Dark-state engineering in Fock-state lattices - Xuan Zhao; Yi Xu; Le-Man Kuang; Jie-Qiao Liao (Physical Review Research)
Fock-state lattices (FSLs) are becoming an emerging research hotspot in quantum physics, not only because the FSLs provide a new perspective for studying atom-field interactions, but also because they build a connection between quantum optics and condensed matter physics. Because of the multiple transition paths in the lattices, an inherent quantum interference effect exists in these systems, and hence finding new quantum-coherent phenomena and exploiting their applications become a significant and desired task in this field. In this work, we study the dark-state effect in the FSLs generated by the multimode Jaynes-Cummings (JC) models. By considering the FSLs in certain excitation-number subspaces, we study the dark states with respect to the states associated with the atomic excited state using the arrowhead-matrix method. We find that dark-state subspaces exist with dimensions determined by the number of orthogonal dark states. When the dimension is greater than one, the forms of these dark-state bases are not unique. Further, we obtain the number and form of the orthogonal dark states in the two-, three-, and four-mode JC models. In addition, we find that for a general N-mode JC model, there are C_{N+n−2}^{N−2} orthogonal dark states in the n-excitation subspace. We also build the relationship between the dark states and dark modes. Our work paves the way for exploring quantum optical effects and quantum information processing based on the FSLs.