Generation and transfer of entangled states between two connected microtoroidal cavities: analysis of different types of coupling

We investigate the generation and transfer of entangled states between two coupled microtoroidal cavities considering two different types of couplings, namely i) via a bridge qubit and ii) via evanescent fields. The cavities support two counter-propagating whispering-gallery modes (WGMs) that may also interact with each other. We firstly show that it is possible to transfer, with high fidelity, a maximally entangled state between the two modes of the first cavity (cavity 1) to the two modes of the second cavity (cavity 2), independently of the type of coupling. Interesting differences, though, arise concerning the generation of entangled states from initial product states; if the cavities are coupled via a bridge qubit, we show that it is possible to generate a 4-partite entangled state involving all four cavity modes. On the other hand, contrarily to what happens in the qubit coupling case, it is possible to generate bipartite maximally entangled states between modes of different cavities from initial separable states for cavities coupled by evanescent waves. Besides, we show that different entangled states between the propagating and counter-propagating modes of distinct cavities may be generated by tuning the interaction between modes belonging to the same cavity (intra-cavity couplings). Again, this is possible only for the couplings via evanescent waves. For the completion of our work, we discuss the effects of losses on the dynamics of the system.