Thouless pumping and topology

Abstract

Thouless pumping provides one of the simplest manifestations of topology in quantum systems, and has attracted a lot of recent interest, both theoretically and experimentally. Since the seminal works by Thouless and Niu in 1983 and 1984, it is argued that the quantization of the pumped charge is robust against weak disorder, but a clear characterization of the localization properties of the relevant states, and the breakdown of quantized transport in the presence of interaction or out of the adiabatic approximation, has been long debated. Thouless pumping is also the first example of a topological phase emerging in a periodically-driven system. Driven systems can exhibit exotic topological phases without any static analogue and have been the subject of many recent proposals both in fermionic and bosonic systems in diverse platforms ranging from cold atoms to photonics and condensed matter systems. In this respect, this review has a twofold purpose: On the one hand, it serves as a basis to understand the robustness of the topology of slowly-driven systems per se; On the other hand, it highlights the rich properties of topological pumps and their diverse range of applications, for instance, in systems with synthetic dimensions or for understanding higher-order topological phases. These examples underline the relevance of topological pumping for the fast growing field of topological quantum matter.

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• Hall response in interacting bosonic and fermionic ladders
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• Topological pumping induced by spatiotemporal modulation of interaction
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• Tutorial: From Topology to Hall Effects -- Implications of Berry Phase Physics
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• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
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• Topological photon pumping in quantum optical systems
• Non-Adiabatic Effect in Topological and Interacting Charge Pumping
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Adiabatic charge transport in extended SSH models
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• Thouless pumping in Josephson junction arrays
• Autonomous Stabilization of Floquet States Using Static Dissipation
• Quantum transport phenomena induced by time-dependent fields
• Recent advances in the combination of nonlinearity and exceptional points
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• The anomalous Floquet Anderson insulator in a continuously driven optical lattice
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Identification and properties of topological states in the bulk of quasicrystals
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Absence of disordered Thouless pumps at finite frequency
• Adiabatic charge transport through non-Bloch bands
• Quantization and quantum oscillations of the sublattice charge order in Dirac insulators
• A symmetry-protected topological optical lattice clock
• Quantum theory of fractional topological pumping of lattice solitons
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Generalized Josephson effect with arbitrary periodicity in quantum magnets
• Quantized transport of solitons in Bose-Einstein condensates driven by spin-orbit coupling
• Galilei covariance of the theory of Thouless pumps
• Quantized Acoustoelectric Floquet Effect in Quantum Nanowires
• Topological anomalous Floquet photon pump
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Many-body localization in a slowly varying potential
• Optimal control over the full counting statistics in a non-adiabatic pump
• Anisotropy-driven topological quantum phase transition in magnetic impurities
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices
• Covariant formulation of the Berry connection in non-Hermitian systems
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach
• Topological dynamics of adiabatic cat states
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• Quantized transport of two-dimensional multifrequency solitons