Dark-state engineering in Fock-state lattices

TL;DR

This paper investigates dark-state phenomena in Fock-state lattices generated by multimode Jaynes-Cummings models, revealing the structure, number, and form of dark states, which are crucial for quantum optics and information processing.

Contribution

It introduces a systematic analysis of dark states in Fock-state lattices within multimode JC models, including their dimensions, forms, and counts across various modes and excitation levels.

Findings

Existence of dark-state subspaces with dimensions determined by the number of orthogonal dark states.

Explicit characterization of dark states in two-, three-, and four-mode JC models.

General formula for the number of dark states in N-mode JC models across excitation subspaces.

Abstract

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 the connection between quantum optics and condensed matter physics. Owing to the multiple transition paths in the lattices, inherent quantum interference effect exists in these systems, and hence how to find new quantum coherent phenomena and exploit their applications becomes 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 there exist dark-state subspaces with the dimensions determined by the number of orthogonal dark states. When the dimension is larger 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 modes and dark states. Our work will pave the way for exploring quantum optical effects and quantum information processing based on the FSLs.