Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice

Abstract

We study topological features of interacting spin-1 2 particles in one-dimensional state-dependent optical lattices. Due to the co-translational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound-states appear as a result of the non-trivial center-ofmass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center-of-mass can be described by a non-trivial center-of-mass Chern number.arXiv:1910.09948v1 [cond-mat.mes-hall] 22 Oct 2019

Radiative topological biphoton states in modulated qubit arrays

“…For an infinite structure, the total energy is invariant if spatial positions of the two excitations are shifted by a unit cell as a whole. It means that the center-of-mass momentum is a good quantum number according to the many-body Bloch theorem [36][37][38][39]. To present the Hamiltonian in a blockdiagonal form with different momenta, we introduce a new basis…”

“…By arranging the positions of qubits and designing the waveguide structure, the topological edge states have been analyzed in singleexcitation systems [30][31][32][33]. However, exotic effects may emerge in interacting topological systems when two or more particles (or quasiparticle excitations) interact [34][35][36][37][38][39]. Being analytically and numerically more challenging, the study of an interplay between photon interaction, non-Hermiticity, and topology is an exciting novel avenue to be explored in this field.…”

Interaction-induced lattices for bound states: Designing flat bands, quantized pumps, and higher-order topological insulators for doublons

“…5 could be instead simulated by using state dependent lattices in a similar fashion as proposed in Ref. [62]. One species would experience a lattice positioned on the blue sites with hopping J 1 whereas the other species would experience a different lattice positions on the red sites with hopping J 2 .…”

“…While preparing this manuscript, we became aware of a recent work [62] investigating topological bound states on a triangular ladder with nearest-neighbor interactions, as realized in state-dependent lattices. Besides, another recent study [73] has shown how fractional corner charges appear in the ground state of a 2D SSH lattice with Bose-Hubbard interactions.…”

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

“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the singleparticle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,…”