Photon-induced dropletlike bound states in a one-dimensional qubit array
Jugal Talukdar, D. Blume · Physical Review A · 2023
We consider an array of ${N}_{e}$ noninteracting qubits or emitters that are coupled to a one-dimensional cavity array with tunneling energy $J$ and nonlinearity of strength $U$. The number of cavities is assumed to be larger than the number of qubits. Working in the two-excitation manifold, we focus on the band-gap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band. A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions; specifically, the Hamiltonian features constrained single-qubit hopping and pair hopping interactions not only between nearest neighbors but also between next-to-nearest and next-to-next-to-nearest spins. For a regularly arranged qubit array, we identify parameter combinations for which the system supports droplet-like bound states whose characteristics depend critically on the pair hopping. The droplet-like states can be probed dynamically. The bound states identified in our work for off-resonance conditions are distinct from localized hybridized states that emerge for on-resonance conditions.