https://doi.org/10.1140/epjp/s13360-024-05261-5
Regular Article
The 1 + 2 vector DKP oscillator as a pseudo-Hermitian model of quantum optics
1
Department of Physics, College of Science, Qassim University, 51452, Buraydah, Qassim, Saudi Arabia
2
Nuclear Physics and High Energy Physics Research Unit, Faculty of Sciences of Tunis, University of Tunis El Manar, 2092, Tunis, Tunisia
Received:
28
January
2024
Accepted:
9
May
2024
Published online:
4
June
2024
We present a full algebraic derivation of the solutions of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons in 
-dimensional space time. Interestingly, for states associated with the spin-projection numbers 
, we unveil an exact mapping between this relativistic model and that of the effective two-level atom coupled to a quantized bimodal field so widely used in quantum optics. For this equivalent model, we found that the associated Hamiltonian involves imaginary coupling constants but we show that it is still pseudo-Hermitian. This provides further support to recent outcomes on the possible physical relevance of Pseudo-Hermitian Hamiltonians. Moreover, using the spectral method, we were able to obtain exact closed forms for the corresponding metric operator and Hermitian Hamiltonian. Notably, it turned out that the latter is diagonal, which allowed us to identify the transformation by which it was obtained from the pseudo-Hermitian Hamiltonian as a Foldy–Wouthuysen (FW) transformation.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
