Double-dot chain as a macroscopic quantum bit

We consider an array of $N$ quantum dot pairs interacting via Coulomb interaction between adjacent dots and hopping inside each pair. We show that at the first order in the ratio of hopping and interaction amplitudes, the array maps in an effective two-level system with energy separation becoming exponentially small in the macroscopic (large-$N$) limit. Decoherence at zero temperature is studied in the limit of weak coupling with phonons. In this case, the macroscopic limit is robust with respect to decoherence. Some possible applications in quantum information processing are discussed.