Generalized lattice Wilson–Dirac fermions in (1 + 1) dimensions for atomic quantum simulation and topological phases

Abstract

The Dirac fermion is an important fundamental particle appearing in high-energy physics and topological insulator physics. In particular, a Dirac fermion in a one-dimensional lattice system exhibits the essential properties of topological physics. However, the system has not been quantum simulated in experiments yet. Herein, we propose a one-dimensional generalized lattice Wilson-Dirac fermion model and study its topological phase structure. We show the experimental setups of an atomic quantum simulator for the model, in which two parallel optical lattices with the same tilt for trapping cold fermion atoms and a laser-assisted hopping scheme are used. Interestingly, we find that the model exhibits nontrivial topological phases characterized by gapless edge modes and a finite winding number in the broad regime of the parameter space. Some of the phase diagrams closely resemble those of the Haldane model. We also discuss topological charge pumping and a lattice Gross-Neveu model in the system of generalized Wilson-Dirac fermions.

Kondo effect with Wilson fermions

“…In addition, cold-atom simulations may be also promising candidates for examining both the interacting Wilson fermion [124][125][126][127] and the Kondo effect, e.g., [128][129][130][131][132][133][134][135][136], where tuning coupling constants rather than chemical potential will be useful for declaring the Kondo effect. ∆ survives.…”

Casimir effect for lattice fermions

“…In this sense, to investigate fermionic Casimir effects in honeycomb lattices will be important. Another possible candidate for studying the Casimir effects for lattice fermions would be cold-atom simulations [93][94][95][96] with a small size.…”

Strongly Interacting Two-component Coupled Bose Gas in Optical Lattices

“…magnetic or a static electric field gradient [95,96]. The tilting of the lattice prevents the natural hopping between components a (or b) and is obtained via light assisted tunneling: resonant two-photon Raman transition [95].…”

“…magnetic or a static electric field gradient [95,96]. The tilting of the lattice prevents the natural hopping between components a (or b) and is obtained via light assisted tunneling: resonant two-photon Raman transition [95]. We introduce to this system inter-component coupling; this can be obtained by applying a microwave field nearly resonant to the transition frequency of the two internal states as can be seen in Fig.…”