Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

Abstract

We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.

Topology and Interactions in the Photonic Creutz and Creutz‐Hubbard Ladders

“…Additionally, a chemical potential appears in the end sites because of their different coordination number than the rest of the lattice. This same phenomenon was demonstrated in other 1D and 2D effective models for doublons …”

“…Doublon edge states, which have been studied for different 1D and 2D systems, cannot be treated in the same way as their single particle counterparts in 1D and quasi‐1D systems, as the usual bulk‐boundary correspondence is not valid and the value of the Zak phase is not correlated to the existence of topological doublon edge states . Consequently a different approach must be employed.…”

Simulation of 1D Topological Phases in Driven Quantum Dot Arrays

“…Consequently, a great effort is being made to simulate the behaviour of TIs by tailoring other quantum systems, whose properties can be more easily controlled. Within this context, timedependent modulations have proven to be useful tools to modify the topology [4][5][6][7][8][9][10][11][12][13][14][15]. Particularly, they have been used to simulate the so-called "Floquet topological insulators" (FTIs) [16][17][18] upon different systems .…”

Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices

“…In this way, we show that the single-particle topological properties of the underlying SSH model are transferred to the bosonic magnonic excitations. Such a transfer of topological band properties to interacting-particle settings is reminiscent of that discussed in [23,24], in the context of topological doublons, and in [25,26] in the context of topological polarons; see also [27][28][29][30][31][32] on interplays between topological properties and magnons.…”