Tunable chiral spin-spin interactions in a spin-mechanical hybrid system: application to causal-effect simulation

Long-range chiral interactions are very attractive due to their potential applications in quantum simulation and quantum information processing. Here we propose and analyze a novel spin-mechanical hybrid quantum device for designing and engineering chiral spin-spin interactions by integrating spin qubits into a programmable mechanical chain. After mapping the Hamiltonian of the mechanical lattice to the Su-Schrieffer-Heeger model, we find that chiral spin-phonon bound states and spin-spin coupling interactions can be achieved. Specifically, the range and strength of chiral spin-spin couplings can be tuned in situ by the on-chip manipulation voltages. We further employ this setup to simulate the causal effects in long-range chiral-coupling systems, showing that the correlation functions propagate individually in two sublattices. These phenomena are very different from the situations in the conventional long-range coupling quantum systems without chiral symmetry.