Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

Abstract

We propose and analyze a general scheme to create chiral topological edge modes within the bulk of two-dimensional engineered quantum systems. Our method is based on the implementation of topological interfaces, designed within the bulk of the system, where topologically-protected edge modes localize and freely propagate in a unidirectional manner. This scheme is illustrated through an optical-lattice realization of the Haldane model for cold atoms [1], where an additional spatiallyvarying lattice potential induces distinct topological phases in separated regions of space. We present two realistic experimental configurations, which lead to linear and radial-symmetric topological interfaces, which both allows one to significantly reduce the effects of external confinement on topological edge properties. Furthermore, the versatility of our method opens the possibility of tuning the position, the localization length and the chirality of the edge modes, through simple adjustments of the lattice potentials. In order to demonstrate the unique detectability offered by engineered interfaces, we numerically investigate the time-evolution of wave packets, indicating how topological transport unambiguously manifests itself within the lattice. Finally, we analyze the effects of disorder on the dynamics of chiral and non-chiral states present in the system. Interestingly, engineered disorder is shown to provide a powerful tool for the detection of topological edge modes in cold-atom setups.

Topological superfluidity of lattice fermions inside a Bose-Einstein condensate

“…The advantage however of using an optical lattice is the available schemes for directly detecting the Majorana edge states. Current experiments with single site resolution [32,33] could specifically image the edge states using for instance their time-evolution in real space [53,54] or RF spectroscopy [34]. Intriguingly, we note that since the two phase separated regions with filling fractions n 1 and 1 − n 1 have Chern numbers ν = −1 and ν = 1 respectively, there will be topologically robust edge states at the boundary between these two phases.…”

Microscopic characteristics and tomography scheme of the local Chern marker

“…A second example is the topological interface [12,21,22] which is used to create an in-situ topological phase separation. In Fig.…”

Fractional topological insulator precursors in spin-orbit fermion ladders

“…The conclusions above are not influenced significantly by the second order interspin terms Eqs. (69)(70)(71)(72)(73)(74)(75)(76). These operators can be separated into two families, each with a single scaling dimension ∆ I,II [see Eqs.…”

“…Among them, the more relevant is O d 6,proj in terms of the low energy description of the FTI dominated phase. The second order operators (69) to (76) are less relevant in RG sense according to the weak coupling analysis of the previous section. Now we are concerned with the strong coupling regime, where these operators have flowed under RG as well.…”