Quantum theory of fractional topological pumping of lattice solitons

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 (AAH) 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 multi-photon 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 (COM) motion, which allows to introduce an effective band structure $E_{\mu }(K)$ with $K$ being the COM 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 AAH model leads to a successive merging of COM 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.

References in corpus (17)

• Repulsively bound atom pairs in an optical lattice
• Thouless pumping and topology
• Quantized Nonlinear Thouless Pumping
• Two-particle states in the Hubbard model
• Quantized Fractional Thouless Pumping of Solitons
• Nonlinear Thouless pumping: solitons and transport breakdown
• Quantisation and its breakdown in a Hubbard-Thouless pump
• Topological pumping of photons in nonlinear resonator arrays
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• Interactions enable Thouless pumping in a nonsliding lattice
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Breakdown of quantization in nonlinear Thouless pumping
• Thouless pumping and trapping of two-component gap solitons
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Topological pumping induced by spatiotemporal modulation of interaction