Local Counterdiabatic Driving for Jaynes-Cummings Lattices

Jaynes-Cummings (JC) lattices can be constructed by connecting quantum two-level systems with cavities and have been widely studied for polariton many-body states and multipartite entanglement. Although adiabatic evolution has been studied for the generation of many-body states in this system, its reliance on long timescales can lead to serious decoherence. Here we present a scheme that utilizes local counterdiabatic (CD) driving to provide fast and high-fidelity state preparation in JC lattices. The exact CD Hamiltonian for this system contains nonlocal couplings between qubits and cavities at different and distant sites, which causes a challenge in the implementation. Leveraging the symmetries of the eigenstates under both periodic and open boundary conditions, we derive a local CD Hamiltonian that generates the same dynamics as the exact CD Hamiltonian and our numerical simulations confirm this result. We also show that a multipartite W-state can be prepared with high fidelity using this method. The implementation and decoherence of this scheme with superconducting quantum devices are also discussed.