Feedback-enhanced distant entanglement of magnon and phonon modes with atomic ensembles in coupled cavities

The generation and manipulation of distant entanglement between disparate systems are crucial for various quantum technologies. In this work, we investigate a system of coupled cavities comprising an ensemble in cavity-1, a yttrium-iron-garnet (YIG) sphere in cavity-2, and a coherent feedback loop (CFL) that feeds the output of cavity-1 back into cavity-1 through a beam splitter. This system features five excitation modes: cavity-1 photons, atomic ensemble, cavity-2 photons, and the magnon and phonon modes of the YIG sphere. Thus various combinations of bipartite entanglements can be studied. Our main focus is the study of various combinations of distant bipartite entanglements, especially the entanglement of the atomic ensemble and photons in cavity-1 with the magnon and phonon modes of the YIG sphere in cavity-2. Compared to the previously reported results, introducing a CFL significantly enhances all the bipartite entanglements. Besides, the degree of entanglement of various modes, the parameter space, where the strong entanglement exists, is also significantly enhanced due to CFL. Moreover, the entanglement is more robust against thermal noise. We believe our results are important for quantum technologies where the distribution of entanglement on quantum networks is crucial.