Giant Atom Bounded in Continuum*

Tremendous progress in coupling light to matter has enabled strong coupling of qubits to modes of a photonic or phononic resonator. Here we consider what happens in the phononic case when the qubit is coupled to an electromagnetic antenna that enables supersonic propagation of the qubit oscillations. One can consider this as a giant – many wavelength-long – atom from the perspective of the phonons. We find that even in the absence of phononic resonances, as the atom size is increased, new bound states emerge from the continuum. We find a toy model that captures these effects while being exactly solvable. Compared to a sub-wavelength size atom, the bound states of this non-Markovian giant atom has localized wavefunctions, reduced dissipation, and amplified vacuum Rabi frequencies. This result also agrees with our generalized Levinson’s theorem, as the number of bound states always equals the winding number of transmission phase. Application of this approach to surface acoustic wave devices will be considered.