Cusp solitons mediated by a topological nonlinearity - part 2

For an introduction see part 1, which I wrote when our paper was uploaded to arXiv.

After a few rounds of review our paper was published in Chaos last week!

With so much negativity surrounding peer review nowadays, it is important to highlight when it works well. Our original manuscript mentioned a few possible experimental realizations of our new model, without going into specifics - it seemed like a hard problem which could not be solved before Harvey was due to graduate. So we left it for future work.

The referees correctly pointed out that a vague discussion of possible implementations is not very helpful - this hard problem is then delegated to the reader. Could we provide specifics?

We could not at the time of writing the manuscript. But the referee comments inspired (forced?) us to try harder. During our search we stumbled upon a very nice experiment published in Physical Review Letters: Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal Photonic Feedforward Lattices

We realized that the feedforward nonlinearity used in this work could be readily adapted to realize our model. We added the recipe to our manuscript as an appendix, giving strong evidence for the experimental feasibility of observing our results!

Peer review isn't meant to be just a rubber stamp or a hard rejection; it should also be a way to help present the research in the best possible way. While "open science" and "open peer review" are trending topics, anonymity gives referees the safety to ask hard (or annoying) questions. 

What's in a name?

Giving your model or result a catchy name greatly increases the impact of your research. 

Compare the citations of Two-dimensional massless electrons in an inverted contact and Quantum spin Hall effect.

The title you give your paper is important. Don't rush it.

On a related note, those working on soliton theory will be familiar with the nonlinear wave equation

$$\partial_t^2 \phi - \partial_x^2 \phi  + m^2 \sin \phi = 0,$$

which is called the Sine-Gordon equation "for obvious reasons" in Rubinstein's original analysis of its soliton solutions. A footnote in this paper gives credit for this brilliant name to Professor Martin Kruskal, who has an impressive list of scientific achievements spanning nonlinear waves, surreal numbers, and wormholes.

arXiv picks

 

Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit

Here the authors show conditions under which electrons in highly excited orbitals of Rydberg atoms (or interacting atoms) can be used to emulate topological tight binding models. The key idea is that a periodically-modulated driving field (or interaction strength) induces "hopping" on an effective tight binding lattice formed by the electron orbitals (or orbitals of the atomic related position)

 

Quantized Fractional Thouless Pumping of Solitons

Following up on previous work (summarised here and here), Jurgensen and collaborators now observe fractional topological pumping of solitons in a periodically-driven waveguide lattice. Here fractional pumping means that multiple cycles of the periodic modulation are required to obtain a shifted copy of the original beam profile. It is quite remarkable that such an analogy with fractional quantum Hall systems can be observed using a classical nonlinear optical system.

Persistent Homology of ℤ2 Gauge Theories

Here the authors use persistent homology to study topological order in Z2 gauge theories, whose ground states consist of loops of occupied links. The idea here is that the positions of the occupied links in the ground state define a point cloud, whose shape can be reliably analyzed using persistent homology to detect phase transitions. Potential applications to models of topological quantum error-correcting codes are discussed as a direction for future work.

Roadmap on Topological Photonics

A comprehensive survey on current and future directions of topological photonics by many big names in the field.

 

More on nonlinear Thouless pumping

A follow-up to my earlier summary on the experimental observation of quantized nonlinear Thouless pumping.

A few theoretical groups have now posted preprints to arXiv proposing explanations for this effect:

The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps, by two of the authors of the original experimental study, focuses on the weakly nonlinear limit. By rewriting the governing discrete nonlinear Schrodiner equation in the basis formed by the lattice's Wannier functions, the weakly nonlinear dynamics in the complex topological lattices reduces to that of a simple 1D lattice, in which the nonlinear modes are peaked at the centre of the Wannier functions. Thus, the pumping of the solitons follows from the pumping of the linear Wannier functions, which is protected and quantized by the Chern number. Using their theory, the authors design and simulate a soliton pump in a two-dimensional lattice.

Quantized transport of solitons in nonlinear Thouless pumps: From Wannier drags to topological polarons also uses the Wannier function picture to explain the quantization of nonlinear pumping for weak mean-field nonlinearities. In addition, the authors analyze the underlying quantum model (from which the nonlinear Schrodinger equation is obtained by taking the mean field limit) of a Bose gas strongly interacting with massive impurities. Strong coupling between the Bose-gas results in formation of a quasi-particle (Bose polaron), which also exhibits stable quantized pumping.

Nonlinear Thouless pumping: solitons and transport breakdown, submitted before publication of the Nature paper, uses the Wannier function representation to understand the strongly nonlinear limit. In the Wannier basis high power solitons are a superposition of Wannier functions from multiple bands. In this case, the energy difference between the constituent bands leads to a rapid oscillatory motion of the wavepacket during the pumping cycle, superimposed with a slower (average) drift. The average drift speed is quantized by the sum of the bands' Chern numbers. The transition between the low and high power pumping is sharp, occurring as a nonlinear bifurcation (also reported in the experimental paper).