Spin chains with trapped electrons

We propose to use a linear array of singly trapped electrons to implement a spin chain for quantum communication. The effective spin-spin interaction is realized by means of a magnetic field gradient, which couples the electron spin to the motional degrees of freedom. Then the Coulomb repulsion between the particles transmits this coupling throughout the array. The resulting system can be described in terms of a Heisenberg model with long-range interactions showing a dipolar decay. We estimate the fidelity of the system in reproducing an ideal spin chain by taking into account the influence of the electron spatial motion.