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  • Open Access

Dark-state engineering in Fock-state lattices

Xuan Zhao1,2, Yi Xu1,2, Le-Man Kuang1,2, and Jie-Qiao Liao1,2,3,*

  • 1Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
  • 2Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies,  Hunan Normal University, Changsha 410081, China
  • 3Institute of Interdisciplinary Studies, Hunan Normal University, Changsha 410081, China

  • *Contact author: jqliao@hunnu.edu.cn
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Phys. Rev. Research 7, 033070 – Published 17 July, 2025

DOI: https://doi.org/10.1103/myc3-2km2

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 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 CN+n−2N−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.

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Phys. Rev. Research 7, 033070– Published 17 July, 2025
  • Received 5 October 2024
  • Accepted 7 July 2025
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