Doublons, topology and interactions in a one-dimensional lattice

Abstract

We investigate theoretically the Bose–Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called ‘doublons’, when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.

Edge state behavior in a Su–Schrieffer–Heeger like model with periodically modulated hopping

“…In order to understand these models more extensively, one can add further complexities such as studying varieties of spinful SSH models that incorporate Hubbard interactions between electrons [33,34] and investigate the behavior of edge modes in presence of periodic modulation of hopping between the neighboring sites. Similar study can also be imagined for an interacting Bosonic system with SSH-like dimerization [35]. One can also play with both space periodic as well as time periodic hopping modulations in a SSH model and do a Floquet analysis [36] to understand the stroboscopic dynamics of such system and to get a complete phase diagram of the same.…”

Topological pumping induced by spatiotemporal modulation of interaction

“…Interactions between particles cause novel correlation and entanglement, which may introduce rich correlated topological phenomena [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Understanding the interaction effect in topological pumping could open a window to the largely unexplored field.…”

Non-reciprocal population dynamics in a quantum trimer

“…This progress promises a new paradigm of quantum technologies which seek to transform the modern world [5,6]. In particular, the field of quantum optics provides the ideal framework to describe light-matter interactions and the quantum aspects of the latest metamaterials, which are commonly built from nanoscopic lattices of meta-atoms [7][8][9][10]. Recently, it was noticed that the introduction of the concept of non-reciprocity into nanophotonic systems will have sweeping implications for the control of light-matter coupling [11][12][13][14], and hence for future quantum technology.…”