In many contexts, the interaction between particles gives rise to emergent and perhaps unanticipated physical phenomena. An example is the fractional quantum Hall effect, where interaction between electrons gives rise to fractionally quantized Hall conductance. In photonic systems, the nonlinear response of an ambient medium acts to mediate interaction between photons; in the mean-field limit these dynamics are described by the nonlinear Schrödinger (also called Gross-Pitaevskii) equation. Recently, it was shown that at weak nonlinearity, soliton motion in nonlinear Thouless pumps (a dimensionally reduced implementation of a Chern insulator) could be quantized to the Chern number of the band from which the soliton bifurcates. Here, we show theoretically and experimentally using arrays of coupled optical waveguides that sufficiently strong nonlinearity acts to fractionally quantize the motion of solitons. Specifically, we find that the soliton returns to itself after multiple cycles of the Thouless pump - but displaced by an integer number of unit cells - leading to a rich fractional plateaux structure describing soliton motion. Our results demonstrate a perhaps surprising example of the behavior of non-trivial topological systems in the presence of interactions.
We theoretically investigate a Thouless pumping scheme in the 1D topological Su-Schrieffer-Heeger (SSH) model for single and multiple band-gaps systems when implemented in a discrete nematic liquid crystal arrangement. For an electrically controlled SSH waveguide array, we numerically demonstrate edge-to-edge light transport at low power levels. On the other hand, at higher powers, the transport is frustrated by light-induced nonlinear defect states, giving rise to robust all-optical switching.
Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this p…
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in a two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: quasi-linear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and multi-soliton regime when initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a …
One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold the transfer of both dispersive wavepackets and solitons occurs in accordance with the predictions of the linear theory, i.e. it is quantized and determined by the dynamical Chern numbers of the lowest band. The breakdown of the transport is also explained by nontrivial topology of th…
Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves th…
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, w…
Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-André-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In c…
Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that for low power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that the soliton's position is dictated …
Quantized dynamics is essential for natural processes and technological applications alike. The work of Thouless on quantized particle transport in slowly varying potentials (Thouless pumping) has played a key role in understanding that such quantization may be caused not only by discrete eigenvalues of a quantum system, but also by invariants associated with the nontrivial topology of the Hamiltonian parameter space. Since its discovery, quantized Thouless pumping has been believed to be restricted to the limit of slow driving, a fundamental obstacle for experimental applications. Here, we in…
Adiabatic quantum pumping in one-dimensional lattices is extended by adding a tilted potential to probe better topologically nontrivial bands. This extension leads to almost perfectly quantized pumping for an arbitrary initial state selected in a band of interest, including Bloch states. In this approach, the time variable offers not only a synthetic dimension as in the case of the Thouless pumping, but it assists also in the uniform sampling of all momenta due to the Bloch oscillations induced by the tilt. The quantized drift of Bloch oscillations is determined by a one-dimensional time integ…
Quantized transport of two-dimensional multifrequency solitons
Chengdu University of Technology（成都理工大学）；Shanghai Jiao Tong University（上海交通大学）；Institute of Spectroscopy, Russian Academy of Sciences（俄罗斯科学院光谱研究所）；Universidade de Lisboa（里斯本大学）
