https://doi.org/10.1140/epjp/s13360-025-06852-6
Regular Article
Vacuum-induced 
-symmetry in one- and two-dimensional optical lattices
1
Quantum Optics Lab. Department of Physics, COMSATS University, Islamabad, Pakistan
2
Department of Physics, Faculty of Science, King Khalid University, P.O. Box 960, Abha, Saudi Arabia
3
Department of Mechanical Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia
4
Laboratory of Materials, Crystal Chemistry and Applied Thermodynamics, Faculty of Sciences of Tunis, University of Tunis El Manar, 2092 El Manar II, Tunis, Tunisia
5
Chemistry Department, faculty of Science of Sfax, University of Sfax, Sfax, Tunisia
Received:
28
May
2025
Accepted:
12
September
2025
Published online:
29
September
2025
We investigate a system comprising three-level atoms confined within one- and two-dimensional optical lattices, confined inside the optical cavities. The spatial distribution of atoms follows a Gaussian profile, enabling the realization of parity-time ()-symmetry through controlled vacuum-induced field modulation. Additionally, we introduce a microwave field to couple the atomic ground states, introducing an additional degree of control over the system dynamics. By carefully tuning the probe field detuning in the presence of both vacuum and microwave fields, we derive the precise conditions necessary for achieving -symmetry. Furthermore, we investigate the unique reflection and transmission properties of the system, opening potential applications in advanced optical devices such as non-reciprocal photonic components and quantum light manipulation platforms. Our findings provide a deeper understanding of symmetry-controlled atom-light interactions, paving the way for novel quantum optical technologies.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
