Hybrid quantum lattice model: Polaritons, photons, and spin waves propagation

Abstract: Controlling the propagation of quantum excitations in low-dimensional quantum systems is pivotal for advancing quantum technologies, including communication networks and quantum simulators. We propose a one-dimensional hybrid quantum lattice model comprising coupled cavity quantum electrodynamics (QED) units. Each unit integrates a single-mode cavity that interacts with a two-level system (TLS), featuring direct coupling between adjacent TLLs. This configuration enables the coherent propagation of polaritons, spin waves, and photons, depending on the interplay between light-matter coupling and spin-spin interactions. Employing the time-evolving block decimation (TEBD) algorithm, we simulate the dynamics of various excitation configurations and analyze their transport characteristics using local observables. Our analysis reveals the importance of matching impedance and resonance conditions via system parameters for the propagation of different types of excitations or swapping the nature of excitations along the hybrid lattice. These findings offer insight into designing controllable quantum links and single-excitation swaps in low-dimensional quantum systems.