Quantized Nonlinear Thouless Pumping

TL;DR

This paper demonstrates that nonlinearity in a photonic system enables quantized topological transport through soliton formation, extending Thouless pumping beyond the traditional linear, equilibrium fermionic models.

Contribution

It introduces a novel nonlinear photonic Thouless pump where solitons induce quantized transport, differing from conventional linear models.

Findings

Nonlinear effects lead to quantized photon transport.

Solitons form and stabilize the quantized pump cycle.

Quantization persists despite non-uniform band occupation.

Abstract

The sharply quantized transport observed in the integer quantum Hall effect can be explained via a simple one-dimensional model with a time-periodic, adiabatically varying potential in which electronic charge is pumped from one side of the system to the other. This so-called `Thouless pump' captures the topological physics of the quantum Hall effect using the notion of dimensional reduction: The time-varying potential mathematically maps onto a momentum coordinate in a conceptual second dimension. Importantly, this assumes an electronic system in equilibrium and in its ground state, that is, with uniformly filled bands below a Fermi energy. Here, we theoretically propose and experimentally demonstrate quantized nonlinear Thouless pumping of photons with a band that is decidedly not uniformly occupied. In our system, nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry breaking bifurcations. Quantization follows from the fact that the instantaneous soliton solutions centered upon a given unit cell are identical after each pump cycle, up to translation invariance; this is an entirely different mechanism from traditional Thouless pumping of fermions in equilibrium. Our result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behavior even where the linear limit does not.