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.
Highlights
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
The present topology of the system can be probed by the eigenfrequencies ωm(2) as a function of the full range of potential dimerizations −1 ≤ ǫ ≤ 1 in Fig. 3 for a chain of N = 10 dimers
We have studied the two-particle Bose–Hubbard version of the celebrated Su-Schrieffer-Heeger topological model
Summary
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. The simplicity and beauty of the field has ensured that many theoretical works do not need to stray beyond the single-particle level in order to describe and predict some fascinating topological photonic effects [8,9,10,11]. This is especially true when considering phenomena in photonic lattices inspired by iconic topological theories, such as the HarperHofstadter 12, Su-Schrieffer-Heeger 13 and Haldane models 14. There are two key quantities in this nearest-neighbor tight-binding model: (i) the frequency scale J , and (ii) the dimerization parameter ǫ , which are defined using J1 and J2 by
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