Photon-induced dropletlike bound states in a one-dimensional qubit array

We consider an array of Ne 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.

Automated summary

We investigate an array of noninteracting qubits or emitters coupled to a one-dimensional cavity array with tunneling energy and nonlinearity. By eliminating the photonic degrees of freedom, we obtain a one-dimensional spin Hamiltonian with effective interactions, featuring constrained single-qubit hopping and pair hopping interactions. We identify parameter combinations for the system to support droplet-like bound states.