Photon-induced droplet-like bound states in one-dimensional qubit array

TL;DR

This paper investigates droplet-like bound states in a one-dimensional qubit array coupled to a cavity, revealing novel off-resonance bound states with potential for dynamic probing and distinct from on-resonance hybridized states.

Contribution

It introduces a new class of droplet-like bound states in a 1D qubit-cavity system under off-resonance conditions, derived through adiabatic elimination and effective Hamiltonian analysis.

Findings

Identification of parameter regimes supporting droplet-like states

Demonstration of the states' dependence on pair hopping interactions

Distinction between off-resonance bound states and on-resonance hybridized states

Abstract

We consider an array of $N_e$ non-interacting qubits or emitters that are coupled to a one-dimensional cavity array with tunneling energy $J$ and non-linearity 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 bandgap 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 novel 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.