Topological pumping of ultracold atomic gases has recently been demonstrated in two experiments (Nat. Phys. 12, 296; 12, 350 (2016)). Here we study the topological pumping of a single magnon in a dynamically controlled spin-dependent optical superlattice. When the interaction between atoms is strong, this system supports a dynamical version of topological magnon insulator phase. By initially putting a single magnon in the superlattice and slowly varying the dynamical controlled parameter over one period, the shift of the magnon density center is quantized and equal to the topological Chern number. Moreover, we also find that the direction of this quantized shift is entanglement-dependent. Our result provides a route for realizing topological pumping of quasiparticles in strongly correlated ultracold atomic system and for studying the interplay between topological pumping and quantum entanglement.
Abstract Wepropose a scheme realizing topological insulators and quantized pumps for magnon excitations, based on strongly-interacting two-component ultracold atoms trapped in optical superlattices. Specifically, we show how to engineer the Su–Schrieffer–Heeger model for magnons using state-independent superlattices, and the Rice-Mele model using state-dependent superlattices. We describe realistic experimental protocols to detect the topological signatures of magnon excitations in these two models. In particular, we show that the non-equilibrium dynamics of a single magnon can be exploited to directly detect topological winding numbers and phase transitions. We also describe how topological (quantized) pumps can be realized with magnons, and study how this phenomenon depends on the initial magnon state preparation. Our study opens a new avenue for exploring magnonic topological phases of matter and their potential applications in the context of topological magnon transport.
Topological phases of ultracold atoms recently have been intensively studied in both optical superlattices and Raman lattices. However, the topological features induced by the interplay between such two lattices remain largely unexplored. Here we present an optical Raman superlattice system that incorporates an optical superlattice and a Raman superlattice. The Raman superlattice presented here supports tunable dimerized spin-orbit couplings and staggered on-site spin flips. We find that such a system respects a spin-rotation symmetry and has much richer topological properties. Specifically, we show that various topological phases could emerge in the optical Raman superlattice, such as four different chiral topological insulator phases and two different quantum spin Hall insulator phases, identified by spin winding and spin Chern numbers, respectively. We also demonstrate that the spin-dependent topological invariants could be directly measured by quench dynamics.
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 present exactly solvable examples showing that topological Mott insulators can emerge from topologically trivial states due to strong interactions between atoms for atomic mixtures trapped in one-dimensional optical superlattice systems. The topological Mott insulating state is characterized by a nonzero Chern number and appears in the strongly interacting limit as long as the total band filling factor is an integer that is not sensitive to the filling of each component. The topological nature of the Mott phase can be revealed by observing the density profile of the trapped system. Our results can be also generalized to multicomponent atomic systems.
Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from $\ensuremath{-}1$ to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.
In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.