https://doi.org/10.1140/epjp/s13360-025-06824-w
Regular Article
Investigation of knot bundles-based normal and anomalous rotary photon drag in duplicated two-level atomic medium
1
Mathematics Department, Faculty of Science, Northern Border University, Arar, Saudi Arabia
2
Government, Higher Secondary School Lal Qilla, Maidan, Khyber Pakhtunkhwa, Pakistan
3
Department of Mathematics, College of Sciences and Arts (Majardah), King Khalid University, 61937, Magardah, Saudi Arabia
4
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, 61421, Muhyil, Saudi Arabia
5
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan
6
Government, Postgraduate Jahanzeb College Saidu Sharif, Swat, Khyber Pakhtunkhwa, Pakistan
Received:
3
February
2025
Accepted:
2
September
2025
Published online:
15
September
2025
The rotary photon drag based on knot bundles is investigated via control fields of the Milnor Gaussian polynomial in a duplicated two-state atomic configuration driven by probe and control fields. The photon drag is a function of wavelength-normalized spatial axes 
and 
. Photon drag is connected to refractive index and group index as 
. Both anomalous and normal photon drag is investigated in this study. The trefoil knot, Solomon knot, Hopf links, and double Hopf links types of photon drag are observed. The highest value of normal photon drag is investigated to 
, and the highest value of anomalous photon drag is reported to 
within the spatial region 
. The results have important uses in quantum imaging, telecommunication, quantum memory, quantum sensors, optical systems, and photonic circuits.
Copyright comment 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.
© 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.
