Abstract Topological pumping provides a robust route to quantized motion under adiabatic modulation, yet its extension to nonlinear matter waves with internal spin degrees of freedom remains an open question. Here we demonstrate quantized soliton transport in a two-component Bose–Einstein condensate with helicoidal spin–orbit coupling, subjected to an adiabatically sliding optical lattice. With each pumping cycle, the helicoidal coupling sustains a periodic inter-component population exchange, while the soliton center-of-mass advances by a quantized displacement set by the Chern number, which is insensitive to both the spin–orbit coupling strength and the Zeeman field. We further identify the Zeeman field as a key control parameter governing both the inter-component dynamics during pumping and the soliton stability after the lattice motion ceases: depending on the Zeeman field strength, the soliton either retains its profile or develops persistent breathing modes. These results demonstrate that the combination of helicoidal spin–orbit coupling and Zeeman field enables topological transport of nonlinear matter waves with independently tunable internal spin dynamics.
We demonstrate that linear and nonlinear Thouless pumping can be realized in two-component elongated Bose-Einstein condensates using helicoidal spin-orbit coupling that slides with respect to a static optical lattice, identical for both spinor components. Stable quantized transport is found for solitons in semi-infinite and finite gaps, within certain intervals of chemical potentials and numbers of atoms. In the semi-infinite gap, the transport is arrested for solitons with sufficiently large number of atoms. We elucidate the important role of Zeeman splitting in the control of quantized transport, which disappears when the longitudinal component of the Zeeman field is removed.
Abstract We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.
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.
Abstract We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose–Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.
We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for the existence of stable propagating solitons. Such states are found in the rotating frame, where the helicoidal SO coupling is reduced to a homogeneous one. In the absence of the Zeeman splitting, the coupled Gross-Pitaevskii equations describing localized states feature many properties of the integrable systems. In particular, four-parametric families of solitons can be obtained in the exact form. Such solitons interact elastically. Zeeman splitting still allows for the existence of two families of moving solitons, but makes collisions of solitons inelastic.
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.