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Register a new userArtificial topological models based on a one-dimensional spin-dependent optical lattice
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Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional (1D) spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.
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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.
We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.
We investigate topological supersolidity of dipolar Fermi gases in a spin-dependent 2D optical lattice. Numerical results show that the topological supersolid states can be synthesized via the combination of topological superfluid states with the stripe order, where the topological superfluid states generated with dipolar interaction possess the $Delta_{x}+iDelta_{y}$ order, and it is of D class topological classification. By adjusting the ratio between hopping amplitude $t_{x}/t_{y}$ and interaction strength $U$ with dipole orientation $phi approx frac{pi}{4}$, the system will undergo phase transitions among the $p_{x}+ip_{y}$-wave topological superfluid state, the p-wave superfluid state, and the topological supersolid state. The topological supersolid state is proved to be stable by the positive sign of the inverse compressibility. We design an experimental protocol to realize the staggered next-next-nearest-neighbour hopping via the laser assisted tunneling technique, which is the key to synthesize topological supersolid states.
We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength $U$ is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of $U$ and a continuous deformation parameter $beta$ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.
The realization of artificial gauge fields and spin-orbit coupling for ultra-cold quantum gases promises new insight into paradigm solid state systems. Here we experimentally probe the dispersion relation of a spin-orbit coupled Bose-Einstein condensate loaded into a translating optical lattice by observing its dynamical stability, and develop an effective band structure that provides a theoretical understanding of the locations of the band edges. This system presents exciting new opportunities for engineering condensed-matter analogs using the flexible toolbox of ultra-cold quantum gases.
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