We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the 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 wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
Abstract We study the pumping of matter-wave solitons formed in Bose–Einstein condensates with attractive atomic interactions that are loaded into optical superlattices, in which one of the lattices is moving with respect to the other. We find that the matter-wave solitons exhibit lattice-parameter-dependent nonlinear integer (fractional) pumping and trapping. Different from the perspective of linear band Chern numbers, treating solitons as effective classical particles provides a good understanding of the quantized pumping or trapping. This reveals an unexpected insight: the nonlinear adiabatic pumping may be classical, and the quantization may be accidental, as dictated by the spatial period of the sliding sublattice. This alternative perspective on understanding soliton pumping highlights the parameter-dependent transition between soliton quantized pumping and trapping, and it exposes the nonlinear transition from a trapped soliton to a pumped soliton with increasing nonlinearity, which has never been reported before.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.
In nonlinear topological physics, Thouless pumping of nonlinear excitations is a central topic, often illustrated by scalar solitons. Vector solitons, with the additional spin degree of freedom, exhibit phenomena absent in scalar solitons due to the enriched interplay between nonlinearity and topology. Here, we theoretically investigate Thouless pumping of vector solitons in a two-component Bose-Einstein condensate confined in spin-dependent optical superlattices, using both numerical solutions of the Gross-Pitaevskii equation and the Lagrangian variational approach. The spin-up and spin-down components experience superlattice potentials that are displaced by a tunable distance
dr, leading to a vector soliton state with a relative shift between its components. We demonstrate that
dr, as an independent degree of freedom, offers a novel control parameter for manipulating the nonlinear topological phase transition of vector solitons. Specifically, when
dr=0, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying
dr, remarkably, we find that an arrested vector soliton can reenter the pumped regime and exhibits a quantized shift. As
dr continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in
dr, the quantized shift revives. Our work paves new routes for engineering nonlinear topological pumping of solitons in spinor systems by utilizing the relative motion degrees of freedom between different spin components.
We study the pumping of matter-wave solitons formed in Bose-Einstein condensates (BECs) with attractive atomic interactions that are loaded into optical superlattices in which one of the lattices is moving with respect to the other. We find that solitons exhibit the remarkably similar pumping properties in both shallow and deep lattices, and that for exactly the same soliton initially excited, switching between integer (fractional) pumping and trapping can be achieved by simply adjusting the lattice parameters. In addition, we find that the gap solitons, which bifurcate from the lowest energy band in a semi-infinite band gap, also exhibit this lattice-parameter-dependent pumping and trapping. The treatment of solitons as classical particles with effective centre-of-mass equations of motion provides a good description of this parameter-dependent integer (fractional) pumping and trapping of solitons.
Thouless pumping provides a paradigmatic platform for studying the effects of interactions on topological transport in periodically driven systems. However, most studies have been constrained by adiabatic conditions, which preclude exploration of interaction-driven novel topological states at high driving frequencies. Here, we experimentally investigate the interplay between interaction and modulation frequency in Thouless pumping realized in a periodically modulated lattice in momentum space of atomic Bose-Einstein condensate. We observe fast Thouless pumping of matterwave solitons at intermediate interactions, with no counterpart in the non- or weakly interacting regimes. Beyond the boundary of topological phase transition induced by interaction, nonadiabatic quantized pumping of solitons emerges at high modulation frequencies over a broad interaction range, in good agreement with theoretical calculations, while the solitons remain trapped in the low-frequency adiabatic pumping regime. Our work opens new avenues for accelerating topological transport in driven quantum systems and engineering fast topological devices.