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Register a new userPredicting Large-Chern-Number Phases in a Shaken Optical Dice Lattice
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With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial large-Chern-number phases is an intriguing subject. Motivated by recent research on Floquet topological phases, this study proposes a periodic driving protocol to engineer large-Chern-number phases using QAHE. Herein, spinless ultracold fermionic atoms are studied in a two-dimensional optical dice lattice with nearest-neighbor hopping and a $Lambda$/V-type sublattice potential subjected to a circular driving force. Results suggest that large-Chern-number phases exist with Chern numbers equal to $C=-2$, which is consistent with the edge-state energy spectra.
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For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity. Motivated by these researches, the topological properties of a non-Hermitian dice model are studied in two non-Hermitian cases, viz. in the imbalanced and the balanced dissipations. Our results suggest that the topological phases are protected by the real gaps and the bulk-edge correspondence readily seen in the real edge-state spectra. Besides, we show that the principle of the bulk-edge correspondence in Hermitian case is still effective in analyzing the three-band non-Hermitian system. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.
We report the experimental realization of a topological Creutz ladder for ultracold fermionic atoms in a resonantly driven 1D optical lattice. The two-leg ladder consists of the two lowest orbital states of the optical lattice and the cross inter-leg links are generated via two-photon resonant coupling between the orbitals by periodic lattice shaking. The characteristic pseudo-spin winding in the topologically non-trivial bands of the ladder system is demonstrated using momentum-resolved Ramsey-type interferometric measurements. We discuss a two-tone driving method to extend the inter-leg link control and propose a topological charge pumping scheme for the Creutz ladder system.
With topologcial semimetal developing, semimetal with nodal-line ring comes into peoples vision as a powerful candidate for practical application of topological devices. We propose a method using ultracold atoms in two-dimensional amplitude-shaken bipartite hexagonal optical lattice to simulate nodal-line semimetal, which can be achieved in experiment by attaching one triangular optical lattice to a hexangonal optical lattice and periodically modulating the intensity and position of the triangular lattice. By amplitude shaking, a time-reversal-symmetry-unstable mode is introduced into the bipartite optical lattice, and then the nodal-line semimetal is gotten by adjusting the proportion of such mode and the trivial mode of hexagonal lattice. Through calculating the energy spectrum of effective Hamiltonian, the transformation from Dirac semimetal to nodal-line semimetal in pace with changing shaking parameters is observed. We also study the change of Berry curvature and Berry phase in the transformation, which provides guidance on measuring the transformation in experiment. By analyzing the symmetry of the system, the emergence of the time-reversal-symmetry-unstable mode is researched. This proposal provides a way to research the pure nodal-line semimetal without the influence of other bands, which may contribute to the study of those unique features of surface states and bulk states of nodal-line semimetal.
We show that a new state of matter, the d-wave Mott-insulator state (d-Mott state) (introduced recently by [H. Yao, W. F. Tsai, and S. A. Kivelson, Phys. Rev. B 76, 161104 (2007)]), which is characterized by a non-zero expectation value of a local plaquette operator embedded in an insulating state, can be engineered using ultra-cold atomic fermions in two-dimensional double-well optical lattices. We characterize and analyze the parameter regime where the $d$-Mott state is stable. We predict the testable signatures of the state in the time-of-flight measurements.
We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.
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