We introduce an extended Dicke model with controllable long-range atom-atom interaction to simulate topologically ordered states and achieve decoherence-protected qubits. We illustrate our idea in an experimentally feasible circuit quantum electrodynamics scenario. Due to the intrinsic competition with the atom-field coupling strength, we first demonstrate that this atom-atom interaction can exhibit a novel topological quantum interference effect arising from the instanton and anti-instanton tunneling paths. As a consequence, this proposed model only with a few odd-number of atoms has a two-fold absolute degenerate ground-subspace with a large energy gap, which can become larger with the increasing of the system-size. It may also support the excitation of anyonic statistics, and thus can be regarded as a possible candidate for processing topological quantum memory.
@article{arxiv.0806.0677,
title = {Topological degeneracy and decoherence-protected qubits in circuit QED},
author = {Gang Chen and Zheng-Yuan Xue and J. -Q. Liang},
journal= {arXiv preprint arXiv:0806.0677},
year = {2008}
}