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Quantum Theory of Fractional Topological Pumping of Lattice Solitons

Julius Bohm1, Hugo Gerlitz1, Christina Jörg1,2, and Michael Fleischhauer1,2

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Phys. Rev. X 16, 011038 – Published 26 February, 2026

DOI: https://doi.org/10.1103/hhgy-9rd4

Abstract

One of the hallmarks of topological systems is the robust quantization of particle transport. It is the origin of the integer-valued quantum Hall conductivity and a potential tool for quantum information technology. Recent experiments on topological pumps constructed by using arrays of photonic waveguides and described by the (lattice-translational invariant) Aubry-André-Harper model, have demonstrated both integer and fractional transport of lattice solitons. In these systems, a background medium mediates interactions between photons via a Kerr nonlinearity and leads to the formation of self-bound multiphoton states. Upon increasing the interaction strength, a sequence of transitions was observed from a phase with integer transport in a pump cycle through different phases of fractional transport to a phase with no transport. We here present a quantum description of topological pumps of self-bound many-particle states in terms of an effective Hamiltonian of their center-of-mass (c.m.) motion, which allows one to introduce an effective band structure Eμ(K) with K being the c.m. momentum and to classify topological phases in terms of generalized symmetries. We provide an explicit analytic expression of the effective Hamiltonian for few particles in the strong interaction limit and present numerical results in the more general case. We identify a topological invariant, an effective single-particle Chern number, which fully governs the soliton transport. Increasing the interaction strength in the Aubry-André-Harper model leads to a successive merging of c.m. bands, which is the origin of the observed sequence of topological phase transitions and also the potential breakdown of topological quantization for some interaction strength.

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Topological protection is a central mechanism for ensuring robust quantum transport, yet the traditional understanding based on integer topological invariants often fails to account for the behavior of interacting many-particle systems. We addressed this by developing a quantum theory for topological pumps of self-bound composite objects, using an effective lattice Hamiltonian to describe their center-of-mass motion. Our analysis identified a specific topological invariant that governs the transport of these clusters, showing that increasing interaction strength modifies the composite band structure. We found that these interactions drive transitions between phases with integer and fractional topological charges, allowing for precisely controlled rational transport steps. These findings demonstrate that forming and manipulating self-bound objects through interactions provides a versatile tool for controlling topological properties in quantum systems.

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Outline

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Phys. Rev. X 16, 011038– Published 26 February, 2026
  • Received 5 September 2025
  • Accepted 26 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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