Quantum state transfer between distant nodes is at the heart of quantum processing and quantum networking. Stimulated by this, we propose a scheme where one can highly achieve quantum state transfer between sites in a cavity quantum optomechanical network. There, each individual cell site is composed of a localized mechanical mode which interacts with a laser-driven cavity mode via radiation pressure, and photons exchange between neighboring sites is allowed. After the diagonalization of the Hamiltonian of each cell, we show that the system can be reduced to an effective Hamiltonian of two decoupled bosonic chains, and therefore we can apply the well-known results regarding quantum state transfer in conjuction with an additional condition on the transfer times. In fact, we show that our transfer protocol works for any arbitrary quantum state, a result that we will illustrate within the red sideband regime. Finally, in order to give a more realistic scenario we take into account the effects of independent thermal reservoirs for each site. Thus, solving the standard master equation within the Born-Markov approximation, we reassure both the effective model as well as the feasibility of our protocol.

In this letter we present a strategy that combines the action of cavity damping mechanisms with that of an engineered atomic reservoir to drive an initial thermal distribution to a Fock equilibrium state. The same technique can be used to slice probability distributions in the Fock space, thus allowing the preparation of a variety of nonclassical equilibrium states. 42.50.Ct, 42.50.Dv The development of strategies to prepare nonclassical states [1] and, in particular, to circumvent their decoherence -via decoherence-free subspaces [2], dynamical decoupling [3], and reservoir engineering [4, 5]-have long played a significant role in quantum optics. On the conceptual side, the need for these states stems from their use in the study of fundamental quantum processes, such as decoherence [6] and the quantum to classical transition [7]. On the pragmatic side, the advent of quantum computation and communication -which depends strongly on successfully producing highly nonclassical states and ensuring their long-term coherence [8]-has certainly put extra pressure on researchers to implement efficient techniques of engineering and protection of nonclassical states. The proposition of schemes that enable the generation of nonclassical equilibrium states thus represents an ideal approach to the current challenges. In this regard, the reservoir engineering technique proposed in Ref. [4] and experimentally demonstrated in a trapped ion system [9] signals an important step toward the implementation of quantum information processes [8], a goal that has recently mobilized practically all areas of low-energy physics. Reservoir engineering,however, has major limitations, starting with the fact that it prevents, for example, the generation of Fock equilibrium states (a key goal of the present letter). Moreover, the protection of a particular state demands the (not-always-easy) engineering of a specific interaction which the system of interest is forced to perform with other auxiliary quantum systems.

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