Interaction-induced topological properties of two bosons in flat-band systems

Abstract

In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum l = 1 states of a diamond-chain lattice, wherein an effective π flux may yield a completely flat single-particle energy landscape. In the weakly-interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

Enhanced repulsively bound atom pairs in topological optical lattice ladders

“…In particular, the latter system must have a very precise value for the tunnelling phases in order for it to manifest a pair superfluid, in contrast to the robustness of these phases in the Creutz ladder to similar phase deviations [36] and even to an interaction imbalance or finite temperatures as analysed in this paper. The stability of these features in the Creutz ladder is due to the enhanced properties for single repulsively bound pairs, which in contrast to the sawtooth lattice [46] or the diamond chain [51], we find have a kinetic energy that grows with increasing interaction strength, due to the particular topology of the Creutz ladder. This distinct behaviour for the Creutz ladder opens up many questions relating to the features of other flat band systems, in particular those with additional dispersive energy bands [65].…”

“…Nevertheless, we will see below that the enhanced properties of the lowest effective two-atom energy band leads to shorter timescales for the dynamical features, for example allowing for the preparation of states with (quasi) long range pair correlations in experimentally feasible timescales. Note that previous studies on the properties of interacting pairs in other flat band systems do not observe a strong enhancement of kinetic energy [46], even in those that are also characterised by a topological invariant [51]. This indicates that the enhancement is not a general feature for flat band systems but is unique to the Creutz ladder geometry due to the unique form of the underlying Wannier basis, which are completely localised on only two neighbouring unit cells.…”

“…In this system geometrical frustration results from the combination of these tunnelling terms where there is a destructive interference effect that completely suppresses the single-particle kinetic energy and gives rise to flat energy bands. However, it has been previously shown that including an onsite interaction can lead to the formation of bound pairs that are stable even for infinitesimal interaction strength which now have dispersion completely dictated by the interactions [35][36][37][38][39][40][46][47][48][49][50][51][52][53][54][55][56]. There is growing interest in repulsively interacting bound pairs in general cold-atom systems [57,58] as well as in more novel band structures [59][60][61][62][63][64], but pairs are usually only stable for large interaction strengths compared to the tunnelling.…”

Enhanced repulsively bound atom pairs in topological optical lattice ladders

“…In this system geometrical frustration results from the combination of these tunnelling terms where there is a destructive interference effect that completely suppresses the single-particle kinetic energy and gives rise to flat energy bands. However, it has been previously shown that including an onsite interaction can lead to the formation of bound pairs that are stable even for infinitesimal interaction strength which now have dispersion completely dictated by the interactions [35][36][37][38][39][40][46][47][48][49][50][51][52][53]. There is growing interest in repulsively interacting bound pairs in general cold-atom systems [54,55], but pairs are usually only stable for large interaction strengths compared to the tunnelling.…”