Abstract
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays (arrays of two-level atoms) coupled to a waveguide. While bound pairs behave like Bloch waves, they are topologically nontrivial in the parameter space formed by the center-of-mass momentum and the modulation phase, where the latter plays the role of a synthetic dimension. In a superlattice where each unit cell contains three two-level atoms (qubits), we calculate the Chern numbers for the bound-state photon bands, which are found to be $(1,-2,1)$. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. Unlike the conventional case of the bulk-edge correspondence, these novel edge modes not only exist in gaps separating the bound-pair bands, but they also may merge with and penetrate into the bands. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
Highlights
While bound pairs behave like Bloch waves, they are topologically nontrivial in the parameter space formed by the center-of-mass momentum and the modulation phase, where the latter plays the role of a synthetic dimension
Topological photonics has attracted a lot of attention recently [1,2]
Seminal works on topological photonics have focused on basic topological effects, such as topological edge states [3,4,5], Floquet topological insulators [6,7], and Weyl and Dirac points [8,9]
Summary
Topological photonics has attracted a lot of attention recently [1,2]. Seminal works on topological photonics have focused on basic topological effects, such as topological edge states [3,4,5], Floquet topological insulators [6,7], and Weyl and Dirac points [8,9]. In this paper we study the topological properties of two excitations in an atomic array with spatial modulation and photon-mediated long-range coupling. By varying the phase of spatial modulation and the center-of-mass momentum of two quasiparticle excitations, we observe the emergence of three bound-state bands of nontrivial topological invariants characterized by a set of the Chern numbers (−1, 2, −1). There exist long-lived interface states between the two arrays with different spatial modulation phases. We choose β = 3, which means that we consider three qubits per unit cell Such modulation, inspired by the Aubry-AndréHarper model [40], is known to give rise to a nontrivial topology of single-photon bands [41] and radiative edge states [22]. We only consider the subspace of two excitations, where the state can be expanded in the two-excitation
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