Thouless Pumping of One-Dimensional Dark Solitons and Domain Walls

summary

The gist

We predict that quantized transport of dark solitons and domain walls can be observed in mutually sliding optical lattices in both focusing and defocusing nonlinear materials.

This episode discusses

The paper

Thouless Pumping of One-Dimensional Dark Solitons and Domain Walls · Read on arXiv

Fangwei Ye, Aidar H. Ryazhapov, Yaroslav V. Kartashov, Vladimir V. Konotop

School of Physics, Chengdu University of Technology · School of Physics and Astronomy, Shanghai Jiao Tong University · Institute of Spectroscopy, Russian Academy of Sciences · Faculty of Physics, Higher School of Economics · Departamento de Fósica and Centro de Fósica Teóorica e Computacional, Faculdade de Ci⸔ncias, Universidade de Lisboa

We predict that quantized transport of dark solitons and domain walls can be observed in mutually sliding optical lattices in both focusing and defocusing nonlinear materials. Two different classes of underlying periodic backgrounds are considered here -- unstaggered and staggered -- which are accurately represented, respectively, by the in-phase and out-of-phase trains of Wannier functions. The nonlinear excitations formed on top of these backgrounds -- dark solitons and domain walls -- are sustained by defocusing or focusing Kerr nonlinearities of the optical medium. Despite non-zero asymptotics, dark solitons and domain walls can still undergo quantized topological transport in dynamically changing refractive index landscape when they and background on which they are constructed are dynamically stable. The extended intervals of propagation constants (and, correspondingly, of the background amplitude) and lattice depths, where stable quantized transport occurs, are identified for both dark solitons and domain walls. Outside these intervals, the quantized transport regime is found to be unstable. Our results extend the concept of nonlinear topological transport from bright to dark soliton states.

Transcript

Introduction to the show: ident: Nonlinear Sciences. The day in nonlinear science: chaos, patterns, networks and adaptation.

Kai: We're looking at the paper: "Thouless Pumping of One-Dimensional Dark Solitons and Domain Walls".

Mira: Here's the gist of the paper. We predict that quantized transport of dark solitons and domain walls can be observed in mutually sliding optical lattices in both focusing and defocusing nonlinear materials.

Kai: This work extends the concept of nonlinear topological transport from bright to dark soliton states.

Mira: Theoretical Framework and Model The study investigates quantized transport in a model where pumping is implemented through an optical potential consisting of two mutually sliding sublattices.

Kai: The background field on which a dark soliton can be constructed must necessarily become complex-valued once the explicit z-dependence is taken into account.

Paper summary: Kai: So, to recap, this paper by Fangwei Ye and his team is predicting that you can observe quantized transport of dark solitons and domain walls in mutually sliding optical lattices across both focusing and defocusing nonlinear materials >

Mira: The thesis claims this quantization is possible when the background on which these excitations are built is dynamically stable, even though the underlying mechanism for sustained transport hasn't been fully explored yet >

Lev: They set up two specific classes of periodic backgrounds—unstaggered and staggered—to model this, where unstaggered means in-phase Wannier functions and staggered means out-of-phase ones >

Kai: And they find that the nonlinear excitations, which are the dark solitons and domain walls, can be sustained by either defocusing or focusing Kerr nonlinearities in the optical medium >

Mira: The key finding is that despite having non-zero asymptotics, these dark solitons and domain walls can still undergo quantized topological transport when they and their background are dynamically stable >

Lev: The paper specifically identifies extended intervals of propagation constants and lattice depths where this stable quantized transport happens for both types of excitations >

Kai: Outside those identified intervals, the quantized transport regime is found to be unstable, which sets the boundaries for what we can expect in this setup >

Mira: And they also mention that their results extend the concept of nonlinear topological transport from bright soliton states over to dark solitons as well >

Conclusion: Kai: Thinking about the title, "Thouless Pumping of One-Dimensional Dark Solitons and Domain Walls," it sounds very specific about what they are modeling >

Mira: It is. It focuses on how a process called Thouless pumping works in the context of these specific excitations within these optical lattices >

Lev: The implication for us as an experimentalists is that we need to focus our measurements on those identified intervals, because outside those ranges, we expect instability >

Kai: So, to put it simply, they’ve shown that you can have stable topological transport for dark solitons and domain walls in these sliding lattices under both focusing and defocusing conditions >

Mira: That’s the main point. It means that the quantization of transverse displacement is determined by the Chern number of the upper band of the linear optical potential >

Lev: And they also found that this concept applies to both dark and bright solitons in terms of quantized adiabatic transport, which is quite significant for how we look at these systems >

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