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

• URL: http://arxiv.org/abs/2307.05868v1
• Date: Wed, 12 Jul 2023 01:46:55 GMT
• Title: Photon-induced droplet-like bound states in one-dimensional qubit array
• Authors: J. Talukdar, D. Blume
• Abstract summary: We study 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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