Bound states in the continuum in one-dimensional qubit arrays

Abstract: Bound states in the continuum are extensively studied both theoretically and experimentally. In quantum optics, models adopted for their description make use of the dipolar interaction, representing the exactly solvable Friedrichs-Lee model in the one-excitation sector. A key ingredient resides in constraining the system in one-dimension, as actually implemented in waveguide quantum electrodynamics. A system composed by two atoms in the single-excitation sector provides the emergence of bound states in the continuum subject to the condition linked to their distance partitioned by a half-integer multiple of the emitted wavelength. In the double-excitation sector such kind of bound states cease to be observed. We characterize the eigensystem for any number of equally spaced qubits with one excitation using non-perturbative techniques, giving an explicit proof of excitation amplitude profiles ruled by excitation-waves and including a description of the degeneracy lifting obtained through the full analytic structure of the complex energy plane imposed by the form factor. For any number of qubits, the singularity condition can be factorized, so yielding the emergence of multimers, consisting in subsystems separated by two lattice spacings. An overview about closed loop waveguides will be introduced, with an highlight about the infinite radius limit reaching the same results of open waveguides.