern number of the occupied nonlinear band. Consequently, the pumped charge is quantized to an integer value. As the nonlinearity increases, the nonlinear bands start to intertwine, leading to a situation where the invariant is expressed as the non-Abelian Chern number divided by the number of interacting bands. This could result in a fractional quantization of the pumped charge. Our unified topological invariant approach not only advances the understanding of the soliton dynamics, but also provides implications for the future design of nonlinear topological systems.

Related papers

• Suppressing excitations in the nonlinear Landau-Zener model [0.0]
  We show that in a generalized Landau-Zener model, nonlinear dynamics can be leveraged to suppress excitations and coherences of the corresponding linear scenario.<n>We show that the nonlinear term in the evolution equation acts like an effective shortcut to adiabaticity for the linear Landau-Zener problem.
  arXiv  Detail & Related papers  (2025-06-13T13:13:09Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• On the quantization of AB phase in nonlinear systems [3.515802569456161]
  We study the Aharonov-Bohm phase associated with an adiabatic process in the momentum space. For and only for Kerr nonlinearity, the AB phase experiences a jump of $pi$ at the critical nonlinearity. Our results may be useful for experimental measurement of power-law nonlinearity.
  arXiv  Detail & Related papers  (2022-12-05T08:02:17Z)
• Breakdown of quantization in nonlinear Thouless pumping [0.0]
  This work uncovers the fate of nonlinear Thouless pumping in the regime of intermediate nonlinearity. We identify the presence of critical nonlinearity strength at which quantized pumping of solitons breaks down regardless of the protocol time scale.
  arXiv  Detail & Related papers  (2022-05-23T01:06:33Z)
• Quantum transport in nonlinear Rudner-Levitov models [0.7874708385247353]
  Quantum transport in a class of nonlinear extensions of the Rudner-Levitov model is numerically studied in this paper. We show that the quantization of the mean displacement, which embodies the quantum coherence and the topological characteristics of the model, is markedly modified by nonlinearities.
  arXiv  Detail & Related papers  (2021-12-23T05:04:59Z)
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials [5.33024001730262]
  We extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. Our work opens a new avenue in quantum physics beyond the linear-response regime.
  arXiv  Detail & Related papers  (2021-10-15T18:25:26Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Convolutional Filtering and Neural Networks with Non Commutative Algebras [153.20329791008095]
  We study the generalization of non commutative convolutional neural networks. We show that non commutative convolutional architectures can be stable to deformations on the space of operators.
  arXiv  Detail & Related papers  (2021-08-23T04:22:58Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Sparse Quantized Spectral Clustering [85.77233010209368]
  We exploit tools from random matrix theory to make precise statements about how the eigenspectrum of a matrix changes under such nonlinear transformations. We show that very little change occurs in the informative eigenstructure even under drastic sparsification/quantization.
  arXiv  Detail & Related papers  (2020-10-03T15:58:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.